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Query: /api/nf_fields/?degree=i12&r2=i5&_offset=0
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  1. label: 12.2.167630295667.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 4, -1, -6, 15, -19, 15, -6, -1, 4, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 167630295667, 'disc_rad': 2684791, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[4, 3]]], [5, [[12, 1]]], [7, [[5, 2], [2, 1]]], [11, [[10, 1], [2, 1]]], [13, [[6, 1], [2, 3]]], [17, [[6, 2]]], [19, [[12, 1]]], [23, [[6, 2]]], [29, [0]], [31, [[6, 2]]], [37, [[3, 2], [2, 3]]], [41, [[6, 2]]], [43, [0]], [47, [[6, 1], [2, 1], [1, 4]]], [53, [[3, 2], [2, 2], [1, 2]]], [59, [[5, 2], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [23040, 23040, 23040], 'galois_label': '12T293', 'galt': 293, 'grd': 1638.5331855046452, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.167630295667.1', 'local_algs': ['29.2.0.1', '29.3.0.1', '29.3.0.1', '29.4.2.1', '43.2.1.1', '43.10.0.1', 'm2153.1.1.0', 'm2153.1.1.0', 'm2153.1.1.0', 'm2153.1.1.0', 'm2153.2.1.1', 'm2153.2.1.1', 'm2153.1.4.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [29, 43, 2153], 'rd': 8.61713127762, 'regulator': {'__RealLiteral__': 0, 'data': '3.5044254879', 'prec': 40}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.1.2.-1.-1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{11} - a^{10} + 2 a^{8} - 3 a^{7} + 5 a^{6} - a^{5} + a^{3} + a + 1 \\)', '\\( 2 a^{10} - 3 a^{9} + 2 a^{8} + 3 a^{7} - 9 a^{6} + 15 a^{5} - 10 a^{4} + 4 a^{3} + 3 a^{2} - 4 a + 3 \\)', '\\( 3 a^{11} - 7 a^{10} + 7 a^{9} + 2 a^{8} - 17 a^{7} + 34 a^{6} - 34 a^{5} + 20 a^{4} - 2 a^{3} - 8 a^{2} + 9 a - 3 \\)', '\\( 2 a^{11} - 3 a^{10} + a^{9} + 4 a^{8} - 8 a^{7} + 12 a^{6} - 7 a^{5} + 2 a^{4} + a^{3} + a \\)', '\\( a^{11} - 3 a^{10} + 3 a^{9} + a^{8} - 7 a^{7} + 13 a^{6} - 13 a^{5} + 7 a^{4} - a^{3} - a^{2} + 2 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  2. label: 12.2.168661105243.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, 1, -3, 4, -3, 1, -4, 12, -16, 12, -5, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 168661105243, 'disc_rad': 3361591, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[4, 3]]], [5, [[12, 1]]], [7, [[5, 2], [2, 1]]], [11, [[12, 1]]], [13, [[6, 1], [4, 1], [2, 1]]], [17, [[6, 2]]], [19, [[6, 2]]], [23, [[4, 2], [2, 2]]], [29, [[6, 1], [2, 3]]], [31, [[12, 1]]], [37, [[10, 1], [2, 1]]], [41, [[6, 1], [2, 2], [1, 2]]], [43, [[5, 2], [2, 1]]], [47, [[6, 2]]], [53, [[8, 1], [1, 4]]], [59, [[8, 1], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [23040, 23040, 23040], 'galois_label': '12T293', 'galt': 293, 'grd': 1833.46420744993, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.168661105243.1', 'local_algs': ['67.2.1.1', '67.2.0.1', '67.2.0.1', '67.6.0.1', '131.2.1.1', '131.2.1.1', '131.4.0.1', '131.4.0.1', 'm383.2.2.2', 'm383.1.8.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [67, 131, 383], 'rd': 8.62153466041, 'regulator': {'__RealLiteral__': 0, 'data': '3.51670744388', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.3.-4.2.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{8} - 3 a^{7} + 4 a^{6} - 2 a^{5} + a^{2} - a \\)', '\\( a^{11} - 3 a^{10} + 3 a^{9} + 2 a^{8} - 6 a^{7} + 4 a^{6} - a^{3} - a \\)', '\\( a \\)', '\\( 2 a^{11} - 9 a^{10} + 18 a^{9} - 18 a^{8} + 8 a^{7} - a^{6} + 3 a^{5} - 6 a^{4} + 5 a^{3} - 3 a^{2} + 1 \\)', '\\( a^{10} - 3 a^{9} + 4 a^{8} - a^{7} - 2 a^{6} + 2 a^{5} - a^{2} - 1 \\)', '\\( a^{3} - a^{2} + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  3. label: 12.2.173809422763.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -3, 4, 0, -2, 0, 4, -2, -2, 3, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 173809422763, 'disc_rad': 110081, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[4, 3]]], [5, [[12, 1]]], [7, [[6, 1], [3, 2]]], [11, [[8, 1], [2, 2]]], [13, [[8, 1], [2, 2]]], [17, [[8, 1], [4, 1]]], [19, [[6, 2]]], [23, [[4, 2], [2, 2]]], [29, [[8, 1], [4, 1]]], [31, [0]], [37, [[4, 1], [2, 3], [1, 2]]], [41, [[12, 1]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[4, 1], [2, 3], [1, 2]]], [53, [0]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1536, 1536, 1536], 'galois_label': '12T250', 'galt': 250, 'grd': 331.7845686586403, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.173809422763.1', 'local_algs': ['31.4.0.1', '31.4.2.1', '31.4.2.1', '53.4.2.1', '53.8.0.1', '67.1.0.1', '67.1.0.1', '67.2.0.1', '67.2.1.1', '67.2.0.1', '67.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [31, 53, 67], 'rd': 8.64316445422, 'regulator': {'__RealLiteral__': 0, 'data': '3.58278358615', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.0.1', '-1.3.-3.4.-1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{666}{401} a^{11} - \\frac{985}{401} a^{10} + \\frac{1601}{401} a^{9} - \\frac{714}{401} a^{8} - \\frac{1415}{401} a^{7} + \\frac{1825}{401} a^{6} + \\frac{589}{401} a^{5} - \\frac{361}{401} a^{4} - \\frac{220}{401} a^{3} + \\frac{2270}{401} a^{2} - \\frac{849}{401} a - \\frac{608}{401} \\)', '\\( a \\)', '\\( \\frac{570}{401} a^{11} - \\frac{666}{401} a^{10} + \\frac{962}{401} a^{9} - \\frac{15}{401} a^{8} - \\frac{1659}{401} a^{7} + \\frac{1179}{401} a^{6} + \\frac{1335}{401} a^{5} - \\frac{663}{401} a^{4} - \\frac{564}{401} a^{3} + \\frac{1773}{401} a^{2} - \\frac{33}{401} a - \\frac{990}{401} \\)', '\\( \\frac{370}{401} a^{11} - \\frac{369}{401} a^{10} + \\frac{533}{401} a^{9} + \\frac{138}{401} a^{8} - \\frac{1098}{401} a^{7} + \\frac{702}{401} a^{6} + \\frac{951}{401} a^{5} - \\frac{156}{401} a^{4} - \\frac{746}{401} a^{3} + \\frac{1172}{401} a^{2} + \\frac{464}{401} a - \\frac{516}{401} \\)', '\\( \\frac{162}{401} a^{11} - \\frac{413}{401} a^{10} + \\frac{552}{401} a^{9} - \\frac{553}{401} a^{8} - \\frac{290}{401} a^{7} + \\frac{639}{401} a^{6} - \\frac{106}{401} a^{5} - \\frac{543}{401} a^{4} - \\frac{21}{401} a^{3} + \\frac{563}{401} a^{2} - \\frac{575}{401} a - \\frac{7}{401} \\)', '\\( \\frac{185}{401} a^{11} - \\frac{385}{401} a^{10} + \\frac{467}{401} a^{9} - \\frac{332}{401} a^{8} - \\frac{549}{401} a^{7} + \\frac{752}{401} a^{6} + \\frac{275}{401} a^{5} - \\frac{479}{401} a^{4} + \\frac{28}{401} a^{3} + \\frac{586}{401} a^{2} - \\frac{570}{401} a - \\frac{659}{401} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/401*a^11 + 193/401*a^10 - 56/401*a^9 - 95/401*a^8 - 81/401*a^7 - 152/401*a^6 + 34/401*a^5 - 189/401*a^4 + 37/401*a^3 + 1/401*a^2 + 192/401*a + 146/401']}
  4. label: 12.2.175113024319.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 5, -12, 19, -24, 23, -16, 5, 4, -9, 8, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 175113024319, 'disc_rad': 161713, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[12, 1]]], [5, [[8, 1], [4, 1]]], [7, [[4, 1], [2, 4]]], [11, [[8, 1], [4, 1]]], [13, [[6, 2]]], [17, [[4, 1], [2, 4]]], [19, [[4, 2], [2, 2]]], [23, [0]], [29, [[12, 1]]], [31, [[6, 2]]], [37, [[4, 2], [2, 1], [1, 2]]], [41, [[12, 1]]], [43, [[8, 1], [2, 2]]], [47, [[6, 1], [3, 2]]], [53, [[4, 3]]], [59, [[4, 1], [2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1536, 1536, 1536], 'galois_label': '12T250', 'galt': 250, 'grd': 402.1355492865559, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.175113024319.1', 'local_algs': ['23.2.0.1', '23.2.0.1', '23.8.4.1', '79.1.0.1', '79.1.0.1', '79.2.0.1', '79.2.0.1', '79.2.1.1', '79.4.0.1', '89.2.1.2', '89.2.1.2', '89.4.0.1', '89.4.0.1'], 'minimal_sibling': [1, -5, 11, -12, 6, 0, 0, -3, 4, -2, 2, -2, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [23, 79, 89], 'rd': 8.64854807832, 'regulator': {'__RealLiteral__': 0, 'data': '3.59783369219', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.-1.3.3.-3.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{33}{19} a^{11} - \\frac{100}{19} a^{10} + \\frac{163}{19} a^{9} - \\frac{128}{19} a^{8} - \\frac{14}{19} a^{7} + 9 a^{6} - \\frac{357}{19} a^{5} + 20 a^{4} - \\frac{374}{19} a^{3} + \\frac{239}{19} a^{2} - \\frac{132}{19} a + \\frac{18}{19} \\)', '\\( \\frac{32}{19} a^{11} - \\frac{101}{19} a^{10} + \\frac{169}{19} a^{9} - \\frac{146}{19} a^{8} + \\frac{6}{19} a^{7} + 9 a^{6} - \\frac{379}{19} a^{5} + 22 a^{4} - \\frac{388}{19} a^{3} + \\frac{264}{19} a^{2} - \\frac{147}{19} a + \\frac{33}{19} \\)', '\\( \\frac{34}{19} a^{11} - \\frac{99}{19} a^{10} + \\frac{157}{19} a^{9} - \\frac{129}{19} a^{8} + \\frac{4}{19} a^{7} + 8 a^{6} - \\frac{373}{19} a^{5} + 21 a^{4} - \\frac{379}{19} a^{3} + \\frac{252}{19} a^{2} - \\frac{136}{19} a + \\frac{22}{19} \\)', '\\( \\frac{31}{19} a^{11} - \\frac{83}{19} a^{10} + \\frac{118}{19} a^{9} - \\frac{69}{19} a^{8} - \\frac{50}{19} a^{7} + 8 a^{6} - \\frac{287}{19} a^{5} + 13 a^{4} - \\frac{212}{19} a^{3} + \\frac{99}{19} a^{2} - \\frac{29}{19} a - \\frac{9}{19} \\)', '\\( \\frac{9}{19} a^{11} - \\frac{29}{19} a^{10} + \\frac{60}{19} a^{9} - \\frac{66}{19} a^{8} + \\frac{29}{19} a^{7} + 2 a^{6} - \\frac{125}{19} a^{5} + 8 a^{4} - \\frac{197}{19} a^{3} + \\frac{136}{19} a^{2} - \\frac{93}{19} a + \\frac{36}{19} \\)', '\\( \\frac{25}{19} a^{11} - \\frac{70}{19} a^{10} + \\frac{97}{19} a^{9} - \\frac{44}{19} a^{8} - \\frac{63}{19} a^{7} + 7 a^{6} - \\frac{210}{19} a^{5} + 9 a^{4} - \\frac{144}{19} a^{3} + \\frac{59}{19} a^{2} - \\frac{43}{19} a + \\frac{5}{19} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/19*a^11 + 1/19*a^10 - 6/19*a^9 - 1/19*a^8 - 1/19*a^7 + 3/19*a^5 - 5/19*a^3 - 6/19*a^2 - 4/19*a + 4/19']}
  5. label: 12.2.175122415616.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 6, -17, 30, -37, 30, -12, -6, 17, -16, 10, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 175122415616, 'disc_rad': 13774, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[8, 1], [4, 1]]], [7, [[6, 1], [4, 1], [2, 1]]], [11, [[12, 1]]], [13, [[4, 3]]], [17, [[3, 2], [2, 3]]], [19, [[8, 1], [4, 1]]], [23, [[3, 2], [2, 3]]], [29, [[4, 2], [2, 2]]], [31, [[6, 1], [2, 2], [1, 2]]], [37, [[4, 2], [2, 2]]], [41, [[6, 1], [4, 1], [2, 1]]], [43, [[4, 2], [2, 2]]], [47, [[4, 2], [2, 1], [1, 2]]], [53, [[12, 1]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6912, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 234.72537144501445, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.175122415616.1', 'local_algs': ['2.12.18.23', '71.1.0.1', '71.1.0.1', '71.1.0.1', '71.1.0.1', '71.2.0.1', '71.2.1.2', '71.4.0.1', '97.1.0.1', '97.1.0.1', '97.2.0.1', '97.2.0.1', '97.2.0.1', '97.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 71, 97], 'rd': 8.64858672911, 'regulator': {'__RealLiteral__': 0, 'data': '3.6007962841', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '-1.0.0.-2.3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{61}{17} a^{11} - \\frac{219}{17} a^{10} + \\frac{530}{17} a^{9} - \\frac{790}{17} a^{8} + \\frac{779}{17} a^{7} - \\frac{127}{17} a^{6} - \\frac{735}{17} a^{5} + \\frac{1582}{17} a^{4} - \\frac{1736}{17} a^{3} + \\frac{1281}{17} a^{2} - \\frac{631}{17} a + \\frac{140}{17} \\)', '\\( \\frac{42}{17} a^{11} - \\frac{148}{17} a^{10} + \\frac{339}{17} a^{9} - \\frac{479}{17} a^{8} + \\frac{426}{17} a^{7} + \\frac{14}{17} a^{6} - \\frac{520}{17} a^{5} + \\frac{946}{17} a^{4} - \\frac{991}{17} a^{3} + \\frac{678}{17} a^{2} - \\frac{311}{17} a + \\frac{78}{17} \\)', '\\( \\frac{3}{17} a^{11} - \\frac{30}{17} a^{10} + \\frac{74}{17} a^{9} - \\frac{135}{17} a^{8} + \\frac{130}{17} a^{7} - \\frac{50}{17} a^{6} - \\frac{144}{17} a^{5} + \\frac{223}{17} a^{4} - \\frac{293}{17} a^{3} + \\frac{182}{17} a^{2} - \\frac{89}{17} a + \\frac{25}{17} \\)', '\\( \\frac{25}{17} a^{11} - \\frac{97}{17} a^{10} + \\frac{237}{17} a^{9} - \\frac{360}{17} a^{8} + \\frac{358}{17} a^{7} - \\frac{71}{17} a^{6} - \\frac{333}{17} a^{5} + \\frac{708}{17} a^{4} - \\frac{787}{17} a^{3} + \\frac{610}{17} a^{2} - \\frac{294}{17} a + \\frac{78}{17} \\)', '\\( \\frac{47}{17} a^{11} - \\frac{130}{17} a^{10} + \\frac{281}{17} a^{9} - \\frac{330}{17} a^{8} + \\frac{246}{17} a^{7} + \\frac{163}{17} a^{6} - \\frac{420}{17} a^{5} + \\frac{717}{17} a^{4} - \\frac{601}{17} a^{3} + \\frac{358}{17} a^{2} - \\frac{159}{17} a + \\frac{29}{17} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/17*a^11 + 7/17*a^10 + 2/17*a^9 + 6/17*a^8 - 2/17*a^7 + 6/17*a^6 + 3/17*a^5 - 5/17*a^4 - 7/17*a^3 + 4/17*a^2 - 7/17*a - 3/17']}
  6. label: 12.2.177788874752.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -6, 13, -14, 8, -8, 11, -4, 3, -4, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 177788874752, 'disc_rad': 2914, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1], [4, 1]]], [5, [[6, 1], [3, 2]]], [7, [[6, 2]]], [11, [[4, 1], [2, 4]]], [13, [[8, 1], [2, 2]]], [17, [[8, 1], [4, 1]]], [19, [[6, 1], [3, 2]]], [23, [[4, 3]]], [29, [[4, 3]]], [31, [0]], [37, [[4, 2], [2, 2]]], [41, [[6, 1], [3, 2]]], [43, [[8, 1], [2, 2]]], [47, [0]], [53, [[4, 1], [2, 3], [1, 2]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 768, 768], 'galois_label': '12T227', 'galt': 227, 'grd': 107.96295661012624, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.177788874752.1', 'local_algs': ['2.12.12.11', '31.1.0.1', '31.1.0.1', '31.2.0.1', '31.8.4.1', '47.1.0.1', '47.1.0.1', '47.2.0.1', '47.2.1.1', '47.2.0.1', '47.4.0.1'], 'minimal_sibling': [1, 0, -3, 0, 3, 0, -1, 0, 1, 0, -1, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 31, 47], 'rd': 8.65948468434, 'regulator': {'__RealLiteral__': 0, 'data': '3.63511170932', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.0.1', '-1.0.1.0.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1709}{3551} a^{11} + \\frac{1665}{3551} a^{10} + \\frac{1138}{3551} a^{9} - \\frac{6280}{3551} a^{8} - \\frac{1330}{3551} a^{7} - \\frac{5495}{3551} a^{6} + \\frac{13593}{3551} a^{5} + \\frac{558}{3551} a^{4} + \\frac{7604}{3551} a^{3} - \\frac{14201}{3551} a^{2} + \\frac{3933}{3551} a + \\frac{2876}{3551} \\)', '\\( \\frac{343}{3551} a^{11} + \\frac{2252}{3551} a^{10} + \\frac{1793}{3551} a^{9} - \\frac{315}{3551} a^{8} - \\frac{7344}{3551} a^{7} - \\frac{2495}{3551} a^{6} - \\frac{4885}{3551} a^{5} + \\frac{14690}{3551} a^{4} + \\frac{2270}{3551} a^{3} + \\frac{8021}{3551} a^{2} - \\frac{13184}{3551} a + \\frac{6285}{3551} \\)', '\\( \\frac{10618}{3551} a^{11} + \\frac{4988}{3551} a^{10} + \\frac{2281}{3551} a^{9} - \\frac{41058}{3551} a^{8} + \\frac{13504}{3551} a^{7} - \\frac{35038}{3551} a^{6} + \\frac{99854}{3551} a^{5} - \\frac{39328}{3551} a^{4} + \\frac{64556}{3551} a^{3} - \\frac{117929}{3551} a^{2} + \\frac{83743}{3551} a - \\frac{23904}{3551} \\)', '\\( \\frac{4736}{3551} a^{11} + \\frac{4105}{3551} a^{10} + \\frac{2923}{3551} a^{9} - \\frac{17104}{3551} a^{8} - \\frac{1157}{3551} a^{7} - \\frac{18517}{3551} a^{6} + \\frac{37320}{3551} a^{5} - \\frac{3135}{3551} a^{4} + \\frac{33186}{3551} a^{3} - \\frac{41197}{3551} a^{2} + \\frac{26300}{3551} a - \\frac{9438}{3551} \\)', '\\( \\frac{8454}{3551} a^{11} + \\frac{4249}{3551} a^{10} + \\frac{2388}{3551} a^{9} - \\frac{32331}{3551} a^{8} + \\frac{9285}{3551} a^{7} - \\frac{30509}{3551} a^{6} + \\frac{77595}{3551} a^{5} - \\frac{29153}{3551} a^{4} + \\frac{54593}{3551} a^{3} - \\frac{92120}{3551} a^{2} + \\frac{67659}{3551} a - \\frac{17942}{3551} \\)', '\\( \\frac{6058}{3551} a^{11} + \\frac{2991}{3551} a^{10} + \\frac{1686}{3551} a^{9} - \\frac{23246}{3551} a^{8} + \\frac{7528}{3551} a^{7} - \\frac{21228}{3551} a^{6} + \\frac{56435}{3551} a^{5} - \\frac{23893}{3551} a^{4} + \\frac{40641}{3551} a^{3} - \\frac{67502}{3551} a^{2} + \\frac{52614}{3551} a - \\frac{17432}{3551} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/3551*a^11 - 1360/3551*a^10 - 471/3551*a^9 + 1376/3551*a^8 + 20/3551*a^7 + 1204/3551*a^6 - 418/3551*a^5 + 312/3551*a^4 - 1743/3551*a^3 - 1602/3551*a^2 - 1581/3551*a - 1752/3551']}
  7. label: 12.2.204800642687.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 5, -3, -4, 12, -15, 12, -4, -3, 5, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 204800642687, 'disc_rad': 2170349, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [[12, 1]]], [7, [[8, 1], [2, 2]]], [11, [[12, 1]]], [13, [[4, 2], [2, 2]]], [17, [[5, 2], [2, 1]]], [19, [[8, 1], [2, 2]]], [23, [0]], [29, [[4, 1], [3, 2], [2, 1]]], [31, [[3, 4]]], [37, [[4, 1], [3, 2], [1, 2]]], [41, [[6, 2]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[3, 2], [2, 2], [1, 2]]], [53, [[6, 1], [4, 1], [2, 1]]], [59, [[6, 1], [2, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [23040, 23040, 23040], 'galois_label': '12T293', 'galt': 293, 'grd': 1473.2104398218198, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.204800642687.1', 'local_algs': ['23.2.0.1', '23.2.1.1', '23.4.0.1', '23.4.0.1', '197.2.1.2', '197.2.1.2', '197.4.0.1', '197.4.0.1', 'm479.2.1.1', 'm479.2.1.1', 'm479.1.8.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [23, 197, 479], 'rd': 8.76215523154, 'regulator': {'__RealLiteral__': 0, 'data': '3.96195936431', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.3.0.-2.-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( 2 a^{11} - 3 a^{10} + 4 a^{9} + 3 a^{8} - 8 a^{7} + 11 a^{6} - 6 a^{5} + 2 a^{4} + 4 a^{3} - 3 a^{2} + 2 a + 1 \\)', '\\( 2 a^{11} - 3 a^{10} + 4 a^{9} + 2 a^{8} - 8 a^{7} + 11 a^{6} - 9 a^{5} + 3 a^{4} + 4 a^{3} - 4 a^{2} + 2 a - 1 \\)', '\\( a^{11} - 3 a^{10} + 4 a^{9} - a^{8} - 6 a^{7} + 11 a^{6} - 10 a^{5} + 6 a^{4} - 5 a^{2} + 3 a \\)', '\\( a^{11} - a^{9} + 5 a^{8} - 3 a^{7} - 2 a^{6} + 7 a^{5} - 7 a^{4} + 5 a^{3} + a^{2} - 4 a + 2 \\)', '\\( 2 a^{11} - 6 a^{10} + 9 a^{9} - 4 a^{8} - 11 a^{7} + 24 a^{6} - 26 a^{5} + 16 a^{4} - a^{3} - 10 a^{2} + 9 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  8. label: 12.2.205567038859.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 2, -4, 4, -8, 4, -5, 4, 1, 0, 2, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 205567038859, 'disc_rad': 19201, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 1], [3, 2]]], [5, [[6, 2]]], [7, [0]], [11, [[6, 2]]], [13, [0]], [17, [[6, 1], [3, 2]]], [19, [[6, 2]]], [23, [[6, 1], [3, 2]]], [29, [[4, 1], [2, 4]]], [31, [[12, 1]]], [37, [[6, 2]]], [41, [[4, 1], [2, 2], [1, 4]]], [43, [[4, 1], [2, 3], [1, 2]]], [47, [[6, 2]]], [53, [[6, 2]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1024, 768, 768], 'galois_label': '12T222', 'galt': 222, 'grd': 191.65122394707694, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.205567038859.1', 'local_algs': ['7.12.8.1', '13.2.0.1', '13.2.0.1', '13.2.0.1', '13.2.0.1', '13.4.2.1', 'm211.1.2.0', 'm211.1.2.0', 'm211.1.2.0', 'm211.1.2.0', 'm211.1.2.0', 'm211.2.1.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [7, 13, 211], 'rd': 8.7648830029, 'regulator': {'__RealLiteral__': 0, 'data': '3.97256263188', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '1.-2.2.-3.2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - a^{10} + 2 a^{9} + a^{7} + 4 a^{6} - 5 a^{5} + 4 a^{4} - 8 a^{3} + 4 a^{2} - 4 a + 2 \\)', '\\( \\frac{68}{117} a^{11} - \\frac{166}{117} a^{10} + \\frac{155}{117} a^{9} - \\frac{41}{117} a^{8} - \\frac{131}{117} a^{7} + \\frac{244}{117} a^{6} - \\frac{671}{117} a^{5} + \\frac{451}{117} a^{4} - \\frac{227}{117} a^{3} + \\frac{40}{9} a^{2} - \\frac{17}{39} a + \\frac{34}{117} \\)', '\\( \\frac{43}{39} a^{11} - \\frac{22}{39} a^{10} + \\frac{55}{39} a^{9} + \\frac{15}{13} a^{8} + \\frac{14}{13} a^{7} + \\frac{55}{13} a^{6} - \\frac{44}{13} a^{5} + \\frac{17}{13} a^{4} - \\frac{85}{13} a^{3} + a^{2} - \\frac{68}{39} a + \\frac{28}{39} \\)', '\\( \\frac{35}{117} a^{11} - \\frac{82}{117} a^{10} + \\frac{140}{117} a^{9} - \\frac{71}{117} a^{8} + \\frac{10}{117} a^{7} + \\frac{160}{117} a^{6} - \\frac{323}{117} a^{5} + \\frac{430}{117} a^{4} - \\frac{473}{117} a^{3} + \\frac{28}{9} a^{2} - \\frac{116}{39} a + \\frac{193}{117} \\)', '\\( \\frac{62}{117} a^{11} - \\frac{133}{117} a^{10} + \\frac{131}{117} a^{9} - \\frac{50}{117} a^{8} - \\frac{77}{117} a^{7} + \\frac{172}{117} a^{6} - \\frac{590}{117} a^{5} + \\frac{316}{117} a^{4} - \\frac{371}{117} a^{3} + \\frac{40}{9} a^{2} - \\frac{61}{39} a + \\frac{109}{117} \\)', '\\( \\frac{103}{117} a^{11} - \\frac{92}{117} a^{10} + \\frac{178}{117} a^{9} + \\frac{44}{117} a^{8} + \\frac{35}{117} a^{7} + \\frac{443}{117} a^{6} - \\frac{487}{117} a^{5} + \\frac{218}{117} a^{4} - \\frac{661}{117} a^{3} + \\frac{8}{9} a^{2} - \\frac{27}{13} a + \\frac{71}{117} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/3*a^10 + 1/3*a^8 + 1/3*a^7 + 1/3*a^6 + 1/3*a^5 + 1/3*a^4 + 1/3*a^3 + 1/3*a^2 + 1/3*a - 1/3', '1/117*a^11 + 1/117*a^10 + 4/117*a^9 + 8/117*a^8 + 17/117*a^7 + 38/117*a^6 - 46/117*a^5 + 29/117*a^4 + 50/117*a^3 - 1/9*a^2 - 10/39*a - 58/117']}
  9. label: 12.2.206487484375.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 3, -8, 13, -17, 16, -13, 8, -3, 1, 2, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 206487484375, 'disc_rad': 161555, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[12, 1]]], [5, [0]], [7, [[8, 1], [2, 2]]], [11, [[6, 1], [2, 3]]], [13, [[8, 1], [4, 1]]], [17, [[12, 1]]], [19, [[6, 1], [2, 3]]], [23, [[6, 2]]], [29, [[2, 5], [1, 2]]], [31, [[4, 1], [3, 2], [2, 1]]], [37, [[4, 3]]], [41, [[6, 1], [3, 2]]], [43, [[8, 1], [2, 2]]], [47, [[8, 1], [2, 2]]], [53, [[12, 1]]], [59, [[6, 1], [2, 2], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 401.9390501058587, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.206487484375.1', 'local_algs': ['5.4.2.1', '5.8.4.1', '79.1.0.1', '79.1.0.1', '79.2.1.1', '79.2.0.1', '79.2.0.1', '79.4.0.1', 'm409.1.1.0', 'm409.1.1.0', 'm409.2.2.2', 'm409.1.6.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 79, 409], 'rd': 8.76814677513, 'regulator': {'__RealLiteral__': 0, 'data': '3.98211224603', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.3.-2.0.2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{12}{49} a^{11} + \\frac{43}{49} a^{10} - \\frac{4}{7} a^{9} + \\frac{96}{49} a^{8} + \\frac{61}{49} a^{7} - \\frac{94}{49} a^{6} + \\frac{34}{7} a^{5} - \\frac{375}{49} a^{4} + \\frac{466}{49} a^{3} - \\frac{444}{49} a^{2} + \\frac{270}{49} a - \\frac{123}{49} \\)', '\\( \\frac{17}{49} a^{11} - \\frac{33}{49} a^{10} + \\frac{6}{7} a^{9} - \\frac{11}{49} a^{8} - \\frac{81}{49} a^{7} + \\frac{169}{49} a^{6} - \\frac{51}{7} a^{5} + \\frac{412}{49} a^{4} - \\frac{475}{49} a^{3} + \\frac{351}{49} a^{2} - \\frac{230}{49} a + \\frac{83}{49} \\)', '\\( \\frac{1}{7} a^{11} + \\frac{10}{7} a^{10} - a^{9} + \\frac{15}{7} a^{8} + \\frac{15}{7} a^{7} - \\frac{30}{7} a^{6} + 8 a^{5} - \\frac{96}{7} a^{4} + \\frac{96}{7} a^{3} - \\frac{93}{7} a^{2} + \\frac{54}{7} a - \\frac{19}{7} \\)', '\\( \\frac{80}{49} a^{11} - \\frac{40}{49} a^{10} + \\frac{13}{7} a^{9} + \\frac{150}{49} a^{8} - \\frac{214}{49} a^{7} + \\frac{435}{49} a^{6} - \\frac{100}{7} a^{5} + \\frac{685}{49} a^{4} - \\frac{601}{49} a^{3} + \\frac{323}{49} a^{2} - \\frac{111}{49} a + \\frac{13}{49} \\)', '\\( \\frac{6}{49} a^{11} - \\frac{3}{49} a^{10} + \\frac{5}{7} a^{9} - \\frac{1}{49} a^{8} + \\frac{6}{49} a^{7} + \\frac{100}{49} a^{6} - \\frac{18}{7} a^{5} + \\frac{180}{49} a^{4} - \\frac{257}{49} a^{3} + \\frac{170}{49} a^{2} - \\frac{159}{49} a + \\frac{12}{49} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/49*a^11 + 24/49*a^10 + 2/7*a^9 + 8/49*a^8 + 1/49*a^7 - 16/49*a^6 - 3/7*a^5 - 19/49*a^4 - 2/49*a^3 + 12/49*a^2 - 2/49*a + 2/49']}
  10. label: 12.2.208976546875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 5, -12, 19, -22, 18, -9, 1, 4, -5, 4, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 208976546875, 'disc_rad': 79705, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [[6, 2]]], [11, [[6, 1], [2, 3]]], [13, [[8, 1], [2, 2]]], [17, [[4, 2], [2, 2]]], [19, [0]], [23, [[6, 2]]], [29, [[6, 1], [4, 1], [2, 1]]], [31, [[2, 5], [1, 2]]], [37, [[12, 1]]], [41, [[6, 1], [4, 1], [2, 1]]], [43, [[6, 2]]], [47, [[6, 2]]], [53, [[4, 1], [2, 4]]], [59, [[4, 1], [2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 282.32073958531635, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.208976546875.1', 'local_algs': ['5.6.3.1', '5.6.3.1', '19.2.1.1', '19.2.0.1', '19.4.0.1', '19.4.0.1', 'm839.1.1.0', 'm839.1.1.0', 'm839.2.1.1', 'm839.2.1.1', 'm839.1.6.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [5, 19, 839], 'rd': 8.7769063085, 'regulator': {'__RealLiteral__': 0, 'data': '4.01927343849', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.1.2.1.-1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{11} - a^{10} + 3 a^{9} - 2 a^{8} + 2 a^{7} + 3 a^{6} - 6 a^{5} + 12 a^{4} - 10 a^{3} + 9 a^{2} - 4 a + 1 \\)', '\\( 3 a^{11} - 3 a^{10} + 9 a^{9} - 7 a^{8} + 6 a^{7} + 7 a^{6} - 19 a^{5} + 35 a^{4} - 35 a^{3} + 28 a^{2} - 15 a + 4 \\)', '\\( a^{11} + a^{9} + a^{8} - 2 a^{7} + 4 a^{6} - 4 a^{5} + a^{4} + 4 a^{3} - 7 a^{2} + 5 a - 2 \\)', '\\( a^{11} - 2 a^{10} + 3 a^{9} - 4 a^{8} + 2 a^{7} + 3 a^{6} - 9 a^{5} + 15 a^{4} - 16 a^{3} + 10 a^{2} - 5 a + 2 \\)', '\\( 2 a^{11} - 3 a^{10} + 6 a^{9} - 6 a^{8} + 4 a^{7} + 6 a^{6} - 15 a^{5} + 27 a^{4} - 26 a^{3} + 19 a^{2} - 9 a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  11. label: 12.2.225117671875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, 0, -2, -2, 0, 3, 3, -1, -1, -1, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 225117671875, 'disc_rad': 72037655, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [[10, 1], [2, 1]]], [11, [[4, 2], [2, 2]]], [13, [[8, 1], [2, 2]]], [17, [[8, 1], [2, 2]]], [19, [[5, 1], [4, 1], [2, 1], [1, 1]]], [23, [[12, 1]]], [29, [[5, 1], [3, 1], [2, 1], [1, 2]]], [31, [[6, 1], [3, 2]]], [37, [[6, 1], [2, 3]]], [41, [[4, 1], [3, 1], [2, 1], [1, 3]]], [43, [[8, 1], [4, 1]]], [47, [[10, 1], [2, 1]]], [53, [[10, 1], [2, 1]]], [59, [[6, 1], [5, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [518400, 518400, 518400], 'galois_label': '12T299', 'galt': 299, 'grd': 8487.499926362298, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.225117671875.1', 'local_algs': ['5.12.6.1', '179.1.0.1', '179.1.0.1', '179.2.0.1', '179.2.1.2', '179.2.0.1', '179.4.0.1', 'm80489.1.1.0', 'm80489.1.1.0', 'm80489.1.2.0', 'm80489.2.1.1', 'm80489.1.6.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 179, 80489], 'rd': 8.83149306815, 'regulator': {'__RealLiteral__': 0, 'data': '4.20942666663', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{85}{163} a^{11} - \\frac{6}{163} a^{10} - \\frac{98}{163} a^{9} - \\frac{80}{163} a^{8} - \\frac{41}{163} a^{7} + \\frac{302}{163} a^{6} + \\frac{203}{163} a^{5} - \\frac{22}{163} a^{4} - \\frac{272}{163} a^{3} - \\frac{53}{163} a^{2} + \\frac{184}{163} a - \\frac{36}{163} \\)', '\\( \\frac{22}{163} a^{11} - \\frac{61}{163} a^{10} + \\frac{36}{163} a^{9} + \\frac{56}{163} a^{8} + \\frac{45}{163} a^{7} + \\frac{82}{163} a^{6} - \\frac{191}{163} a^{5} - \\frac{115}{163} a^{4} + \\frac{60}{163} a^{3} + \\frac{249}{163} a^{2} + \\frac{132}{163} a - \\frac{40}{163} \\)', '\\( \\frac{41}{163} a^{11} - \\frac{47}{163} a^{10} - \\frac{7}{163} a^{9} - \\frac{29}{163} a^{8} + \\frac{32}{163} a^{7} + \\frac{138}{163} a^{6} - \\frac{67}{163} a^{5} + \\frac{45}{163} a^{4} - \\frac{66}{163} a^{3} + \\frac{101}{163} a^{2} + \\frac{83}{163} a - \\frac{119}{163} \\)', '\\( \\frac{45}{163} a^{11} - \\frac{147}{163} a^{10} + \\frac{44}{163} a^{9} - \\frac{4}{163} a^{8} + \\frac{55}{163} a^{7} + \\frac{227}{163} a^{6} - \\frac{324}{163} a^{5} - \\frac{50}{163} a^{4} - \\frac{144}{163} a^{3} + \\frac{87}{163} a^{2} + \\frac{107}{163} a - \\frac{67}{163} \\)', '\\( \\frac{44}{163} a^{11} + \\frac{41}{163} a^{10} - \\frac{91}{163} a^{9} - \\frac{51}{163} a^{8} - \\frac{73}{163} a^{7} + \\frac{164}{163} a^{6} + \\frac{270}{163} a^{5} - \\frac{67}{163} a^{4} - \\frac{43}{163} a^{3} - \\frac{154}{163} a^{2} - \\frac{62}{163} a + \\frac{83}{163} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/163*a^11 - 25/163*a^10 - 28/163*a^9 + 47/163*a^8 - 35/163*a^7 + 63/163*a^6 + 58/163*a^5 + 17/163*a^4 + 62/163*a^3 + 78/163*a^2 + 6/163*a + 13/163']}
  12. label: 12.2.233544944483.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, -1, 1, 3, -7, 6, 3, -9, 5, 2, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 233544944483, 'disc_rad': 19194949, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[9, 1], [3, 1]]], [5, [[6, 1], [4, 1], [2, 1]]], [7, [[8, 1], [2, 2]]], [11, [[6, 1], [4, 1], [2, 1]]], [13, [[12, 1]]], [17, [[4, 2], [2, 2]]], [19, [[6, 1], [4, 1], [2, 1]]], [23, [0]], [29, [[9, 1], [3, 1]]], [31, [[9, 1], [3, 1]]], [37, [[8, 1], [4, 1]]], [41, [[3, 4]]], [43, [[6, 1], [3, 1], [2, 1], [1, 1]]], [47, [[9, 1], [3, 1]]], [53, [[6, 1], [3, 1], [2, 1], [1, 1]]], [59, [[3, 2], [2, 2], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [41472, 41472, 41472], 'galois_label': '12T294', 'galt': 294, 'grd': 4381.204058247002, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.233544944483.1', 'local_algs': ['23.2.1.2', '23.4.0.1', '23.6.3.2', '101.1.0.1', '101.1.0.1', '101.2.1.2', '101.2.0.1', '101.2.0.1', '101.4.0.1', 'm8263.1.1.0', 'm8263.1.1.0', 'm8263.1.1.0', 'm8263.1.1.0', 'm8263.1.1.0', 'm8263.1.2.0', 'm8263.2.1.1', 'm8263.1.3.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [23, 101, 8263], 'rd': 8.8585819242, 'regulator': {'__RealLiteral__': 0, 'data': '4.29199444222', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{8} - a^{7} - a^{6} + 3 a^{5} - a^{4} + 2 a^{2} - a \\)', '\\( a \\)', '\\( a^{11} - 2 a^{10} + 5 a^{8} - 4 a^{7} - 2 a^{6} + 6 a^{5} - 2 a^{4} - a^{3} + 2 a^{2} + 1 \\)', '\\( a^{8} - a^{7} - a^{6} + 3 a^{5} - a^{3} + 2 a^{2} \\)', '\\( a^{9} - 2 a^{8} + a^{7} + 3 a^{6} - 4 a^{5} + 2 a^{4} + 2 a^{3} - 2 a^{2} + 2 a - 1 \\)', '\\( a^{11} - 3 a^{10} + 2 a^{9} + 4 a^{8} - 7 a^{7} + 2 a^{6} + 4 a^{5} - 4 a^{4} + a^{3} + a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  13. label: 12.2.238362687139.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 4, -2, -3, 7, -8, 3, 1, -4, 4, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 238362687139, 'disc_rad': 19590917, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[8, 1], [4, 1]]], [7, [[8, 1], [4, 1]]], [11, [[8, 1], [2, 2]]], [13, [[12, 1]]], [17, [[8, 1], [3, 1], [1, 1]]], [19, [[6, 1], [4, 1], [2, 1]]], [23, [0]], [29, [[6, 2]]], [31, [[9, 1], [3, 1]]], [37, [[4, 1], [3, 1], [2, 2], [1, 1]]], [41, [[9, 1], [3, 1]]], [43, [[4, 1], [3, 1], [2, 2], [1, 1]]], [47, [[9, 1], [3, 1]]], [53, [[4, 1], [2, 3], [1, 2]]], [59, [[3, 1], [2, 2], [1, 5]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [41472, 41472, 41472], 'galois_label': '12T294', 'galt': 294, 'grd': 4426.162785076934, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.238362687139.1', 'local_algs': ['23.2.0.1', '23.2.0.1', '23.2.1.2', '23.6.3.2', 'm317.1.1.0', 'm317.1.1.0', 'm317.1.1.0', 'm317.1.1.0', 'm317.2.1.1', 'm317.1.3.0', 'm317.1.3.0', 'm2687.1.1.0', 'm2687.1.1.0', 'm2687.1.2.0', 'm2687.2.1.1', 'm2687.1.6.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [23, 317, 2687], 'rd': 8.87366827443, 'regulator': {'__RealLiteral__': 0, 'data': '4.36197960563', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a^{11} - 3 a^{10} + 6 a^{9} - 4 a^{8} - 2 a^{7} + 7 a^{6} - 13 a^{5} + 6 a^{4} - 6 a^{2} + 5 a - 2 \\)', '\\( a \\)', '\\( a^{10} - a^{9} + 2 a^{8} - a^{7} - a^{6} + a^{5} - 2 a^{4} + a^{2} - 1 \\)', '\\( a^{10} + a^{8} + a^{7} - 2 a^{6} - a^{4} - 3 a^{3} + a^{2} - 1 \\)', '\\( a^{11} - 2 a^{10} + 4 a^{9} - 3 a^{8} + 5 a^{6} - 9 a^{5} + 6 a^{4} - a^{3} - 5 a^{2} + 5 a - 3 \\)', '\\( a^{11} - 2 a^{10} + 4 a^{9} - 4 a^{8} + a^{7} + 3 a^{6} - 8 a^{5} + 7 a^{4} - 3 a^{3} - 2 a^{2} + 3 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  14. label: 12.2.239557046875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 0, 1, 1, 0, -2, 2, 0, -1, -1, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 239557046875, 'disc_rad': 76658255, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [[10, 1], [2, 1]]], [11, [[6, 1], [4, 1], [2, 1]]], [13, [[4, 2], [2, 2]]], [17, [[6, 1], [4, 1], [2, 1]]], [19, [0]], [23, [[12, 1]]], [29, [[5, 1], [3, 1], [2, 1], [1, 2]]], [31, [[5, 1], [4, 1], [2, 1], [1, 1]]], [37, [[12, 1]]], [41, [[6, 1], [5, 1], [1, 1]]], [43, [[12, 1]]], [47, [[12, 1]]], [53, [[12, 1]]], [59, [[5, 1], [2, 3], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [518400, 518400, 518400], 'galois_label': '12T299', 'galt': 299, 'grd': 8755.470004517176, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.239557046875.1', 'local_algs': ['5.12.6.1', '19.2.0.1', '19.2.1.2', '19.4.0.1', '19.4.0.1', 'm806929.1.1.0', 'm806929.1.2.0', 'm806929.2.1.1', 'm806929.1.3.0', 'm806929.1.4.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 19, 806929], 'rd': 8.87736505338, 'regulator': {'__RealLiteral__': 0, 'data': '4.3666138828', 'prec': 40}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - a^{9} - a^{8} + 2 a^{6} - 2 a^{5} + a^{3} + a^{2} - 1 \\)', '\\( \\frac{7}{13} a^{11} - \\frac{1}{13} a^{10} - \\frac{5}{13} a^{9} - \\frac{10}{13} a^{8} - \\frac{6}{13} a^{7} + a^{6} - \\frac{1}{13} a^{5} + \\frac{15}{13} a^{4} + \\frac{3}{13} a^{3} + \\frac{1}{13} a^{2} - \\frac{2}{13} a - \\frac{3}{13} \\)', '\\( \\frac{7}{13} a^{11} + \\frac{12}{13} a^{10} - \\frac{5}{13} a^{9} - \\frac{23}{13} a^{8} - \\frac{19}{13} a^{7} + a^{6} + \\frac{12}{13} a^{5} - \\frac{11}{13} a^{4} + \\frac{3}{13} a^{3} + \\frac{14}{13} a^{2} + \\frac{11}{13} a - \\frac{3}{13} \\)', '\\( \\frac{9}{13} a^{11} + \\frac{8}{13} a^{10} - \\frac{12}{13} a^{9} - \\frac{24}{13} a^{8} - \\frac{4}{13} a^{7} + 2 a^{6} + \\frac{8}{13} a^{5} - \\frac{16}{13} a^{4} + \\frac{2}{13} a^{3} + \\frac{18}{13} a^{2} + \\frac{3}{13} a - \\frac{15}{13} \\)', '\\( \\frac{7}{13} a^{11} - \\frac{1}{13} a^{10} - \\frac{18}{13} a^{9} - \\frac{10}{13} a^{8} + \\frac{7}{13} a^{7} + 2 a^{6} - \\frac{1}{13} a^{5} - \\frac{11}{13} a^{4} + \\frac{16}{13} a^{3} + \\frac{1}{13} a^{2} - \\frac{2}{13} a - \\frac{3}{13} \\)', '\\( \\frac{8}{13} a^{11} + \\frac{10}{13} a^{10} - \\frac{2}{13} a^{9} - \\frac{17}{13} a^{8} - \\frac{18}{13} a^{7} - \\frac{3}{13} a^{5} - \\frac{7}{13} a^{4} + \\frac{9}{13} a^{3} + \\frac{16}{13} a^{2} + \\frac{7}{13} a + \\frac{4}{13} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/13*a^11 - 2/13*a^10 + 3/13*a^9 + 6/13*a^8 + 1/13*a^7 - 2/13*a^5 + 4/13*a^4 + 6/13*a^3 + 2/13*a^2 - 4/13*a - 6/13']}
  15. label: 12.2.247087671875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 0, -3, 0, 1, 3, 1, 0, -3, 0, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 247087671875, 'disc_rad': 5995, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 2]]], [5, [0]], [7, [[4, 3]]], [11, [0]], [13, [[12, 1]]], [17, [[4, 3]]], [19, [[6, 1], [3, 2]]], [23, [[4, 2], [2, 2]]], [29, [[3, 2], [2, 3]]], [31, [[2, 6]]], [37, [[4, 2], [2, 2]]], [41, [[2, 5], [1, 2]]], [43, [[4, 3]]], [47, [[4, 2], [2, 2]]], [53, [[4, 2], [2, 2]]], [59, [[2, 2], [1, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [144, 144, 144], 'galois_label': '12T125', 'galt': 125, 'grd': 77.42738533619743, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.247087671875.1', 'local_algs': ['5.12.6.1', '11.2.0.1', '11.2.0.1', '11.2.1.1', '11.2.0.1', '11.4.2.1', '109.1.0.1', '109.1.0.1', '109.2.0.1', '109.2.0.1', '109.2.0.1', '109.2.1.1', '109.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [5, 11, 109], 'rd': 8.9002920261, 'regulator': {'__RealLiteral__': 0, 'data': '4.50528335209', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '-1.2.0.-1.1', '1.3.1.-2.-3.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - a^{10} - 3 a^{8} + a^{6} + 3 a^{5} + a^{4} - 3 a^{2} - 1 \\)', '\\( 2 a^{11} - a^{10} - 2 a^{9} - 5 a^{8} - 2 a^{7} + 4 a^{6} + 6 a^{5} + 2 a^{4} - a^{3} - 4 a^{2} - a \\)', '\\( a^{11} - a^{10} - a^{9} - 2 a^{8} + a^{7} + 3 a^{6} + 2 a^{5} - 2 a^{4} - 2 a^{3} - 2 a^{2} + 2 a + 1 \\)', '\\( a^{10} - a^{9} - a^{8} - 2 a^{7} + a^{6} + 2 a^{5} + 3 a^{4} - a^{3} - a^{2} - 2 a \\)', '\\( a^{11} + a^{10} - 3 a^{9} - 3 a^{8} - 3 a^{7} + 2 a^{6} + 6 a^{5} + 3 a^{4} - 2 a^{3} - 2 a^{2} - 3 a + 1 \\)', '\\( a^{11} - 2 a^{10} + a^{9} - 2 a^{8} + 2 a^{7} + a^{6} - a^{5} - 2 a^{4} + a^{3} - a^{2} + 3 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  16. label: 12.2.255609008128.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 4, -11, 22, -28, 18, -2, -8, 7, -4, 3, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 255609008128, 'disc_rad': 10258, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 1], [3, 2]]], [5, [[4, 3]]], [7, [[8, 1], [4, 1]]], [11, [[8, 1], [2, 2]]], [13, [[6, 1], [3, 2]]], [17, [[4, 2], [2, 2]]], [19, [[4, 2], [2, 2]]], [23, [0]], [29, [[3, 4]]], [31, [[3, 4]]], [37, [[8, 1], [4, 1]]], [41, [[6, 2]]], [43, [[2, 6]]], [47, [[3, 4]]], [53, [[4, 1], [2, 3], [1, 2]]], [59, [[4, 2], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 768, 768], 'galois_label': '12T227', 'galt': 227, 'grd': 202.56357026869367, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.255609008128.1', 'local_algs': ['2.12.12.11', '23.1.0.1', '23.1.0.1', '23.2.0.1', '23.4.2.1', '23.4.2.1', 'm223.1.1.0', 'm223.1.1.0', 'm223.1.1.0', 'm223.1.1.0', 'm223.1.1.0', 'm223.1.1.0', 'm223.1.2.0', 'm223.1.2.0', 'm223.2.1.1'], 'minimal_sibling': [1, 0, -4, 0, 4, 0, 1, 0, 2, 0, 3, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 23, 223], 'rd': 8.92547517214, 'regulator': {'__RealLiteral__': 0, 'data': '4.5370381911', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.0.0.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{144}{347} a^{11} + \\frac{48}{347} a^{10} + \\frac{197}{347} a^{9} - \\frac{232}{347} a^{8} + \\frac{351}{347} a^{7} + \\frac{14}{347} a^{6} - \\frac{718}{347} a^{5} + \\frac{107}{347} a^{4} - \\frac{775}{347} a^{3} + \\frac{550}{347} a^{2} - \\frac{879}{347} a + \\frac{260}{347} \\)', '\\( \\frac{711}{347} a^{11} - \\frac{1151}{347} a^{10} + \\frac{1645}{347} a^{9} - \\frac{2013}{347} a^{8} + \\frac{4097}{347} a^{7} - \\frac{3878}{347} a^{6} - \\frac{3415}{347} a^{5} + \\frac{12001}{347} a^{4} - \\frac{15039}{347} a^{3} + \\frac{8311}{347} a^{2} - \\frac{2887}{347} a + \\frac{503}{347} \\)', '\\( \\frac{95}{347} a^{11} - \\frac{431}{347} a^{10} + \\frac{436}{347} a^{9} - \\frac{635}{347} a^{8} + \\frac{1034}{347} a^{7} - \\frac{1586}{347} a^{6} + \\frac{42}{347} a^{5} + \\frac{3543}{347} a^{4} - \\frac{5150}{347} a^{3} + \\frac{3722}{347} a^{2} - \\frac{1151}{347} a + \\frac{239}{347} \\)', '\\( \\frac{244}{347} a^{11} - \\frac{497}{347} a^{10} + \\frac{729}{347} a^{9} - \\frac{1010}{347} a^{8} + \\frac{1549}{347} a^{7} - \\frac{2039}{347} a^{6} - \\frac{619}{347} a^{5} + \\frac{4567}{347} a^{4} - \\frac{7164}{347} a^{3} + \\frac{5308}{347} a^{2} - \\frac{1634}{347} a + \\frac{402}{347} \\)', '\\( \\frac{586}{347} a^{11} - \\frac{1077}{347} a^{10} + \\frac{1327}{347} a^{9} - \\frac{1908}{347} a^{8} + \\frac{3467}{347} a^{7} - \\frac{3654}{347} a^{6} - \\frac{2758}{347} a^{5} + \\frac{10590}{347} a^{4} - \\frac{12865}{347} a^{3} + \\frac{7742}{347} a^{2} - \\frac{2724}{347} a + \\frac{1193}{347} \\)', '\\( \\frac{162}{347} a^{11} + \\frac{54}{347} a^{10} - \\frac{82}{347} a^{9} - \\frac{261}{347} a^{8} + \\frac{178}{347} a^{7} + \\frac{623}{347} a^{6} - \\frac{1415}{347} a^{5} + \\frac{77}{347} a^{4} + \\frac{1080}{347} a^{3} - \\frac{509}{347} a^{2} - \\frac{78}{347} a - \\frac{228}{347} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/347*a^11 + 116/347*a^10 + 158/347*a^9 - 98/347*a^8 - 106/347*a^7 - 24/347*a^6 - 58/347*a^5 + 114/347*a^4 - 109/347*a^3 - 1/347*a^2 - 129/347*a + 50/347']}
  17. label: 12.2.257978421875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -5, 12, -19, 20, -16, 10, -5, 0, 2, 0, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 257978421875, 'disc_rad': 6785, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 2]]], [5, [0]], [7, [[4, 2], [2, 2]]], [11, [[4, 1], [2, 4]]], [13, [[12, 1]]], [17, [[4, 2], [2, 2]]], [19, [[4, 1], [2, 3], [1, 2]]], [23, [0]], [29, [[6, 2]]], [31, [[6, 1], [3, 2]]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[4, 1], [2, 4]]], [47, [[12, 1]]], [53, [[4, 2], [2, 2]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [384, 384, 384], 'galois_label': '12T193', 'galt': 193, 'grd': 82.37111144084436, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.257978421875.1', 'local_algs': ['5.4.2.1', '5.8.4.1', '23.4.0.1', '23.8.4.1', '59.1.0.1', '59.1.0.1', '59.1.0.1', '59.1.0.1', '59.2.0.1', '59.2.0.1', '59.2.0.1', '59.2.1.1'], 'minimal_sibling': [1, 1, 0, 1, -2, -5, 3, 5, -2, -1, 0, -1, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 23, 59], 'rd': 8.93234074331, 'regulator': {'__RealLiteral__': 0, 'data': '4.57996864178', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '1.0.-1.1', '-1.0.3.4.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{78}{59} a^{11} - \\frac{174}{59} a^{10} + \\frac{22}{59} a^{9} + \\frac{219}{59} a^{8} - \\frac{46}{59} a^{7} - \\frac{511}{59} a^{6} + \\frac{848}{59} a^{5} - \\frac{1244}{59} a^{4} + \\frac{1661}{59} a^{3} - 26 a^{2} + \\frac{818}{59} a - \\frac{252}{59} \\)', '\\( \\frac{18}{59} a^{11} - \\frac{22}{59} a^{10} - \\frac{63}{59} a^{9} + \\frac{46}{59} a^{8} + \\frac{121}{59} a^{7} - \\frac{68}{59} a^{6} - \\frac{4}{59} a^{5} - \\frac{101}{59} a^{4} + \\frac{52}{59} a^{3} + 2 a^{2} - \\frac{138}{59} a + \\frac{78}{59} \\)', '\\( \\frac{96}{59} a^{11} - \\frac{137}{59} a^{10} - \\frac{100}{59} a^{9} + \\frac{147}{59} a^{8} + \\frac{134}{59} a^{7} - \\frac{402}{59} a^{6} + \\frac{667}{59} a^{5} - \\frac{1109}{59} a^{4} + \\frac{1182}{59} a^{3} - 17 a^{2} + \\frac{503}{59} a - \\frac{174}{59} \\)', '\\( \\frac{16}{59} a^{11} + \\frac{46}{59} a^{10} - \\frac{115}{59} a^{9} - \\frac{64}{59} a^{8} + \\frac{160}{59} a^{7} + \\frac{51}{59} a^{6} - \\frac{233}{59} a^{5} + \\frac{238}{59} a^{4} - \\frac{511}{59} a^{3} + 10 a^{2} - \\frac{398}{59} a + \\frac{148}{59} \\)', '\\( \\frac{283}{59} a^{11} - \\frac{418}{59} a^{10} - \\frac{312}{59} a^{9} + \\frac{520}{59} a^{8} + \\frac{411}{59} a^{7} - \\frac{1351}{59} a^{6} + \\frac{1930}{59} a^{5} - \\frac{3099}{59} a^{4} + \\frac{3525}{59} a^{3} - 45 a^{2} + \\frac{1095}{59} a - \\frac{229}{59} \\)', '\\( \\frac{39}{59} a^{11} - \\frac{146}{59} a^{10} + \\frac{70}{59} a^{9} + \\frac{198}{59} a^{8} - \\frac{82}{59} a^{7} - \\frac{344}{59} a^{6} + \\frac{660}{59} a^{5} - \\frac{976}{59} a^{4} + \\frac{1332}{59} a^{3} - 21 a^{2} + \\frac{763}{59} a - \\frac{244}{59} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/59*a^11 + 25/59*a^10 + 26/59*a^9 - 4/59*a^8 + 10/59*a^7 + 29/59*a^6 + 26/59*a^5 - 22/59*a^4 + 16/59*a^3 + 12/59*a + 24/59']}
  18. label: 12.2.266846228071.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 2, -3, 3, -4, 3, -4, 3, -3, 2, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 266846228071, 'disc_rad': 2876149, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[12, 1]]], [5, [[8, 1], [4, 1]]], [7, [[6, 2]]], [11, [[12, 1]]], [13, [[12, 1]]], [17, [[4, 2], [2, 1], [1, 2]]], [19, [[6, 2]]], [23, [[5, 2], [2, 1]]], [29, [[8, 1], [2, 2]]], [31, [0]], [37, [[8, 1], [2, 2]]], [41, [[5, 2], [1, 2]]], [43, [[5, 2], [2, 1]]], [47, [[4, 1], [3, 2], [2, 1]]], [53, [[8, 1], [2, 2]]], [59, [[8, 1], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [23040, 23040], 'galois_label': '12T293', 'galt': 293, 'grd': 1695.9212835506253, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.266846228071.1', 'local_algs': ['31.2.1.1', '31.10.0.1', 'm92779.1.2.0', 'm92779.2.1.1', 'm92779.2.1.1', 'm92779.1.3.0', 'm92779.1.3.0'], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [31, 92779], 'rd': 8.95753311463, 'regulator': {'__RealLiteral__': 0, 'data': '4.68688998752', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-2.-1.3.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - a^{10} + 2 a^{9} - 3 a^{8} + 3 a^{7} - 4 a^{6} + 3 a^{5} - 4 a^{4} + 3 a^{3} - 3 a^{2} + 2 a - 1 \\)', '\\( a^{9} - a^{8} + a^{7} - 2 a^{6} + 2 a^{5} - 2 a^{4} + a^{3} - 2 a^{2} + a - 1 \\)', '\\( a^{11} - a^{7} + a^{6} - 2 a^{5} + a^{4} - 2 a^{3} + a^{2} - 2 a + 1 \\)', '\\( a^{10} - 2 a^{9} + 3 a^{8} - 4 a^{7} + 4 a^{6} - 5 a^{5} + 4 a^{4} - 4 a^{3} + 4 a^{2} - 3 a + 2 \\)', '\\( a^{10} - a^{9} + 2 a^{8} - 3 a^{7} + 3 a^{6} - 4 a^{5} + 3 a^{4} - 4 a^{3} + 2 a^{2} - 2 a + 1 \\)', '\\( a^{11} - 2 a^{10} + 2 a^{9} - 3 a^{8} + 3 a^{7} - 3 a^{6} + 2 a^{5} - 2 a^{4} + 2 a^{3} - 2 a^{2} + a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  19. label: 12.2.273636802651.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -3, 1, -5, 9, -6, 15, -6, 12, -4, 5, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 273636802651, 'disc_rad': 3416659, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[8, 1], [4, 1]]], [7, [[6, 1], [3, 2]]], [11, [[6, 1], [3, 2]]], [13, [[6, 1], [3, 1], [2, 1], [1, 1]]], [17, [[6, 1], [3, 1], [2, 1], [1, 1]]], [19, [[8, 1], [4, 1]]], [23, [[6, 1], [3, 2]]], [29, [[3, 4]]], [31, [[12, 1]]], [37, [[6, 1], [3, 2]]], [41, [[6, 1], [3, 2]]], [43, [[8, 1], [4, 1]]], [47, [[8, 1], [4, 1]]], [53, [[4, 1], [2, 2], [1, 4]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [15552, 15552], 'galois_label': '12T289', 'galt': 289, 'grd': 1848.420677226913, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.273636802651.1', 'local_algs': ['m283.1.1.0', 'm283.1.1.0', 'm283.1.1.0', 'm283.1.1.0', 'm283.1.2.0', 'm283.2.1.1', 'm283.2.2.2', 'm12073.1.1.0', 'm12073.1.1.0', 'm12073.1.2.0', 'm12073.1.2.0', 'm12073.2.1.1', 'm12073.1.4.0'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [283, 12073], 'rd': 8.97631068037, 'regulator': {'__RealLiteral__': 0, 'data': '4.7852559363', 'prec': 40}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{4}{67} a^{11} + \\frac{42}{67} a^{10} - \\frac{33}{67} a^{9} + \\frac{174}{67} a^{8} - \\frac{95}{67} a^{7} + \\frac{324}{67} a^{6} - \\frac{33}{67} a^{5} + \\frac{233}{67} a^{4} + \\frac{2}{67} a^{3} + \\frac{3}{67} a^{2} + \\frac{5}{67} a - \\frac{55}{67} \\)', '\\( \\frac{31}{67} a^{11} - \\frac{43}{67} a^{10} + \\frac{163}{67} a^{9} - \\frac{159}{67} a^{8} + \\frac{386}{67} a^{7} - \\frac{236}{67} a^{6} + \\frac{431}{67} a^{5} - \\frac{154}{67} a^{4} + \\frac{250}{67} a^{3} - \\frac{94}{67} a^{2} + \\frac{22}{67} a - \\frac{41}{67} \\)', '\\( \\frac{3}{67} a^{11} - \\frac{2}{67} a^{10} - \\frac{8}{67} a^{9} + \\frac{30}{67} a^{8} - \\frac{88}{67} a^{7} + \\frac{109}{67} a^{6} - \\frac{209}{67} a^{5} + \\frac{158}{67} a^{4} - \\frac{233}{67} a^{3} + \\frac{86}{67} a^{2} - \\frac{147}{67} a + \\frac{76}{67} \\)', '\\( \\frac{55}{67} a^{11} - \\frac{59}{67} a^{10} + \\frac{233}{67} a^{9} - \\frac{187}{67} a^{8} + \\frac{486}{67} a^{7} - \\frac{235}{67} a^{6} + \\frac{501}{67} a^{5} - \\frac{230}{67} a^{4} + \\frac{195}{67} a^{3} - \\frac{143}{67} a^{2} - \\frac{15}{67} a - \\frac{36}{67} \\)', '\\( \\frac{23}{67} a^{11} + \\frac{7}{67} a^{10} + \\frac{28}{67} a^{9} + \\frac{96}{67} a^{8} - \\frac{27}{67} a^{7} + \\frac{255}{67} a^{6} - \\frac{106}{67} a^{5} + \\frac{184}{67} a^{4} - \\frac{156}{67} a^{3} + \\frac{34}{67} a^{2} - \\frac{122}{67} a + \\frac{2}{67} \\)', '\\( a^{2} + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/67*a^11 - 23/67*a^10 - 25/67*a^9 + 10/67*a^8 - 7/67*a^7 + 14/67*a^6 - 25/67*a^5 + 8/67*a^4 - 33/67*a^3 - 16/67*a^2 + 18/67*a + 3/67']}
  20. label: 12.2.279198105664.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, 3, 0, 1, 0, -7, 0, 9, 0, -5, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 279198105664, 'disc_rad': 514, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[4, 3]]], [5, [[8, 1], [4, 1]]], [7, [[4, 3]]], [11, [[6, 1], [3, 2]]], [13, [[6, 2]]], [17, [[6, 2]]], [19, [[4, 1], [2, 4]]], [23, [[6, 1], [3, 2]]], [29, [[6, 2]]], [31, [[6, 1], [3, 2]]], [37, [[4, 2], [2, 2]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [[8, 1], [2, 2]]], [47, [[4, 1], [2, 4]]], [53, [[4, 2], [2, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2688, 768], 'galois_label': '12T227', 'galt': 227, 'grd': 53.92238017965345, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.279198105664.1', 'local_algs': ['2.6.6.6', '2.6.0.1', 'm257.1.2.0', 'm257.1.2.0', 'm257.2.2.2', 'm257.2.2.2'], 'minimal_sibling': [1, 0, 4, -8, -1, 20, -29, 14, 10, -20, 15, -6, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 257], 'rd': 8.99137350807, 'regulator': {'__RealLiteral__': 0, 'data': '4.94368204571', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['3.-4.-1.1', '1.-1.-1.1.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 1 \\)', '\\( \\frac{1}{2} a^{10} - \\frac{5}{2} a^{8} + \\frac{1}{2} a^{7} + 4 a^{6} - a^{5} - 2 a^{4} + \\frac{1}{2} a^{3} - a^{2} - \\frac{1}{2} a + \\frac{3}{2} \\)', '\\( a^{11} - 5 a^{9} + 9 a^{7} - 7 a^{5} + a^{3} + 2 a \\)', '\\( a^{10} - 4 a^{8} + 5 a^{6} - 2 a^{4} + 1 \\)', '\\( a^{11} - \\frac{1}{2} a^{10} - \\frac{9}{2} a^{9} + 2 a^{8} + \\frac{13}{2} a^{7} - \\frac{5}{2} a^{6} - \\frac{7}{2} a^{5} + \\frac{1}{2} a^{4} + a^{2} + \\frac{5}{2} a - 1 \\)', '\\( a^{11} - \\frac{9}{2} a^{9} - \\frac{1}{2} a^{8} + 7 a^{7} + \\frac{3}{2} a^{6} - \\frac{9}{2} a^{5} - \\frac{3}{2} a^{4} + \\frac{1}{2} a^{3} + 2 a + \\frac{1}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^8 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2', '1/2*a^10 - 1/2*a^8 - 1/2*a^7 - 1/2*a^3 - 1/2*a - 1/2', '1/2*a^11 - 1/2*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2']}
  21. label: 12.2.288323843827.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, 4, 1, -7, 1, 10, -7, -6, 8, 0, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 288323843827, 'disc_rad': 3600043, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[4, 3]]], [5, [[4, 3]]], [7, [[9, 1], [3, 1]]], [11, [[9, 1], [3, 1]]], [13, [[3, 3], [2, 1], [1, 1]]], [17, [[3, 1], [2, 4], [1, 1]]], [19, [[8, 1], [4, 1]]], [23, [[9, 1], [3, 1]]], [29, [[6, 1], [3, 2]]], [31, [[8, 1], [4, 1]]], [37, [[4, 1], [3, 1], [2, 2], [1, 1]]], [41, [[9, 1], [2, 1], [1, 1]]], [43, [[4, 3]]], [47, [[8, 1], [4, 1]]], [53, [[2, 5], [1, 2]]], [59, [[6, 1], [3, 1], [2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [15552, 15552], 'galois_label': '12T289', 'galt': 289, 'grd': 1897.3779275621396, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.288323843827.1', 'local_algs': ['m283.1.1.0', 'm283.1.1.0', 'm283.1.2.0', 'm283.1.2.0', 'm283.2.1.1', 'm283.2.1.1', 'm283.2.1.1', 'm12721.1.1.0', 'm12721.1.1.0', 'm12721.1.1.0', 'm12721.1.1.0', 'm12721.1.2.0', 'm12721.1.2.0', 'm12721.1.2.0', 'm12721.2.1.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [283, 12721], 'rd': 9.01550475138, 'regulator': {'__RealLiteral__': 0, 'data': '4.93877212902', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{3} a^{11} - \\frac{7}{3} a^{10} + \\frac{4}{3} a^{9} + \\frac{11}{3} a^{8} - 5 a^{7} - \\frac{1}{3} a^{6} + 4 a^{5} - \\frac{4}{3} a^{4} - a^{3} - \\frac{2}{3} a^{2} + \\frac{4}{3} a + \\frac{1}{3} \\)', '\\( a \\)', '\\( \\frac{2}{3} a^{10} - 2 a^{9} + \\frac{1}{3} a^{8} + \\frac{13}{3} a^{7} - \\frac{13}{3} a^{6} - 2 a^{5} + 6 a^{4} - \\frac{7}{3} a^{3} - \\frac{8}{3} a^{2} + 2 a + \\frac{4}{3} \\)', '\\( \\frac{4}{3} a^{11} - 4 a^{10} + \\frac{2}{3} a^{9} + \\frac{26}{3} a^{8} - \\frac{23}{3} a^{7} - 5 a^{6} + 10 a^{5} - \\frac{5}{3} a^{4} - \\frac{16}{3} a^{3} + a^{2} + \\frac{11}{3} a \\)', '\\( \\frac{2}{3} a^{11} - \\frac{7}{3} a^{10} + \\frac{4}{3} a^{9} + \\frac{14}{3} a^{8} - 7 a^{7} - \\frac{4}{3} a^{6} + 9 a^{5} - \\frac{13}{3} a^{4} - 4 a^{3} + \\frac{10}{3} a^{2} + \\frac{4}{3} a - \\frac{2}{3} \\)', '\\( \\frac{2}{3} a^{11} - \\frac{5}{3} a^{10} - \\frac{2}{3} a^{9} + 4 a^{8} - \\frac{2}{3} a^{7} - \\frac{11}{3} a^{6} + a^{5} + \\frac{8}{3} a^{4} - \\frac{1}{3} a^{3} - \\frac{10}{3} a^{2} + \\frac{4}{3} a + \\frac{5}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/3*a^10 - 1/3*a^8 - 1/3*a^7 + 1/3*a^6 + 1/3*a^3 - 1/3*a^2 - 1/3', '1/3*a^11 - 1/3*a^9 - 1/3*a^8 + 1/3*a^7 + 1/3*a^4 - 1/3*a^3 - 1/3*a']}
  22. label: 12.2.293890894259.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 293890894259, 'disc_rad': 293890894259, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 2]]], [5, [[7, 1], [5, 1]]], [7, [[12, 1]]], [11, [[8, 1], [4, 1]]], [13, [[8, 1], [4, 1]]], [17, [[6, 1], [4, 1], [2, 1]]], [19, [[5, 1], [4, 1], [2, 1], [1, 1]]], [23, [[10, 1], [1, 2]]], [29, [[6, 1], [2, 3]]], [31, [[10, 1], [2, 1]]], [37, [[5, 1], [3, 1], [2, 1], [1, 2]]], [41, [[6, 1], [4, 1], [2, 1]]], [43, [[11, 1], [1, 1]]], [47, [[8, 1], [3, 1], [1, 1]]], [53, [[8, 1], [3, 1], [1, 1]]], [59, [[12, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [239500800, 239500800], 'galois_label': '12T301', 'galt': 301, 'grd': 542117.0484858413, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.293890894259.1', 'local_algs': ['103.2.1.1', '103.2.0.1', '103.8.0.1', 'm2853309653.2.1.1', 'm2853309653.1.3.0', 'm2853309653.1.7.0'], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [103, 2853309653], 'rd': 9.02988412951, 'regulator': {'__RealLiteral__': 0, 'data': '4.93923668618', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( 2 a^{11} - a^{10} + a^{9} - 3 a^{8} + 2 a^{7} - 2 a^{6} + 2 a^{5} - a^{4} - a^{3} + 3 \\)', '\\( a^{5} - a^{2} \\)', '\\( a^{11} - a^{10} + a^{9} - a^{8} + a^{7} - a^{6} + a^{5} - a^{3} - a + 1 \\)', '\\( 3 a^{11} - 2 a^{10} + 2 a^{9} - 4 a^{8} + 4 a^{7} - 3 a^{6} + 2 a^{5} - 2 a^{4} - a^{3} + a^{2} - a + 3 \\)', '\\( 2 a^{11} - 2 a^{10} + 2 a^{9} - 4 a^{8} + 3 a^{7} - 3 a^{6} + 2 a^{5} - 2 a^{4} + a^{2} - a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  23. label: 12.2.299095170283.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, -2, -2, 2, -2, -4, 6, -2, -1, 4, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 299095170283, 'disc_rad': 27937, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 1], [3, 2]]], [5, [[12, 1]]], [7, [0]], [11, [[6, 2]]], [13, [0]], [17, [[6, 2]]], [19, [[6, 2]]], [23, [[6, 1], [3, 2]]], [29, [[4, 2], [2, 1], [1, 2]]], [31, [[12, 1]]], [37, [[6, 2]]], [41, [[2, 4], [1, 4]]], [43, [[2, 5], [1, 2]]], [47, [[12, 1]]], [53, [[6, 2]]], [59, [[12, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1024, 768, 768], 'galois_label': '12T222', 'galt': 222, 'grd': 231.1743031850907, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.299095170283.1', 'local_algs': ['7.6.4.3', '7.6.4.3', '13.2.0.1', '13.2.0.1', '13.4.2.1', '13.4.0.1', 'm307.1.1.0', 'm307.1.1.0', 'm307.1.2.0', 'm307.1.2.0', 'm307.2.1.1', 'm307.1.4.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [7, 13, 307], 'rd': 9.04310242902, 'regulator': {'__RealLiteral__': 0, 'data': '4.96264024524', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '1.-2.2.-3.2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{11} - \\frac{1}{3} a^{10} + \\frac{2}{3} a^{9} + a^{8} - \\frac{4}{3} a^{7} + 2 a^{6} - a^{5} - \\frac{2}{3} a^{4} - \\frac{2}{3} a^{3} - a^{2} - \\frac{1}{3} \\)', '\\( \\frac{2}{3} a^{11} - \\frac{5}{3} a^{10} + 4 a^{9} - \\frac{10}{3} a^{8} + \\frac{5}{3} a^{7} + \\frac{10}{3} a^{6} - \\frac{14}{3} a^{5} + \\frac{5}{3} a^{4} - \\frac{8}{3} a^{2} - \\frac{4}{3} a \\)', '\\( a \\)', '\\( \\frac{1}{3} a^{10} - a^{9} + \\frac{4}{3} a^{8} - a^{7} - a^{6} + \\frac{1}{3} a^{5} - \\frac{1}{3} a^{4} - a^{3} + \\frac{2}{3} a^{2} + 2 a - \\frac{1}{3} \\)', '\\( \\frac{2}{3} a^{11} - a^{10} + 2 a^{9} + \\frac{1}{3} a^{8} - \\frac{4}{3} a^{7} + \\frac{10}{3} a^{6} - 2 a^{5} - a^{4} + a^{3} - \\frac{4}{3} a^{2} - \\frac{1}{3} a - \\frac{2}{3} \\)', '\\( \\frac{1}{3} a^{10} - \\frac{1}{3} a^{9} + a^{8} + \\frac{1}{3} a^{7} + \\frac{1}{3} a^{6} + \\frac{2}{3} a^{5} + \\frac{2}{3} a^{4} - \\frac{2}{3} a^{3} - a^{2} + \\frac{2}{3} a - \\frac{2}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/3*a^9 + 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 - 1/3*a^3 - 1/3*a^2 + 1/3*a + 1/3', '1/3*a^10 + 1/3*a^8 + 1/3*a^5 - 1/3*a^4 - 1/3*a^2 - 1/3', '1/3*a^11 - 1/3*a^8 + 1/3*a^7 - 1/3*a^6 + 1/3*a^2 + 1/3*a - 1/3']}
  24. label: 12.2.307980921875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 2, -3, 2, 5, -12, 13, -12, 12, -7, 3, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 307980921875, 'disc_rad': 814495, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 2]]], [5, [0]], [7, [[12, 1]]], [11, [0]], [13, [[8, 1], [4, 1]]], [17, [[4, 3]]], [19, [[4, 1], [3, 2], [2, 1]]], [23, [[4, 1], [2, 4]]], [29, [[6, 1], [3, 1], [2, 1], [1, 1]]], [31, [[6, 1], [4, 1], [2, 1]]], [37, [[4, 2], [2, 2]]], [41, [[4, 1], [3, 1], [2, 2], [1, 1]]], [43, [[12, 1]]], [47, [[6, 1], [2, 3]]], [53, [[4, 1], [2, 4]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [5184, 5184, 5184, 5184], 'galois_label': '12T274', 'galt': 274, 'grd': 902.4937672914976, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.307980921875.1', 'local_algs': ['5.4.2.1', '5.8.4.1', '11.2.1.1', '11.4.2.1', '11.6.0.1', '59.1.0.1', '59.1.0.1', '59.1.0.1', '59.1.0.1', '59.1.0.1', '59.2.1.2', '59.2.0.1', '59.3.0.1', 'm251.1.1.0', 'm251.1.1.0', 'm251.1.1.0', 'm251.1.1.0', 'm251.1.1.0', 'm251.1.1.0', 'm251.1.1.0', 'm251.2.1.1', 'm251.1.3.0'], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [5, 11, 59, 251], 'rd': 9.06519153456, 'regulator': {'__RealLiteral__': 0, 'data': '5.1470744096', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.2.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{933}{943} a^{11} - \\frac{1417}{943} a^{10} + \\frac{2204}{943} a^{9} - \\frac{5344}{943} a^{8} + \\frac{374}{41} a^{7} - \\frac{7401}{943} a^{6} + \\frac{8443}{943} a^{5} - \\frac{6580}{943} a^{4} + \\frac{2119}{943} a^{3} + \\frac{2626}{943} a^{2} - \\frac{2077}{943} a + \\frac{729}{943} \\)', '\\( \\frac{318}{943} a^{11} - \\frac{392}{943} a^{10} + \\frac{1015}{943} a^{9} - \\frac{2064}{943} a^{8} + \\frac{128}{41} a^{7} - \\frac{3793}{943} a^{6} + \\frac{4794}{943} a^{5} - \\frac{2931}{943} a^{4} + \\frac{2775}{943} a^{3} - \\frac{900}{943} a^{2} - \\frac{1093}{943} a + \\frac{770}{943} \\)', '\\( \\frac{179}{943} a^{11} - \\frac{191}{943} a^{10} + \\frac{343}{943} a^{9} - \\frac{717}{943} a^{8} + \\frac{54}{41} a^{7} - \\frac{768}{943} a^{6} + \\frac{599}{943} a^{5} - \\frac{93}{943} a^{4} + \\frac{450}{943} a^{3} + \\frac{1842}{943} a^{2} - \\frac{636}{943} a - \\frac{130}{943} \\)', '\\( \\frac{309}{943} a^{11} - \\frac{630}{943} a^{10} + \\frac{924}{943} a^{9} - \\frac{1970}{943} a^{8} + \\frac{153}{41} a^{7} - \\frac{3570}{943} a^{6} + \\frac{3057}{943} a^{5} - \\frac{2252}{943} a^{4} + \\frac{1193}{943} a^{3} + \\frac{1652}{943} a^{2} - \\frac{1925}{943} a + \\frac{766}{943} \\)', '\\( \\frac{906}{943} a^{11} - \\frac{1188}{943} a^{10} + \\frac{1931}{943} a^{9} - \\frac{5062}{943} a^{8} + \\frac{326}{41} a^{7} - \\frac{5789}{943} a^{6} + \\frac{7947}{943} a^{5} - \\frac{5486}{943} a^{4} + \\frac{202}{943} a^{3} + \\frac{2738}{943} a^{2} - \\frac{1744}{943} a + \\frac{1660}{943} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/943*a^11 + 236/943*a^10 - 409/943*a^9 - 220/943*a^8 + 20/41*a^7 + 80/943*a^6 + 193/943*a^5 - 285/943*a^4 + 71/943*a^3 - 74/943*a^2 + 302/943*a + 210/943']}
  25. label: 12.2.314972378176.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, -1, 0, 3, 0, 1, 0, -3, 0, -1, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 314972378176, 'disc_rad': 4526, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[4, 3]]], [5, [[6, 2]]], [7, [[12, 1]]], [11, [[4, 3]]], [13, [[4, 2], [2, 2]]], [17, [[4, 2], [2, 2]]], [19, [[6, 1], [3, 2]]], [23, [[4, 3]]], [29, [[4, 2], [2, 2]]], [31, [0]], [37, [[4, 2], [2, 2]]], [41, [[6, 2]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[4, 3]]], [53, [[4, 2], [2, 2]]], [59, [[12, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [768, 384, 384], 'galois_label': '12T186', 'galt': 186, 'grd': 95.14199913813037, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.314972378176.1', 'local_algs': ['2.6.0.1', '2.6.6.5', '31.2.1.2', '31.2.1.2', '31.4.0.1', '31.4.2.1', '73.2.1.1', '73.2.0.1', '73.2.0.1', '73.2.0.1', '73.2.0.1', '73.2.1.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 31, 73], 'rd': 9.08216468198, 'regulator': {'__RealLiteral__': 0, 'data': '5.32083463663', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.0.1', '-1.-1.3.-5.5.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{8} - a^{6} - 2 a^{4} + 1 \\)', '\\( \\frac{1}{2} a^{11} - \\frac{1}{2} a^{9} - \\frac{1}{2} a^{8} - \\frac{3}{2} a^{7} + a^{5} + \\frac{3}{2} a^{4} + a^{3} + \\frac{1}{2} a^{2} - \\frac{3}{2} a - \\frac{1}{2} \\)', '\\( \\frac{1}{2} a^{11} + \\frac{1}{2} a^{10} - a^{9} - \\frac{1}{2} a^{8} - a^{7} - a^{6} + 2 a^{5} - \\frac{1}{2} a^{4} + \\frac{1}{2} a^{3} + a^{2} - \\frac{3}{2} a \\)', '\\( a^{11} - \\frac{1}{2} a^{10} - a^{9} - \\frac{5}{2} a^{7} + \\frac{3}{2} a^{6} + \\frac{1}{2} a^{5} + \\frac{3}{2} a^{4} + 2 a^{3} - \\frac{1}{2} a^{2} - \\frac{1}{2} a - 1 \\)', '\\( \\frac{1}{2} a^{11} - \\frac{1}{2} a^{10} - \\frac{3}{2} a^{9} + \\frac{1}{2} a^{8} + \\frac{3}{2} a^{6} + \\frac{5}{2} a^{5} - a^{4} - a^{2} - 2 a + \\frac{1}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a - 1/2', '1/2*a^10 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^2 - 1/2*a', '1/2*a^11 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2*a^2']}
  26. label: 12.2.327779546875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, 1, -1, 1, 0, 0, 1, 1, -3, 2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 327779546875, 'disc_rad': 866855, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 1], [4, 1], [2, 1]]], [5, [0]], [7, [[12, 1]]], [11, [0]], [13, [[8, 1], [4, 1]]], [17, [[12, 1]]], [19, [[6, 1], [3, 1], [2, 1], [1, 1]]], [23, [[6, 1], [2, 3]]], [29, [[4, 1], [3, 2], [2, 1]]], [31, [[6, 1], [4, 1], [2, 1]]], [37, [[2, 6]]], [41, [[3, 1], [2, 4], [1, 1]]], [43, [[12, 1]]], [47, [[4, 2], [2, 2]]], [53, [[6, 1], [4, 1], [2, 1]]], [59, [[3, 2], [2, 1], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [5184, 5184, 5184], 'galois_label': '12T274', 'galt': 274, 'grd': 931.0504819825829, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.327779546875.1', 'local_algs': ['5.12.6.1', '11.2.0.1', '11.2.0.1', '11.2.0.1', '11.6.3.1', 'm15761.1.1.0', 'm15761.1.1.0', 'm15761.1.1.0', 'm15761.1.1.0', 'm15761.1.1.0', 'm15761.1.1.0', 'm15761.1.1.0', 'm15761.1.1.0', 'm15761.1.2.0', 'm15761.2.1.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 11, 15761], 'rd': 9.11237997258, 'regulator': {'__RealLiteral__': 0, 'data': '5.41339781061', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.2.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - 2 a^{10} + 2 a^{9} - 3 a^{8} + a^{7} + a^{6} + a^{3} - a^{2} + a + 1 \\)', '\\( \\frac{1}{3} a^{11} - a^{10} + \\frac{2}{3} a^{9} - \\frac{2}{3} a^{8} + \\frac{4}{3} a^{6} - \\frac{1}{3} a^{5} + \\frac{1}{3} a^{4} + \\frac{2}{3} a^{2} - \\frac{1}{3} a + \\frac{2}{3} \\)', '\\( \\frac{1}{3} a^{11} - \\frac{1}{3} a^{9} - \\frac{2}{3} a^{8} - a^{7} + \\frac{1}{3} a^{6} + \\frac{2}{3} a^{5} + \\frac{4}{3} a^{4} + \\frac{2}{3} a^{2} + \\frac{2}{3} a + \\frac{2}{3} \\)', '\\( \\frac{1}{3} a^{11} - a^{10} + \\frac{2}{3} a^{9} - \\frac{2}{3} a^{8} + \\frac{4}{3} a^{6} - \\frac{1}{3} a^{5} - \\frac{2}{3} a^{4} + a^{3} - \\frac{1}{3} a^{2} + \\frac{2}{3} a + \\frac{2}{3} \\)', '\\( \\frac{1}{3} a^{11} - a^{10} + \\frac{5}{3} a^{9} - \\frac{5}{3} a^{8} + a^{7} + \\frac{1}{3} a^{6} - \\frac{4}{3} a^{5} + \\frac{1}{3} a^{4} - \\frac{4}{3} a^{2} + \\frac{2}{3} a + \\frac{2}{3} \\)', '\\( a^{11} - 2 a^{10} + 2 a^{9} - 3 a^{8} + a^{7} + a^{5} + a^{3} + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/3*a^11 - 1/3*a^9 + 1/3*a^8 + 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^2 - 1/3*a - 1/3']}
  27. label: 12.2.336393921875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -1, -1, 3, -1, -1, -1, 3, -1, -1, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 336393921875, 'disc_rad': 76945, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[8, 1], [4, 1]]], [5, [0]], [7, [[12, 1]]], [11, [0]], [13, [[8, 1], [2, 2]]], [17, [[4, 3]]], [19, [[6, 1], [3, 2]]], [23, [[4, 2], [2, 2]]], [29, [[3, 2], [2, 1], [1, 4]]], [31, [[6, 1], [2, 3]]], [37, [[6, 2]]], [41, [[4, 2], [2, 1], [1, 2]]], [43, [[8, 1], [2, 2]]], [47, [[4, 2], [2, 2]]], [53, [[8, 1], [4, 1]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 277.3896176860266, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.336393921875.1', 'local_algs': ['5.12.6.1', '11.2.0.1', '11.2.1.2', '11.2.0.1', '11.2.0.1', '11.4.0.1', 'm1399.1.1.0', 'm1399.1.1.0', 'm1399.2.1.1', 'm1399.2.1.1', 'm1399.1.6.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [5, 11, 1399], 'rd': 9.13210041657, 'regulator': {'__RealLiteral__': 0, 'data': '5.43541349035', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.-3.1.4.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - a^{10} - a^{9} - a^{8} + 3 a^{7} - a^{6} - a^{5} - a^{4} + 3 a^{3} - a^{2} - a - 1 \\)', '\\( a^{11} - a^{10} - a^{9} + 2 a^{7} - a^{6} - 2 a^{5} + a^{3} - a^{2} - a \\)', '\\( a^{11} - 2 a^{9} - a^{8} + a^{7} + a^{6} - 2 a^{5} - a^{4} + a^{3} + a^{2} - a - 1 \\)', '\\( a^{10} - 2 a^{8} - a^{7} + a^{6} + a^{5} - 3 a^{4} + a^{3} + a^{2} + a - 2 \\)', '\\( a^{11} - a^{10} - 2 a^{8} + 2 a^{7} - a^{6} + a^{5} - 3 a^{4} + a^{3} + a - 2 \\)', '\\( 2 a^{11} - 2 a^{10} - a^{9} - 2 a^{8} + 4 a^{7} - 3 a^{6} - a^{5} - a^{4} + 3 a^{3} - 2 a^{2} - a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  28. label: 12.2.341962230519.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -7, 21, -39, 52, -56, 52, -43, 31, -20, 10, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 341962230519, 'disc_rad': 273, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [0]], [5, [[6, 2]]], [7, [0]], [11, [[6, 2]]], [13, [0]], [17, [[6, 1], [3, 2]]], [19, [[12, 1]]], [23, [[6, 1], [3, 2]]], [29, [[2, 5], [1, 2]]], [31, [[12, 1]]], [37, [[12, 1]]], [41, [[2, 4], [1, 4]]], [43, [[4, 2], [2, 2]]], [47, [[6, 2]]], [53, [[6, 1], [3, 2]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [192, 256, 288], 'galois_label': '12T141', 'galt': 141, 'grd': 43.39271609609281, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.341962230519.1', 'local_algs': ['3.6.3.1', '3.6.0.1', '7.12.8.1', '13.2.0.1', '13.2.0.1', '13.4.3.4', '13.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [3, 7, 13], 'rd': 9.14460277171, 'regulator': {'__RealLiteral__': 0, 'data': '5.44076103214', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '1.-2.2.-3.2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{5}{2} a^{11} - 8 a^{10} + \\frac{37}{2} a^{9} - \\frac{71}{2} a^{8} + 50 a^{7} - \\frac{139}{2} a^{6} + \\frac{157}{2} a^{5} - \\frac{163}{2} a^{4} + 71 a^{3} - \\frac{93}{2} a^{2} + 21 a - 5 \\)', '\\( \\frac{9}{2} a^{11} - 17 a^{10} + 40 a^{9} - \\frac{155}{2} a^{8} + \\frac{229}{2} a^{7} - 154 a^{6} + \\frac{363}{2} a^{5} - 187 a^{4} + \\frac{333}{2} a^{3} - 113 a^{2} + 50 a - \\frac{21}{2} \\)', '\\( \\frac{7}{2} a^{11} - 12 a^{10} + \\frac{57}{2} a^{9} - \\frac{109}{2} a^{8} + 79 a^{7} - \\frac{217}{2} a^{6} + \\frac{247}{2} a^{5} - \\frac{261}{2} a^{4} + 112 a^{3} - \\frac{153}{2} a^{2} + 33 a - 7 \\)', '\\( \\frac{9}{2} a^{11} - \\frac{35}{2} a^{10} + 42 a^{9} - 82 a^{8} + 123 a^{7} - 166 a^{6} + 197 a^{5} - \\frac{411}{2} a^{4} + 184 a^{3} - 128 a^{2} + \\frac{117}{2} a - \\frac{25}{2} \\)', '\\( \\frac{1}{2} a^{11} - \\frac{5}{2} a^{10} + \\frac{13}{2} a^{9} - 13 a^{8} + \\frac{41}{2} a^{7} - \\frac{55}{2} a^{6} + 34 a^{5} - 36 a^{4} + \\frac{67}{2} a^{3} - \\frac{49}{2} a^{2} + \\frac{23}{2} a - 3 \\)', '\\( \\frac{9}{2} a^{11} - 17 a^{10} + 40 a^{9} - \\frac{155}{2} a^{8} + \\frac{229}{2} a^{7} - 154 a^{6} + \\frac{363}{2} a^{5} - 187 a^{4} + \\frac{333}{2} a^{3} - 113 a^{2} + 50 a - \\frac{19}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^7 - 1/2*a^6 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2', '1/2*a^10 - 1/2*a^8 - 1/2*a^7 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a', '1/2*a^11 - 1/2*a^8 - 1/2*a^7 - 1/2*a^5 - 1/2*a^3 - 1/2']}
  29. label: 12.2.349257427087.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -2, 5, -9, 14, -18, 18, -12, 9, -10, 8, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 349257427087, 'disc_rad': 29083, 'disc_sign': -1, 'frobs': [[2, [[8, 1], [4, 1]]], [3, [[6, 1], [3, 2]]], [5, [[6, 1], [3, 2]]], [7, [[4, 3]]], [11, [[6, 2]]], [13, [[8, 1], [4, 1]]], [17, [[3, 4]]], [19, [[6, 2]]], [23, [[4, 2], [2, 1], [1, 2]]], [29, [[4, 1], [2, 4]]], [31, [[4, 2], [2, 2]]], [37, [[2, 6]]], [41, [[4, 2], [2, 2]]], [43, [[6, 1], [3, 2]]], [47, [[4, 2], [2, 2]]], [53, [[4, 1], [2, 2], [1, 4]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [768, 768], 'galois_label': '12T227', 'galt': 227, 'grd': 170.53738593047566, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.349257427087.1', 'local_algs': ['127.1.0.1', '127.1.0.1', '127.2.1.1', '127.2.0.1', '127.2.0.1', '127.4.0.1', 'm229.1.1.0', 'm229.1.1.0', 'm229.1.2.0', 'm229.2.4.4'], 'minimal_sibling': [1, -6, 11, 0, -29, 50, -42, 17, 2, -7, 6, -3, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [127, 229], 'rd': 9.16070302373, 'regulator': {'__RealLiteral__': 0, 'data': '5.49728358002', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-4.0.1', '1.0.-1.-1.-1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{491}{4033} a^{11} + \\frac{236}{4033} a^{10} - \\frac{2982}{4033} a^{9} + \\frac{6937}{4033} a^{8} - \\frac{7605}{4033} a^{7} + \\frac{3065}{4033} a^{6} - \\frac{7319}{4033} a^{5} + \\frac{12867}{4033} a^{4} - \\frac{11238}{4033} a^{3} + \\frac{8548}{4033} a^{2} - \\frac{4207}{4033} a + \\frac{1105}{4033} \\)', '\\( \\frac{1520}{4033} a^{11} - \\frac{6974}{4033} a^{10} + \\frac{14638}{4033} a^{9} - \\frac{18280}{4033} a^{8} + \\frac{15941}{4033} a^{7} - \\frac{19449}{4033} a^{6} + \\frac{33328}{4033} a^{5} - \\frac{33632}{4033} a^{4} + \\frac{21278}{4033} a^{3} - \\frac{14722}{4033} a^{2} + \\frac{8628}{4033} a - \\frac{834}{4033} \\)', '\\( \\frac{2011}{4033} a^{11} - \\frac{6738}{4033} a^{10} + \\frac{11656}{4033} a^{9} - \\frac{11343}{4033} a^{8} + \\frac{8336}{4033} a^{7} - \\frac{16384}{4033} a^{6} + \\frac{26009}{4033} a^{5} - \\frac{20765}{4033} a^{4} + \\frac{10040}{4033} a^{3} - \\frac{6174}{4033} a^{2} + \\frac{4421}{4033} a - \\frac{3762}{4033} \\)', '\\( \\frac{297}{4033} a^{11} + \\frac{882}{4033} a^{10} - \\frac{4309}{4033} a^{9} + \\frac{7572}{4033} a^{8} - \\frac{6514}{4033} a^{7} + \\frac{1509}{4033} a^{6} - \\frac{9068}{4033} a^{5} + \\frac{16268}{4033} a^{4} - \\frac{9804}{4033} a^{3} + \\frac{2690}{4033} a^{2} - \\frac{787}{4033} a + \\frac{1498}{4033} \\)', '\\( \\frac{204}{4033} a^{11} - \\frac{1594}{4033} a^{10} + \\frac{3599}{4033} a^{9} - \\frac{4576}{4033} a^{8} + \\frac{3551}{4033} a^{7} - \\frac{3852}{4033} a^{6} + \\frac{9822}{4033} a^{5} - \\frac{11476}{4033} a^{4} + \\frac{5976}{4033} a^{3} - \\frac{5648}{4033} a^{2} + \\frac{2474}{4033} a - \\frac{1619}{4033} \\)', '\\( \\frac{475}{4033} a^{11} - \\frac{667}{4033} a^{10} - \\frac{971}{4033} a^{9} + \\frac{4370}{4033} a^{8} - \\frac{5353}{4033} a^{7} + \\frac{1232}{4033} a^{6} - \\frac{1684}{4033} a^{5} + \\frac{9655}{4033} a^{4} - \\frac{10995}{4033} a^{3} + \\frac{5986}{4033} a^{2} - \\frac{2345}{4033} a + \\frac{2260}{4033} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/4033*a^11 - 1708/4033*a^10 - 1386/4033*a^9 - 1604/4033*a^8 - 1149/4033*a^7 + 1879/4033*a^6 + 404/4033*a^5 + 1209/4033*a^4 + 741/4033*a^3 - 344/4033*a^2 + 1396/4033*a + 684/4033']}
  30. label: 12.2.353996898304.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 4, 0, -2, 2, -4, 4, 0, 0, 1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 353996898304, 'disc_rad': 55118, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [[8, 1], [4, 1]]], [7, [0]], [11, [[6, 1], [4, 1], [2, 1]]], [13, [[8, 1], [4, 1]]], [17, [[6, 1], [3, 1], [2, 1], [1, 1]]], [19, [[12, 1]]], [23, [[3, 2], [2, 2], [1, 2]]], [29, [[6, 1], [2, 3]]], [31, [0]], [37, [[6, 1], [4, 1], [2, 1]]], [41, [[6, 1], [2, 2], [1, 2]]], [43, [[4, 2], [2, 2]]], [47, [[6, 1], [3, 2]]], [53, [[4, 2], [2, 2]]], [59, [[8, 1], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [15552, 5184, 5184, 5184], 'galois_label': '12T274', 'galt': 274, 'grd': 469.54446008871196, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.353996898304.1', 'local_algs': ['2.12.18.23', '7.2.0.1', '7.4.0.1', '7.6.3.1', '31.1.0.1', '31.1.0.1', '31.2.0.1', '31.2.1.2', '31.2.0.1', '31.4.0.1', '127.1.0.1', '127.1.0.1', '127.1.0.1', '127.1.0.1', '127.1.0.1', '127.2.1.2', '127.2.0.1', '127.3.0.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [2, 7, 31, 127], 'rd': 9.170998478582437, 'regulator': {'__RealLiteral__': 0, 'data': '5.5369431385384855', 'prec': 60}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '1.-2.1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{163}{127} a^{11} - \\frac{208}{127} a^{10} - \\frac{39}{127} a^{9} + \\frac{105}{127} a^{8} - \\frac{58}{127} a^{7} + \\frac{730}{127} a^{6} - \\frac{263}{127} a^{5} + \\frac{106}{127} a^{4} - \\frac{162}{127} a^{3} - \\frac{277}{127} a^{2} + \\frac{753}{127} a - \\frac{364}{127} \\)', '\\( -a \\)', '\\( \\frac{163}{127} a^{11} - \\frac{208}{127} a^{10} - \\frac{39}{127} a^{9} + \\frac{105}{127} a^{8} - \\frac{58}{127} a^{7} + \\frac{730}{127} a^{6} - \\frac{263}{127} a^{5} + \\frac{106}{127} a^{4} - \\frac{162}{127} a^{3} - \\frac{150}{127} a^{2} + \\frac{753}{127} a - \\frac{364}{127} \\)', '\\( -\\frac{73}{127} a^{11} + \\frac{69}{127} a^{10} + \\frac{5}{127} a^{9} - \\frac{33}{127} a^{8} + \\frac{40}{127} a^{7} - \\frac{302}{127} a^{6} + \\frac{50}{127} a^{5} - \\frac{222}{127} a^{4} - \\frac{116}{127} a^{3} + \\frac{29}{127} a^{2} - \\frac{331}{127} a + \\frac{216}{127} \\)', '\\( -\\frac{188}{127} a^{11} + \\frac{296}{127} a^{10} - \\frac{8}{127} a^{9} - \\frac{125}{127} a^{8} + \\frac{63}{127} a^{7} - \\frac{863}{127} a^{6} + \\frac{555}{127} a^{5} - \\frac{102}{127} a^{4} + \\frac{211}{127} a^{3} + \\frac{233}{127} a^{2} - \\frac{969}{127} a + \\frac{518}{127} \\)', '\\( \\frac{25}{127} a^{11} - \\frac{88}{127} a^{10} + \\frac{47}{127} a^{9} + \\frac{20}{127} a^{8} - \\frac{5}{127} a^{7} + \\frac{133}{127} a^{6} - \\frac{292}{127} a^{5} - \\frac{4}{127} a^{4} - \\frac{49}{127} a^{3} - \\frac{83}{127} a^{2} + \\frac{216}{127} a - \\frac{154}{127} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/127*a^11 - 34/127*a^10 - 54/127*a^9 - 50/127*a^8 - 51/127*a^7 - 15/127*a^6 - 32/127*a^5 + 10/127*a^4 + 59/127*a^3 + 17/127*a^2 - 32/127*a + 4/127']}
  31. label: 12.2.362031460339.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -1, 1, -2, 2, 1, -1, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 362031460339, 'disc_rad': 362031460339, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[8, 1], [4, 1]]], [7, [[5, 1], [3, 1], [2, 2]]], [11, [[10, 1], [2, 1]]], [13, [[5, 1], [3, 2], [1, 1]]], [17, [[6, 2]]], [19, [[6, 1], [5, 1], [1, 1]]], [23, [[7, 1], [5, 1]]], [29, [[4, 2], [3, 1], [1, 1]]], [31, [[11, 1], [1, 1]]], [37, [[12, 1]]], [41, [[8, 1], [4, 1]]], [43, [[8, 1], [3, 1], [1, 1]]], [47, [[8, 1], [2, 1], [1, 2]]], [53, [[7, 1], [2, 2], [1, 1]]], [59, [[6, 1], [4, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [239500800], 'galois_label': '12T301', 'galt': 301, 'grd': 601690.5021179909, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.362031460339.1', 'local_algs': ['m362031460339.1.1.0', 'm362031460339.1.1.0', 'm362031460339.1.2.0', 'm362031460339.2.1.1', 'm362031460339.1.6.0'], 'monogenic': 0, 'num_ram': 1, 'r2': 5, 'ramps': [362031460339], 'rd': 9.18816656011, 'regulator': {'__RealLiteral__': 0, 'data': '5.64279808125', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{10}{7} a^{11} + \\frac{6}{7} a^{10} + \\frac{5}{7} a^{9} + \\frac{3}{7} a^{8} + \\frac{6}{7} a^{7} - \\frac{5}{7} a^{6} + a^{5} + \\frac{20}{7} a^{4} - \\frac{1}{7} a^{3} + \\frac{8}{7} a^{2} - \\frac{8}{7} a - \\frac{5}{7} \\)', '\\( \\frac{16}{7} a^{11} + \\frac{11}{7} a^{10} + \\frac{8}{7} a^{9} + \\frac{9}{7} a^{8} + \\frac{4}{7} a^{7} - \\frac{15}{7} a^{6} + a^{5} + \\frac{39}{7} a^{4} - \\frac{10}{7} a^{3} + \\frac{17}{7} a^{2} - \\frac{3}{7} a - \\frac{29}{7} \\)', '\\( 2 a^{11} + 2 a^{10} + a^{9} + a^{8} + a^{7} - a^{6} + 5 a^{4} - 2 \\)', '\\( \\frac{8}{7} a^{11} + \\frac{9}{7} a^{10} + \\frac{4}{7} a^{9} + \\frac{1}{7} a^{8} + \\frac{2}{7} a^{7} - \\frac{4}{7} a^{6} + \\frac{16}{7} a^{4} + \\frac{2}{7} a^{3} - \\frac{2}{7} a^{2} - \\frac{5}{7} a - \\frac{11}{7} \\)', '\\( \\frac{31}{7} a^{11} + \\frac{27}{7} a^{10} + \\frac{19}{7} a^{9} + \\frac{17}{7} a^{8} + \\frac{13}{7} a^{7} - \\frac{19}{7} a^{6} + 2 a^{5} + \\frac{76}{7} a^{4} - \\frac{1}{7} a^{3} + \\frac{22}{7} a^{2} - \\frac{8}{7} a - \\frac{40}{7} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/7*a^11 + 2/7*a^10 - 3/7*a^9 + 1/7*a^8 + 2/7*a^7 + 3/7*a^6 + 2/7*a^4 + 2/7*a^3 - 2/7*a^2 + 2/7*a + 3/7']}
  32. label: 12.2.373065296875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, 3, -6, -5, 11, 3, -12, 0, 8, -2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 373065296875, 'disc_rad': 5605, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[4, 3]]], [5, [0]], [7, [[6, 2]]], [11, [[2, 6]]], [13, [[4, 3]]], [17, [[6, 2]]], [19, [0]], [23, [[4, 2], [2, 2]]], [29, [[6, 1], [2, 2], [1, 2]]], [31, [[6, 1], [3, 2]]], [37, [[12, 1]]], [41, [[6, 1], [2, 2], [1, 2]]], [43, [[4, 2], [2, 2]]], [47, [[4, 2], [2, 2]]], [53, [[4, 3]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [144, 144, 144], 'galois_label': '12T125', 'galt': 125, 'grd': 74.86654793697917, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.373065296875.1', 'local_algs': ['5.6.3.1', '5.6.3.1', '19.1.0.1', '19.1.0.1', '19.2.1.2', '19.2.0.1', '19.2.0.1', '19.4.2.1', '59.2.0.1', '59.3.0.1', '59.3.0.1', '59.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 19, 59], 'rd': 9.21118286768, 'regulator': {'__RealLiteral__': 0, 'data': '5.72023263089', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '-1.-1.2.-2.1', '-1.-1.2.-3.3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{23} a^{11} - \\frac{2}{23} a^{10} - \\frac{1}{23} a^{9} - \\frac{8}{23} a^{8} + \\frac{20}{23} a^{7} + \\frac{29}{23} a^{6} - \\frac{52}{23} a^{5} + \\frac{2}{23} a^{4} + \\frac{49}{23} a^{3} - \\frac{14}{23} a^{2} - \\frac{48}{23} a + \\frac{8}{23} \\)', '\\( a \\)', '\\( \\frac{34}{23} a^{11} - \\frac{84}{23} a^{10} - \\frac{19}{23} a^{9} + \\frac{262}{23} a^{8} - \\frac{149}{23} a^{7} - \\frac{254}{23} a^{6} + \\frac{231}{23} a^{5} + \\frac{130}{23} a^{4} - \\frac{219}{23} a^{3} + \\frac{10}{23} a^{2} + \\frac{77}{23} a - \\frac{55}{23} \\)', '\\( \\frac{9}{23} a^{11} - \\frac{29}{23} a^{10} + \\frac{20}{23} a^{9} + \\frac{45}{23} a^{8} - \\frac{78}{23} a^{7} + \\frac{18}{23} a^{6} + \\frac{51}{23} a^{5} - \\frac{40}{23} a^{4} - \\frac{60}{23} a^{3} + \\frac{73}{23} a^{2} - \\frac{6}{23} a - \\frac{22}{23} \\)', '\\( \\frac{7}{23} a^{11} - \\frac{20}{23} a^{10} - \\frac{10}{23} a^{9} + \\frac{81}{23} a^{8} - \\frac{30}{23} a^{7} - \\frac{124}{23} a^{6} + \\frac{55}{23} a^{5} + \\frac{112}{23} a^{4} - \\frac{39}{23} a^{3} - \\frac{71}{23} a^{2} + \\frac{26}{23} a + \\frac{11}{23} \\)', '\\( \\frac{11}{23} a^{11} + \\frac{8}{23} a^{10} - \\frac{88}{23} a^{9} + \\frac{55}{23} a^{8} + \\frac{219}{23} a^{7} - \\frac{185}{23} a^{6} - \\frac{229}{23} a^{5} + \\frac{222}{23} a^{4} + \\frac{172}{23} a^{3} - \\frac{174}{23} a^{2} - \\frac{61}{23} a + \\frac{37}{23} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/23*a^11 + 7/23*a^10 - 8/23*a^9 + 5/23*a^8 - 1/23*a^7 + 2/23*a^6 - 2/23*a^5 - 7/23*a^4 + 1/23*a^3 + 3/23*a^2 + 7/23*a - 5/23']}
  33. label: 12.2.396228830787.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -3, 1, 3, 0, -1, -3, 0, 4, -1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 396228830787, 'disc_rad': 15801, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [0]], [5, [[4, 3]]], [7, [[4, 2], [2, 2]]], [11, [[4, 2], [2, 1], [1, 2]]], [13, [[6, 2]]], [17, [[4, 3]]], [19, [[4, 2], [2, 2]]], [23, [0]], [29, [[12, 1]]], [31, [[6, 2]]], [37, [[4, 2], [2, 2]]], [41, [[12, 1]]], [43, [[4, 2], [2, 2]]], [47, [[12, 1]]], [53, [[4, 3]]], [59, [[4, 1], [2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [384, 384, 384], 'galois_label': '12T186', 'galt': 186, 'grd': 125.70202862324857, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.396228830787.1', 'local_algs': ['3.6.3.1', '3.6.0.1', '23.4.0.1', '23.8.4.1', 'm229.1.4.0', 'm229.1.4.0', 'm229.2.2.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [3, 23, 229], 'rd': 9.25753805701, 'regulator': {'__RealLiteral__': 0, 'data': '6.09548763154', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.-7.6.5.-3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - 2 a^{10} - a^{9} + 3 a^{8} + a^{7} - a^{6} - 3 a^{5} - a^{4} + 3 a^{3} + 2 a^{2} - a - 1 \\)', '\\( a^{10} - 2 a^{9} + 2 a^{7} - a^{6} - a^{4} - a^{3} + 2 a^{2} - 1 \\)', '\\( a^{2} - 1 \\)', '\\( a^{11} - 2 a^{10} - 2 a^{9} + 5 a^{8} + a^{7} - 3 a^{6} - 2 a^{5} - a^{4} + 4 a^{3} + 3 a^{2} - 2 a - 1 \\)', '\\( a^{10} - a^{9} - 2 a^{8} + a^{7} + 2 a^{6} + a^{5} - 2 a^{4} - 3 a^{3} + 2 a + 1 \\)', '\\( 2 a^{11} - 3 a^{10} - 3 a^{9} + 5 a^{8} + 3 a^{7} - 3 a^{6} - 4 a^{5} - 2 a^{4} + 4 a^{3} + 3 a^{2} - 2 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  34. label: 12.2.398786546875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, -1, 4, -4, -1, 7, -7, 4, -3, 4, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 398786546875, 'disc_rad': 5795, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[4, 3]]], [5, [0]], [7, [[4, 2], [2, 2]]], [11, [[6, 1], [2, 3]]], [13, [[4, 3]]], [17, [[4, 2], [2, 2]]], [19, [0]], [23, [[4, 2], [2, 2]]], [29, [[6, 1], [3, 2]]], [31, [[2, 5], [1, 2]]], [37, [[4, 3]]], [41, [[6, 1], [2, 2], [1, 2]]], [43, [[4, 2], [2, 2]]], [47, [[2, 6]]], [53, [[12, 1]]], [59, [[2, 5], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [144, 144, 144], 'galois_label': '12T125', 'galt': 125, 'grd': 76.12489737267302, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.398786546875.1', 'local_algs': ['5.6.3.1', '5.6.3.1', '19.2.1.2', '19.2.1.2', '19.2.1.2', '19.3.0.1', '19.3.0.1', '61.2.0.1', '61.2.0.1', '61.2.0.1', '61.2.0.1', '61.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 19, 61], 'rd': 9.26250328277, 'regulator': {'__RealLiteral__': 0, 'data': '5.94217649784', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '-1.-1.2.-2.1', '1.-3.-2.5.-1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{42}{83} a^{11} - \\frac{62}{83} a^{10} + \\frac{34}{83} a^{9} - \\frac{7}{83} a^{8} + \\frac{102}{83} a^{7} - \\frac{103}{83} a^{6} + \\frac{58}{83} a^{5} + \\frac{78}{83} a^{4} - \\frac{61}{83} a^{3} - \\frac{4}{83} a^{2} + \\frac{110}{83} a + \\frac{12}{83} \\)', '\\( a \\)', '\\( \\frac{8}{83} a^{11} + \\frac{4}{83} a^{10} - \\frac{37}{83} a^{9} + \\frac{54}{83} a^{8} - \\frac{28}{83} a^{7} + \\frac{12}{83} a^{6} - \\frac{68}{83} a^{5} + \\frac{86}{83} a^{4} + \\frac{20}{83} a^{3} - \\frac{147}{83} a^{2} + \\frac{100}{83} a - \\frac{57}{83} \\)', '\\( \\frac{15}{83} a^{11} - \\frac{34}{83} a^{10} + \\frac{24}{83} a^{9} + \\frac{39}{83} a^{8} - \\frac{11}{83} a^{7} - \\frac{19}{83} a^{6} - \\frac{3}{83} a^{5} + \\frac{182}{83} a^{4} - \\frac{170}{83} a^{3} + \\frac{46}{83} a^{2} + \\frac{63}{83} a + \\frac{28}{83} \\)', '\\( \\frac{29}{83} a^{11} - \\frac{110}{83} a^{10} + \\frac{146}{83} a^{9} - \\frac{74}{83} a^{8} + \\frac{106}{83} a^{7} - \\frac{247}{83} a^{6} + \\frac{210}{83} a^{5} + \\frac{42}{83} a^{4} - \\frac{218}{83} a^{3} + \\frac{183}{83} a^{2} - \\frac{11}{83} a + \\frac{32}{83} \\)', '\\( \\frac{3}{83} a^{11} - \\frac{40}{83} a^{10} + \\frac{38}{83} a^{9} + \\frac{41}{83} a^{8} - \\frac{52}{83} a^{7} - \\frac{37}{83} a^{6} + \\frac{16}{83} a^{5} + \\frac{136}{83} a^{4} - \\frac{200}{83} a^{3} + \\frac{59}{83} a^{2} + \\frac{79}{83} a - \\frac{94}{83} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/83*a^11 - 41/83*a^10 - 15/83*a^9 - 14/83*a^8 + 38/83*a^7 - 40/83*a^6 + 33/83*a^5 - 10/83*a^4 - 39/83*a^3 - 8/83*a^2 - 29/83*a + 24/83']}
  35. label: 12.2.417344000000.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 1, -6, 5, 0, 4, -4, 1, -2, 2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 417344000000, 'disc_rad': 65210, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1], [4, 1]]], [5, [0]], [7, [[12, 1]]], [11, [[4, 1], [3, 1], [2, 2], [1, 1]]], [13, [[6, 1], [4, 1], [2, 1]]], [17, [[6, 1], [4, 1], [2, 1]]], [19, [[2, 5], [1, 2]]], [23, [[4, 3]]], [29, [[3, 2], [2, 2], [1, 2]]], [31, [[4, 1], [3, 2], [2, 1]]], [37, [[6, 1], [2, 3]]], [41, [[6, 2]]], [43, [[8, 1], [4, 1]]], [47, [[8, 1], [4, 1]]], [53, [[6, 1], [4, 1], [2, 1]]], [59, [[6, 1], [3, 1], [2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [15552, 5184, 5184], 'galois_label': '12T274', 'galt': 274, 'grd': 510.7249749131131, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.417344000000.1', 'local_algs': ['2.12.12.24', '5.12.6.1', 'm6521.1.1.0', 'm6521.1.1.0', 'm6521.1.1.0', 'm6521.1.1.0', 'm6521.1.2.0', 'm6521.1.2.0', 'm6521.1.2.0', 'm6521.2.1.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 5, 6521], 'rd': 9.297678278879234, 'regulator': {'__RealLiteral__': 0, 'data': '6.215565115061368', 'prec': 57}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.0.-1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - \\frac{23}{19} a^{10} + \\frac{24}{19} a^{9} - \\frac{20}{19} a^{8} + \\frac{2}{19} a^{7} - \\frac{67}{19} a^{6} + \\frac{14}{19} a^{5} + \\frac{5}{19} a^{4} + \\frac{85}{19} a^{3} - \\frac{28}{19} a^{2} - \\frac{15}{19} a - \\frac{2}{19} \\)', '\\( -a \\)', '\\( -\\frac{10}{19} a^{11} - \\frac{1}{19} a^{10} - \\frac{7}{19} a^{9} + \\frac{4}{19} a^{8} - \\frac{4}{19} a^{7} + \\frac{44}{19} a^{6} + \\frac{36}{19} a^{5} + \\frac{18}{19} a^{4} - \\frac{42}{19} a^{3} - \\frac{18}{19} a^{2} - \\frac{1}{19} a + \\frac{17}{19} \\)', '\\( -\\frac{6}{19} a^{11} - \\frac{1}{19} a^{10} + \\frac{2}{19} a^{9} - \\frac{11}{19} a^{8} + \\frac{13}{19} a^{7} + \\frac{14}{19} a^{6} + \\frac{23}{19} a^{5} - \\frac{2}{19} a^{4} - \\frac{11}{19} a^{3} - \\frac{6}{19} a^{2} + \\frac{15}{19} a - \\frac{9}{19} \\)', '\\( -\\frac{2}{19} a^{11} - \\frac{10}{19} a^{10} + \\frac{8}{19} a^{9} - \\frac{14}{19} a^{8} + \\frac{6}{19} a^{7} + \\frac{9}{19} a^{6} + \\frac{32}{19} a^{5} + \\frac{13}{19} a^{4} + \\frac{7}{19} a^{3} - 2 a^{2} + \\frac{21}{19} a + \\frac{8}{19} \\)', '\\( -\\frac{13}{19} a^{11} + \\frac{1}{19} a^{10} - \\frac{2}{19} a^{9} - \\frac{8}{19} a^{8} + \\frac{6}{19} a^{7} + \\frac{43}{19} a^{6} + \\frac{34}{19} a^{5} + \\frac{2}{19} a^{4} - \\frac{46}{19} a^{3} + \\frac{6}{19} a^{2} + \\frac{42}{19} a + \\frac{9}{19} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/19*a^10 - 6/19*a^9 + 5/19*a^8 + 9/19*a^7 - 7/19*a^6 + 6/19*a^5 - 6/19*a^4 - 7/19*a^3 + 7/19*a^2 - 1/19*a - 9/19', '1/19*a^11 + 7/19*a^9 + 1/19*a^8 + 9/19*a^7 + 2/19*a^6 - 8/19*a^5 - 5/19*a^4 + 3/19*a^3 + 3/19*a^2 + 4/19*a + 3/19']}
  36. label: 12.2.419159399791.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, -2, 2, 1, -1, 1, -1, -2, 3, 0, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 419159399791, 'disc_rad': 341, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[4, 3]]], [5, [[3, 4]]], [7, [[6, 2]]], [11, [0]], [13, [[2, 5], [1, 2]]], [17, [[4, 3]]], [19, [[6, 2]]], [23, [[2, 5], [1, 2]]], [29, [[4, 3]]], [31, [0]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[4, 3]]], [47, [[2, 6]]], [53, [[4, 3]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 24], 'galois_label': '12T22', 'galt': 22, 'grd': 18.466185312619388, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.419159399791.1', 'local_algs': ['11.4.0.1', '11.8.4.1', '31.2.0.1', '31.2.1.1', '31.4.2.1', '31.4.2.1'], 'minimal_sibling': [1, -1, 0, 2, -1, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [11, 31], 'rd': 9.30104189993, 'regulator': {'__RealLiteral__': 0, 'data': '6.24841548478', 'prec': 44}, 'res': {'sib': ['-13,-51,-8,23,-22,4,3,-2,1', '-13,97,-317,679,-972,855,-438,114,0,-30,17,-6,1', '-3,-4,-2,-6,2,-1,1', '1,-1,-1,1,1,1,-1,-1,1', '1,-1,0,2,-1,-1,1', '1,-3,4,-6,10,-11,11,-11,10,-6,4,-3,1', '1,2,7,11,10,-22,-16,21,20,-5,-7,0,1', '196,-574,587,-294,239,-268,226,-264,229,-97,57,-59,24,-2,4,-4,1', '279,155,195,54,-29,45,-17,26,13,1,7,-1,1', '4489,-938,-331,1636,-80,-404,-52,103,38,-19,-5,-1,1']}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.0.1', '-1.2.-7.6.0.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{8}{13} a^{11} - \\frac{22}{13} a^{10} + \\frac{10}{13} a^{9} + \\frac{23}{13} a^{8} - \\frac{30}{13} a^{7} + \\frac{8}{13} a^{6} + \\frac{2}{13} a^{5} - \\frac{16}{13} a^{4} + \\frac{20}{13} a^{3} + \\frac{14}{13} a^{2} - \\frac{20}{13} a + \\frac{2}{13} \\)', '\\( a \\)', '\\( \\frac{3}{13} a^{11} - \\frac{5}{13} a^{10} + \\frac{7}{13} a^{9} - \\frac{6}{13} a^{8} - \\frac{8}{13} a^{7} + \\frac{16}{13} a^{6} - \\frac{9}{13} a^{5} - \\frac{6}{13} a^{4} + \\frac{1}{13} a^{3} - \\frac{11}{13} a^{2} + \\frac{12}{13} a + \\frac{17}{13} \\)', '\\( \\frac{6}{13} a^{11} - \\frac{23}{13} a^{10} + \\frac{14}{13} a^{9} + \\frac{27}{13} a^{8} - \\frac{29}{13} a^{7} - \\frac{7}{13} a^{6} + \\frac{8}{13} a^{5} + \\frac{1}{13} a^{4} + \\frac{15}{13} a^{3} + \\frac{4}{13} a^{2} - \\frac{28}{13} a - \\frac{5}{13} \\)', '\\( a^{10} - a^{9} - a^{8} + 2 a^{7} - a^{5} - a^{3} + 2 a \\)', '\\( \\frac{4}{13} a^{11} - \\frac{11}{13} a^{10} + \\frac{5}{13} a^{9} + \\frac{18}{13} a^{8} - \\frac{15}{13} a^{7} - \\frac{9}{13} a^{6} + \\frac{14}{13} a^{5} - \\frac{8}{13} a^{4} + \\frac{10}{13} a^{3} + \\frac{7}{13} a^{2} - \\frac{23}{13} a + \\frac{1}{13} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/13*a^11 - 6/13*a^10 - 2/13*a^9 - 2/13*a^8 + 6/13*a^7 + 1/13*a^6 - 3/13*a^5 - 2/13*a^4 - 4/13*a^3 + 5/13*a^2 + 4/13*a - 3/13']}
  37. label: 12.2.438976000000.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 2, 0, -3, 6, -9, 6, -3, 0, 2, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 438976000000, 'disc_rad': 190, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [0]], [7, [[4, 2], [2, 2]]], [11, [[6, 1], [2, 3]]], [13, [[4, 3]]], [17, [[6, 2]]], [19, [0]], [23, [[4, 2], [2, 2]]], [29, [[6, 1], [2, 2], [1, 2]]], [31, [[6, 1], [3, 2]]], [37, [[4, 3]]], [41, [[2, 5], [1, 2]]], [43, [[4, 2], [2, 2]]], [47, [[4, 2], [2, 2]]], [53, [[4, 3]]], [59, [[2, 5], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [576, 144, 144], 'galois_label': '12T125', 'galt': 125, 'grd': 38.98717737923585, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.438976000000.1', 'local_algs': ['2.4.0.1', '2.8.12.3', '5.6.3.1', '5.6.3.1', '19.2.1.2', '19.3.0.1', '19.3.0.1', '19.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 5, 19], 'rd': 9.33691484757, 'regulator': {'__RealLiteral__': 0, 'data': '6.34204903952', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '-1.-1.2.-2.1', '-1.1.4.-5.2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - a^{10} + 2 a^{9} - 3 a^{7} + 6 a^{6} - 9 a^{5} + 6 a^{4} - 3 a^{3} + 2 a - 1 \\)', '\\( \\frac{1}{2} a^{11} - \\frac{3}{2} a^{10} + a^{9} - a^{8} - 3 a^{7} + 6 a^{6} - 7 a^{5} + 6 a^{4} - 2 a^{2} + \\frac{3}{2} a - \\frac{3}{2} \\)', '\\( \\frac{1}{2} a^{11} - a^{10} + \\frac{3}{2} a^{9} - \\frac{1}{2} a^{8} - \\frac{3}{2} a^{7} + \\frac{11}{2} a^{6} - \\frac{13}{2} a^{5} + \\frac{13}{2} a^{4} - \\frac{5}{2} a^{3} - \\frac{3}{2} a^{2} + a - \\frac{3}{2} \\)', '\\( \\frac{1}{2} a^{11} - a^{10} + \\frac{1}{2} a^{9} - \\frac{1}{2} a^{8} - \\frac{5}{2} a^{7} + \\frac{7}{2} a^{6} - \\frac{9}{2} a^{5} + \\frac{7}{2} a^{4} - \\frac{1}{2} a^{3} + \\frac{1}{2} a^{2} - \\frac{1}{2} \\)', '\\( a^{11} - \\frac{1}{2} a^{10} + a^{9} + a^{8} - 3 a^{7} + 4 a^{6} - 4 a^{5} + a^{4} + a^{3} + \\frac{1}{2} \\)', '\\( \\frac{1}{2} a^{11} - a^{10} + a^{9} - \\frac{1}{2} a^{8} - 2 a^{7} + \\frac{9}{2} a^{6} - 5 a^{5} + \\frac{11}{2} a^{4} - a^{3} + \\frac{1}{2} a^{2} + \\frac{1}{2} a - \\frac{3}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8 - 1/2*a^6 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/2*a^9 - 1/2*a^7 - 1/2*a^5 - 1/2*a^3 - 1/2*a', '1/2*a^10 - 1/2', '1/2*a^11 - 1/2*a']}
  38. label: 12.2.447330484375.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 4, -9, 9, 2, -4, -2, -3, 8, -3, 1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 447330484375, 'disc_rad': 155, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[4, 3]]], [5, [0]], [7, [[6, 2]]], [11, [[2, 5], [1, 2]]], [13, [[4, 3]]], [17, [[4, 3]]], [19, [[6, 2]]], [23, [[4, 3]]], [29, [[2, 5], [1, 2]]], [31, [0]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[4, 3]]], [47, [[2, 6]]], [53, [[4, 3]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12], 'galois_label': '12T13', 'galt': 13, 'grd': 12.449899597988733, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.447330484375.1', 'local_algs': ['5.12.6.1', '31.2.0.1', '31.2.1.1', '31.4.2.1', '31.4.2.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [5, 31], 'rd': 9.35159538434, 'regulator': {'__RealLiteral__': 0, 'data': '6.55949888698', 'prec': 44}, 'res': {'gal': ['1,1,5,-20,-2,10,-39,16,126,7,106,166,81,93,100,22,86,13,10,21,2,3,3,-1,1'], 'sib': ['1,-6,15,-19,13,-4,3,-4,1,2,0,-2,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '-1.1.0.1', '-1.-3.0.-1.1', '-1.-1.1.-4.3.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{356}{349} a^{11} - \\frac{658}{349} a^{10} + \\frac{166}{349} a^{9} - \\frac{984}{349} a^{8} + \\frac{2636}{349} a^{7} - \\frac{327}{349} a^{6} - \\frac{991}{349} a^{5} - \\frac{1690}{349} a^{4} + \\frac{189}{349} a^{3} + \\frac{3266}{349} a^{2} - \\frac{2489}{349} a + \\frac{770}{349} \\)', '\\( a \\)', '\\( \\frac{176}{349} a^{11} - \\frac{141}{349} a^{10} - \\frac{114}{349} a^{9} - \\frac{510}{349} a^{8} + \\frac{864}{349} a^{7} + \\frac{603}{349} a^{6} + \\frac{12}{349} a^{5} - \\frac{1110}{349} a^{4} - \\frac{483}{349} a^{3} + \\frac{999}{349} a^{2} + \\frac{40}{349} a + \\frac{165}{349} \\)', '\\( \\frac{182}{349} a^{11} - \\frac{356}{349} a^{10} + \\frac{128}{349} a^{9} - \\frac{456}{349} a^{8} + \\frac{1528}{349} a^{7} - \\frac{475}{349} a^{6} - \\frac{638}{349} a^{5} - \\frac{1013}{349} a^{4} + \\frac{726}{349} a^{3} + \\frac{1854}{349} a^{2} - \\frac{1545}{349} a + \\frac{476}{349} \\)', '\\( \\frac{203}{349} a^{11} - \\frac{236}{349} a^{10} - \\frac{72}{349} a^{9} - \\frac{616}{349} a^{8} + \\frac{1060}{349} a^{7} + \\frac{638}{349} a^{6} - \\frac{121}{349} a^{5} - \\frac{1197}{349} a^{4} - \\frac{801}{349} a^{3} + \\frac{1182}{349} a^{2} + \\frac{62}{349} a - \\frac{6}{349} \\)', '\\( \\frac{583}{349} a^{11} - \\frac{707}{349} a^{10} + \\frac{15}{349} a^{9} - \\frac{1733}{349} a^{8} + \\frac{3211}{349} a^{7} + \\frac{885}{349} a^{6} - \\frac{571}{349} a^{5} - \\frac{2499}{349} a^{4} - \\frac{1011}{349} a^{3} + \\frac{4378}{349} a^{2} - \\frac{2136}{349} a + \\frac{612}{349} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/349*a^11 - 94/349*a^10 - 76/349*a^9 + 9/349*a^8 - 122/349*a^7 + 53/349*a^6 + 8/349*a^5 - 42/349*a^4 + 27/349*a^3 - 32/349*a^2 + 143/349*a + 110/349']}
  39. label: 12.2.451992187175.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 4, 1, -1, 12, -9, 12, -1, 1, 4, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 451992187175, 'disc_rad': 6095, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [0]], [7, [[4, 3]]], [11, [[8, 1], [2, 2]]], [13, [[3, 4]]], [17, [[4, 1], [2, 4]]], [19, [[4, 2], [2, 1], [1, 2]]], [23, [0]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[8, 1], [2, 2]]], [41, [[6, 2]]], [43, [[8, 1], [2, 2]]], [47, [[6, 2]]], [53, [0]], [59, [[4, 1], [2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [768, 1152, 768], 'galois_label': '12T223', 'galt': 223, 'grd': 170.96956786104076, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.451992187175.1', 'local_algs': ['5.4.2.2', '5.4.0.1', '5.4.0.1', '23.2.1.2', '23.2.1.2', '23.4.0.1', '23.4.3.1', '53.2.0.1', '53.2.0.1', '53.4.2.1', '53.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 23, 53], 'rd': 9.35967805722, 'regulator': {'__RealLiteral__': 0, 'data': '6.4136566416', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.-2.0.3.0.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a^{11} - \\frac{12}{5} a^{10} + \\frac{36}{5} a^{9} + \\frac{7}{5} a^{8} - \\frac{32}{5} a^{7} + \\frac{109}{5} a^{6} - 20 a^{5} + \\frac{74}{5} a^{4} - \\frac{2}{5} a^{3} - \\frac{18}{5} a^{2} + \\frac{21}{5} a - \\frac{12}{5} \\)', '\\( a \\)', '\\( 2 a^{11} - \\frac{4}{5} a^{10} + \\frac{32}{5} a^{9} + \\frac{34}{5} a^{8} - \\frac{9}{5} a^{7} + \\frac{103}{5} a^{6} - 3 a^{5} + \\frac{48}{5} a^{4} + \\frac{51}{5} a^{3} + \\frac{9}{5} a^{2} + \\frac{22}{5} a + \\frac{11}{5} \\)', '\\( \\frac{1}{5} a^{11} + \\frac{4}{5} a^{10} - \\frac{2}{5} a^{9} + \\frac{19}{5} a^{8} + a^{7} - \\frac{4}{5} a^{6} + \\frac{53}{5} a^{5} - \\frac{28}{5} a^{4} + \\frac{36}{5} a^{3} + 4 a^{2} - a + \\frac{17}{5} \\)', '\\( \\frac{6}{5} a^{11} - \\frac{3}{5} a^{10} + \\frac{19}{5} a^{9} + \\frac{16}{5} a^{8} - \\frac{7}{5} a^{7} + 11 a^{6} - \\frac{22}{5} a^{5} + \\frac{36}{5} a^{4} + \\frac{14}{5} a^{3} + \\frac{7}{5} a^{2} + \\frac{16}{5} a \\)', '\\( a^{11} - \\frac{13}{5} a^{10} + \\frac{24}{5} a^{9} - \\frac{22}{5} a^{8} - \\frac{28}{5} a^{7} + \\frac{66}{5} a^{6} - 26 a^{5} + \\frac{86}{5} a^{4} - \\frac{58}{5} a^{3} - \\frac{27}{5} a^{2} + \\frac{19}{5} a - \\frac{28}{5} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/5*a^10 + 2/5*a^9 - 1/5*a^8 + 1/5*a^7 - 2/5*a^6 - 2/5*a^4 + 1/5*a^3 - 1/5*a^2 + 2/5*a + 1/5', '1/5*a^11 - 2/5*a^8 + 1/5*a^7 - 1/5*a^6 - 2/5*a^5 + 2/5*a^3 - 1/5*a^2 + 2/5*a - 2/5']}
  40. label: 12.2.458342033107.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, -2, -1, 8, -10, 4, 3, -6, 3, 2, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 458342033107, 'disc_rad': 301, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[12, 1]]], [7, [0]], [11, [[6, 2]]], [13, [[4, 1], [2, 3], [1, 2]]], [17, [[3, 4]]], [19, [[12, 1]]], [23, [[3, 4]]], [29, [[2, 5], [1, 2]]], [31, [[6, 2]]], [37, [[12, 1]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [0]], [47, [[6, 2]]], [53, [[3, 4]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [128, 96], 'galois_label': '12T104', 'galt': 104, 'grd': 23.99567223510292, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.458342033107.1', 'local_algs': ['7.12.8.1', '43.2.0.1', '43.2.1.2', '43.2.0.1', '43.2.0.1', '43.2.1.1', '43.2.1.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [7, 43], 'rd': 9.37056564065, 'regulator': {'__RealLiteral__': 0, 'data': '6.54549766683', 'prec': 44}, 'res': {'ae': ['1,-4,6,-4,1,-3,5,-3,1,-4,6,-4,1'], 'sib': ['-1,6,47,-3,11,12,-51,-11,7,20,-6,-3,1', '-1,9,-7,-108,208,2,-140,136,-67,8,6,-4,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.3.2.-2.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{49}{97} a^{11} - \\frac{182}{97} a^{10} + \\frac{131}{97} a^{9} + \\frac{192}{97} a^{8} - \\frac{348}{97} a^{7} + \\frac{160}{97} a^{6} + \\frac{248}{97} a^{5} - \\frac{584}{97} a^{4} + \\frac{435}{97} a^{3} - \\frac{41}{97} a^{2} - \\frac{41}{97} a + \\frac{9}{97} \\)', '\\( \\frac{49}{97} a^{11} - \\frac{182}{97} a^{10} + \\frac{131}{97} a^{9} + \\frac{192}{97} a^{8} - \\frac{348}{97} a^{7} + \\frac{160}{97} a^{6} + \\frac{248}{97} a^{5} - \\frac{584}{97} a^{4} + \\frac{435}{97} a^{3} + \\frac{56}{97} a^{2} - \\frac{138}{97} a + \\frac{9}{97} \\)', '\\( \\frac{37}{97} a^{11} - \\frac{82}{97} a^{10} - \\frac{6}{97} a^{9} + \\frac{143}{97} a^{8} - \\frac{144}{97} a^{7} + \\frac{6}{97} a^{6} + \\frac{213}{97} a^{5} - \\frac{342}{97} a^{4} + \\frac{83}{97} a^{3} + \\frac{167}{97} a^{2} - \\frac{124}{97} a + \\frac{84}{97} \\)', '\\( a \\)', '\\( \\frac{49}{97} a^{11} - \\frac{182}{97} a^{10} + \\frac{131}{97} a^{9} + \\frac{192}{97} a^{8} - \\frac{348}{97} a^{7} + \\frac{160}{97} a^{6} + \\frac{248}{97} a^{5} - \\frac{584}{97} a^{4} + \\frac{435}{97} a^{3} + \\frac{56}{97} a^{2} - \\frac{41}{97} a + \\frac{9}{97} \\)', '\\( \\frac{57}{97} a^{11} - \\frac{87}{97} a^{10} - \\frac{101}{97} a^{9} + \\frac{257}{97} a^{8} - \\frac{96}{97} a^{7} - \\frac{190}{97} a^{6} + \\frac{336}{97} a^{5} - \\frac{228}{97} a^{4} - \\frac{171}{97} a^{3} + \\frac{370}{97} a^{2} - \\frac{115}{97} a - \\frac{41}{97} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/97*a^11 + 24/97*a^10 - 29/97*a^9 - 4/97*a^8 - 17/97*a^7 + 29/97*a^6 + 11/97*a^5 - 4/97*a^4 - 3/97*a^3 + 15/97*a^2 + 15/97*a + 18/97']}
  41. label: 12.2.458342033107.2
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 6, -4, 1, -3, 5, -3, 1, -4, 6, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 458342033107, 'disc_rad': 301, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[12, 1]]], [7, [0]], [11, [[6, 2]]], [13, [[4, 1], [2, 3], [1, 2]]], [17, [[3, 4]]], [19, [[12, 1]]], [23, [[3, 4]]], [29, [[2, 5], [1, 2]]], [31, [[6, 2]]], [37, [[12, 1]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [0]], [47, [[6, 2]]], [53, [[3, 4]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [128, 96], 'galois_label': '12T104', 'galt': 104, 'grd': 23.99567223510292, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '12.2.458342033107.2', 'local_algs': ['7.12.8.1', '43.1.0.1', '43.1.0.1', '43.2.0.1', '43.2.1.2', '43.2.0.1', '43.4.2.1'], 'minimal_sibling': [-1, 1, -2, -1, 8, -10, 4, 3, -6, 3, 2, -3, 1], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [7, 43], 'rd': 9.37056564065, 'regulator': {'__RealLiteral__': 0, 'data': '6.54549766683', 'prec': 44}, 'res': {'ae': ['-1,1,-2,-1,8,-10,4,3,-6,3,2,-3,1'], 'sib': ['-1,6,47,-3,11,12,-51,-11,7,20,-6,-3,1', '-1,9,-7,-108,208,2,-140,136,-67,8,6,-4,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.3.2.-2.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( 4 a^{11} - 12 a^{10} + 10 a^{9} - a^{8} + a^{7} - 13 a^{6} + 7 a^{5} + a^{4} + 4 a^{3} - 13 a^{2} + 8 a - 2 \\)', '\\( a^{11} - 4 a^{10} + 5 a^{9} - a^{8} - a^{7} - 4 a^{6} + 5 a^{5} + a^{4} - 6 a^{2} + 5 a \\)', '\\( a^{11} - 5 a^{10} + 9 a^{9} - 6 a^{8} - 3 a^{6} + 9 a^{5} - 4 a^{4} - a^{3} - 6 a^{2} + 10 a - 5 \\)', '\\( a - 1 \\)', '\\( a^{11} - 4 a^{10} + 5 a^{9} - a^{8} - a^{7} - 4 a^{6} + 5 a^{5} + a^{4} - 6 a^{2} + 4 a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  42. label: 12.2.530569362483.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, 5, -11, 10, -6, 4, -7, 6, -3, 1, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 530569362483, 'disc_rad': 14433, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [0]], [5, [[4, 3]]], [7, [[9, 1], [3, 1]]], [11, [[6, 1], [3, 1], [2, 1], [1, 1]]], [13, [[3, 4]]], [17, [0]], [19, [[12, 1]]], [23, [[6, 1], [3, 1], [2, 1], [1, 1]]], [29, [[6, 1], [3, 1], [2, 1], [1, 1]]], [31, [[12, 1]]], [37, [[6, 1], [3, 2]]], [41, [[6, 1], [3, 1], [2, 1], [1, 1]]], [43, [[12, 1]]], [47, [[4, 3]]], [53, [[2, 5], [1, 2]]], [59, [[6, 1], [3, 1], [2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1944, 2592, 1944], 'galois_label': '12T258', 'galt': 258, 'grd': 192.64295262991146, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.530569362483.1', 'local_algs': ['3.4.0.1', '3.8.4.1', '17.1.0.1', '17.2.0.1', '17.3.2.1', '17.6.0.1', 'm283.1.1.0', 'm283.1.1.0', 'm283.1.1.0', 'm283.1.3.0', 'm283.2.3.3'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [3, 17, 283], 'rd': 9.48553536042, 'regulator': {'__RealLiteral__': 0, 'data': '7.20273603042', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{134}{85} a^{11} - \\frac{9}{17} a^{10} + \\frac{21}{17} a^{9} - 4 a^{8} + \\frac{583}{85} a^{7} - \\frac{557}{85} a^{6} + \\frac{222}{85} a^{5} - \\frac{704}{85} a^{4} + \\frac{179}{17} a^{3} - \\frac{56}{5} a^{2} + \\frac{177}{85} a + \\frac{171}{85} \\)', '\\( \\frac{1}{85} a^{11} + \\frac{31}{85} a^{10} + \\frac{7}{85} a^{9} + \\frac{2}{5} a^{8} - \\frac{9}{17} a^{7} + \\frac{20}{17} a^{6} - \\frac{94}{85} a^{5} - \\frac{22}{85} a^{4} - \\frac{133}{85} a^{3} + \\frac{8}{5} a^{2} - \\frac{182}{85} a - \\frac{43}{85} \\)', '\\( \\frac{101}{85} a^{11} - \\frac{48}{85} a^{10} + \\frac{44}{85} a^{9} - \\frac{16}{5} a^{8} + \\frac{453}{85} a^{7} - \\frac{372}{85} a^{6} + \\frac{94}{85} a^{5} - \\frac{488}{85} a^{4} + \\frac{694}{85} a^{3} - 7 a^{2} - \\frac{22}{85} a + \\frac{46}{17} \\)', '\\( \\frac{91}{85} a^{11} - \\frac{52}{85} a^{10} + \\frac{76}{85} a^{9} - \\frac{14}{5} a^{8} + \\frac{461}{85} a^{7} - \\frac{454}{85} a^{6} + \\frac{167}{85} a^{5} - \\frac{489}{85} a^{4} + \\frac{681}{85} a^{3} - \\frac{43}{5} a^{2} + \\frac{98}{85} a + \\frac{133}{85} \\)', '\\( \\frac{59}{85} a^{11} - \\frac{58}{85} a^{10} + \\frac{39}{85} a^{9} - \\frac{11}{5} a^{8} + \\frac{354}{85} a^{7} - \\frac{356}{85} a^{6} + \\frac{183}{85} a^{5} - \\frac{346}{85} a^{4} + \\frac{619}{85} a^{3} - \\frac{32}{5} a^{2} + \\frac{142}{85} a + \\frac{47}{85} \\)', '\\( \\frac{133}{85} a^{11} - \\frac{42}{85} a^{10} + \\frac{81}{85} a^{9} - \\frac{19}{5} a^{8} + \\frac{112}{17} a^{7} - \\frac{94}{17} a^{6} + \\frac{78}{85} a^{5} - \\frac{631}{85} a^{4} + \\frac{841}{85} a^{3} - \\frac{41}{5} a^{2} - \\frac{66}{85} a + \\frac{231}{85} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/5*a^10 + 2/5*a^9 - 1/5*a^8 - 2/5*a^7 - 2/5*a^6 - 2/5*a^5 - 1/5*a^4 + 2/5*a^3 - 1/5*a^2 - 2/5', '1/85*a^11 - 3/85*a^10 + 24/85*a^9 - 1/5*a^8 + 23/85*a^7 - 2/85*a^6 - 26/85*a^5 + 12/85*a^4 - 31/85*a^3 - 12/85*a + 5/17']}
  43. label: 12.2.533806460928.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, 0, -2, 8, -17, 27, -32, 31, -23, 13, -5, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 533806460928, 'disc_rad': 78, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[12, 1]]], [7, [[6, 2]]], [11, [[4, 3]]], [13, [0]], [17, [[6, 1], [3, 2]]], [19, [[2, 6]]], [23, [[2, 5], [1, 2]]], [29, [[2, 5], [1, 2]]], [31, [[2, 6]]], [37, [[6, 2]]], [41, [[4, 3]]], [43, [[3, 4]]], [47, [[12, 1]]], [53, [[2, 5], [1, 2]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 24, 24], 'galois_label': '12T28', 'galt': 28, 'grd': 17.663521732655695, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.533806460928.1', 'local_algs': ['2.4.0.1', '2.8.12.2', '3.6.0.1', '3.6.3.1', '13.4.2.1', '13.4.2.1', '13.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 13], 'rd': 9.49034467201, 'regulator': {'__RealLiteral__': 0, 'data': '7.11195238102', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-3.-1.1', '-2.-1.0.1', '1.-1.-1.-1.1', '-1.-1.-2.1.2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{13}{23} a^{11} - \\frac{62}{23} a^{10} + \\frac{160}{23} a^{9} - \\frac{278}{23} a^{8} + \\frac{376}{23} a^{7} - \\frac{400}{23} a^{6} + \\frac{356}{23} a^{5} - \\frac{222}{23} a^{4} + \\frac{120}{23} a^{3} - \\frac{16}{23} a^{2} + \\frac{14}{23} a + \\frac{18}{23} \\)', '\\( a \\)', '\\( \\frac{4}{23} a^{11} - \\frac{12}{23} a^{10} + \\frac{28}{23} a^{9} - \\frac{59}{23} a^{8} + \\frac{98}{23} a^{7} - \\frac{116}{23} a^{6} + \\frac{129}{23} a^{5} - \\frac{86}{23} a^{4} + \\frac{44}{23} a^{3} + \\frac{11}{23} a^{2} - \\frac{24}{23} a + \\frac{25}{23} \\)', '\\( \\frac{1}{23} a^{11} - \\frac{3}{23} a^{10} + \\frac{7}{23} a^{9} - \\frac{9}{23} a^{8} + \\frac{13}{23} a^{7} - \\frac{29}{23} a^{6} + \\frac{61}{23} a^{5} - \\frac{79}{23} a^{4} + \\frac{80}{23} a^{3} - \\frac{26}{23} a^{2} + \\frac{17}{23} a + \\frac{12}{23} \\)', '\\( \\frac{9}{23} a^{11} - \\frac{27}{23} a^{10} + \\frac{40}{23} a^{9} - \\frac{35}{23} a^{8} + \\frac{25}{23} a^{7} - \\frac{8}{23} a^{6} + \\frac{20}{23} a^{5} + \\frac{2}{23} a^{4} + \\frac{7}{23} a^{3} + \\frac{19}{23} a^{2} - \\frac{8}{23} a + \\frac{16}{23} \\)', '\\( \\frac{2}{23} a^{11} - \\frac{6}{23} a^{10} + \\frac{14}{23} a^{9} - \\frac{18}{23} a^{8} + \\frac{3}{23} a^{7} + \\frac{34}{23} a^{6} - \\frac{62}{23} a^{5} + \\frac{95}{23} a^{4} - \\frac{70}{23} a^{3} + \\frac{63}{23} a^{2} - \\frac{12}{23} a + \\frac{1}{23} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/23*a^11 - 3/23*a^10 + 7/23*a^9 - 9/23*a^8 - 10/23*a^7 - 6/23*a^6 - 8/23*a^5 - 10/23*a^4 + 11/23*a^3 - 3/23*a^2 - 6/23*a - 11/23']}
  44. label: 12.2.562523516779.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -2, 6, -5, -3, 11, -6, -5, 7, -1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 562523516779, 'disc_rad': 683053, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[9, 1], [3, 1]]], [7, [0]], [11, [[6, 1], [3, 2]]], [13, [[4, 2], [3, 1], [1, 1]]], [17, [[3, 4]]], [19, [[6, 2]]], [23, [[12, 1]]], [29, [[4, 2], [3, 1], [1, 1]]], [31, [[9, 1], [3, 1]]], [37, [[3, 4]]], [41, [[3, 3], [1, 3]]], [43, [[4, 1], [3, 1], [2, 1], [1, 3]]], [47, [[6, 1], [3, 2]]], [53, [[9, 1], [3, 1]]], [59, [[9, 1], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [27648, 20736], 'galois_label': '12T292', 'galt': 292, 'grd': 1143.0806547161178, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.562523516779.1', 'local_algs': ['7.3.2.2', '7.9.6.1', 'm97579.1.1.0', 'm97579.1.1.0', 'm97579.1.1.0', 'm97579.1.1.0', 'm97579.1.2.0', 'm97579.2.1.1', 'm97579.1.4.0'], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [7, 97579], 'rd': 9.53187613796, 'regulator': {'__RealLiteral__': 0, 'data': '7.7037339724', 'prec': 40}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{10} - a^{9} - 2 a^{8} + 4 a^{7} + a^{6} - 5 a^{5} + 2 a^{4} + 2 a^{3} - a^{2} + a \\)', '\\( a^{11} - a^{10} - 2 a^{9} + 4 a^{8} + a^{7} - 5 a^{6} + a^{5} + 3 a^{4} - a^{3} + a - 1 \\)', '\\( a^{10} - a^{9} - 2 a^{8} + 5 a^{7} - 6 a^{5} + 5 a^{4} + 2 a^{3} - 3 a^{2} + 2 a + 1 \\)', '\\( a^{11} - 2 a^{10} - a^{9} + 7 a^{8} - 5 a^{7} - 6 a^{6} + 11 a^{5} - 2 a^{4} - 6 a^{3} + 5 a^{2} - 1 \\)', '\\( a^{11} - a^{10} - 3 a^{9} + 6 a^{8} + a^{7} - 9 a^{6} + 5 a^{5} + 3 a^{4} - 4 a^{3} + 3 a^{2} - a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  45. label: 12.2.566636000000.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, -1, 7, 1, -8, -5, 4, 7, -1, -4, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 566636000000, 'disc_rad': 4130, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [0]], [7, [0]], [11, [[6, 1], [3, 2]]], [13, [[12, 1]]], [17, [[6, 2]]], [19, [[4, 1], [2, 3], [1, 2]]], [23, [[4, 1], [2, 4]]], [29, [[6, 2]]], [31, [[4, 1], [2, 4]]], [37, [[4, 1], [2, 4]]], [41, [[4, 2], [1, 4]]], [43, [[4, 3]]], [47, [[12, 1]]], [53, [[4, 2], [2, 2]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [512, 384, 384, 384], 'galois_label': '12T193', 'galt': 193, 'grd': 72.13510890035327, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.566636000000.1', 'local_algs': ['2.12.8.1', '5.4.2.1', '5.8.4.1', '7.2.0.1', '7.2.0.1', '7.8.4.1', '59.2.1.1', '59.2.0.1', '59.4.0.1', '59.4.0.1'], 'minimal_sibling': [1, -5, 10, -10, 9, -16, 23, -16, 9, -10, 10, -5, 1], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [2, 5, 7, 59], 'rd': 9.53766388736, 'regulator': {'__RealLiteral__': 0, 'data': '7.30104222822', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '-2.2.0.1', '1.-1.-2.5.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 1 \\)', '\\( \\frac{4}{3} a^{11} + a^{10} - \\frac{16}{3} a^{9} - 5 a^{8} + 8 a^{7} + 11 a^{6} - 2 a^{5} - 13 a^{4} - 6 a^{3} + 8 a^{2} + \\frac{10}{3} a - \\frac{10}{3} \\)', '\\( \\frac{5}{3} a^{11} + a^{10} - 6 a^{9} - \\frac{17}{3} a^{8} + \\frac{25}{3} a^{7} + \\frac{37}{3} a^{6} - \\frac{2}{3} a^{5} - \\frac{44}{3} a^{4} - \\frac{23}{3} a^{3} + \\frac{22}{3} a^{2} + 4 a - \\frac{10}{3} \\)', '\\( a \\)', '\\( \\frac{2}{3} a^{11} - \\frac{1}{3} a^{10} - 3 a^{9} + 6 a^{7} + 3 a^{6} - 5 a^{5} - 8 a^{4} + a^{3} + 7 a^{2} + \\frac{2}{3} a - 2 \\)', '\\( \\frac{2}{3} a^{11} + a^{10} - \\frac{7}{3} a^{9} - \\frac{13}{3} a^{8} + \\frac{8}{3} a^{7} + \\frac{23}{3} a^{6} + \\frac{5}{3} a^{5} - \\frac{19}{3} a^{4} - \\frac{19}{3} a^{3} + \\frac{5}{3} a^{2} + \\frac{10}{3} a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/3*a^9 - 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 - 1/3*a^4 - 1/3*a^3 - 1/3*a^2 - 1/3*a - 1/3', '1/3*a^10 + 1/3*a^8 + 1/3*a^7 + 1/3*a^6 + 1/3*a^5 + 1/3*a^4 + 1/3*a^3 + 1/3*a^2 + 1/3*a - 1/3', '1/3*a^11 - 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 - 1/3*a^4 - 1/3*a^3 - 1/3*a^2 + 1/3']}
  46. label: 12.2.620200350784.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, -1, 0, 1, 0, 5, 0, 5, 0, 3, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 620200350784, 'disc_rad': 574, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [[6, 2]]], [7, [0]], [11, [[12, 1]]], [13, [[4, 1], [2, 3], [1, 2]]], [17, [[6, 2]]], [19, [[12, 1]]], [23, [[6, 1], [3, 2]]], [29, [[4, 2], [2, 2]]], [31, [[6, 1], [3, 2]]], [37, [[6, 2]]], [41, [0]], [43, [[4, 1], [2, 4]]], [47, [[12, 1]]], [53, [[6, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2688, 1024, 768], 'galois_label': '12T222', 'galt': 222, 'grd': 78.8121389064205, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.620200350784.1', 'local_algs': ['2.6.6.6', '2.6.0.1', '7.12.8.1', '41.1.0.1', '41.1.0.1', '41.2.0.1', '41.2.1.2', '41.2.1.2', '41.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 7, 41], 'rd': 9.609725905426268, 'regulator': {'__RealLiteral__': 0, 'data': '8.168059297232562', 'prec': 57}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.1.1.-5.5.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( -a^{10} + \\frac{1}{2} a^{9} - \\frac{5}{2} a^{8} + a^{7} - \\frac{7}{2} a^{6} + \\frac{3}{2} a^{5} - \\frac{5}{2} a^{4} + \\frac{3}{2} a^{3} + a^{2} + \\frac{1}{2} \\)', '\\( -\\frac{1}{2} a^{10} - \\frac{3}{2} a^{8} + \\frac{1}{2} a^{7} - 2 a^{6} + a^{5} - 2 a^{4} + \\frac{3}{2} a^{3} + \\frac{1}{2} a + \\frac{1}{2} \\)', '\\( a^{10} + 2 a^{8} + 3 a^{6} + 2 a^{4} - a^{2} \\)', '\\( -\\frac{1}{2} a^{11} - \\frac{3}{2} a^{9} + \\frac{1}{2} a^{8} - 2 a^{7} + a^{6} - 2 a^{5} + \\frac{3}{2} a^{4} + \\frac{3}{2} a^{2} + \\frac{1}{2} a \\)', '\\( \\frac{1}{2} a^{11} - \\frac{1}{2} a^{10} + 2 a^{9} - \\frac{3}{2} a^{8} + \\frac{7}{2} a^{7} - \\frac{5}{2} a^{6} + \\frac{7}{2} a^{5} - 2 a^{4} + a^{3} - \\frac{1}{2} a^{2} - a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^8 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2', '1/2*a^10 - 1/2*a^8 - 1/2*a^7 - 1/2*a^3 - 1/2*a - 1/2', '1/2*a^11 - 1/2*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2']}
  47. label: 12.2.644204000000.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 4, -2, -3, -7, 8, -1, 4, -3, -1, 3, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 644204000000, 'disc_rad': 110, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [0]], [7, [[4, 3]]], [11, [0]], [13, [[4, 3]]], [17, [[4, 3]]], [19, [[2, 5], [1, 2]]], [23, [[6, 2]]], [29, [[2, 5], [1, 2]]], [31, [[6, 2]]], [37, [[6, 2]]], [41, [[2, 5], [1, 2]]], [43, [[4, 3]]], [47, [[2, 6]]], [53, [[2, 6]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 12, 12], 'galois_label': '12T13', 'galt': 13, 'grd': 11.772481280020624, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.644204000000.1', 'local_algs': ['2.12.8.1', '5.12.6.1', '11.2.0.1', '11.2.1.1', '11.4.2.1', '11.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 5, 11], 'rd': 9.64018314536, 'regulator': {'__RealLiteral__': 0, 'data': '8.09867909721', 'prec': 44}, 'res': {'gal': ['1,-2,8,-20,29,-28,31,15,10,26,76,-50,100,20,-26,43,25,-30,34,1,-1,5,2,-1,1'], 'sib': ['1,-4,12,-23,37,-48,53,-50,39,-25,13,-5,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '1.1.-1.1', '-1.2.0.-1.1', '-1.1.4.5.2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{436}{199} a^{11} - \\frac{1208}{199} a^{10} + \\frac{936}{199} a^{9} - \\frac{99}{199} a^{8} - \\frac{1380}{199} a^{7} + \\frac{1464}{199} a^{6} + \\frac{86}{199} a^{5} + \\frac{3641}{199} a^{4} - \\frac{1996}{199} a^{3} - \\frac{2434}{199} a^{2} - \\frac{1810}{199} a + \\frac{1296}{199} \\)', '\\( \\frac{827}{199} a^{11} - \\frac{2169}{199} a^{10} + \\frac{1591}{199} a^{9} - \\frac{86}{199} a^{8} - \\frac{2634}{199} a^{7} + \\frac{2315}{199} a^{6} + \\frac{332}{199} a^{5} + \\frac{6568}{199} a^{4} - \\frac{3147}{199} a^{3} - \\frac{4028}{199} a^{2} - \\frac{3100}{199} a + \\frac{2157}{199} \\)', '\\( \\frac{312}{199} a^{11} - \\frac{890}{199} a^{10} + \\frac{741}{199} a^{9} - \\frac{153}{199} a^{8} - \\frac{993}{199} a^{7} + \\frac{1159}{199} a^{6} - \\frac{48}{199} a^{5} + \\frac{2642}{199} a^{4} - \\frac{1547}{199} a^{3} - \\frac{1446}{199} a^{2} - \\frac{1151}{199} a + \\frac{827}{199} \\)', '\\( \\frac{420}{199} a^{11} - \\frac{1045}{199} a^{10} + \\frac{699}{199} a^{9} + \\frac{16}{199} a^{8} - \\frac{1375}{199} a^{7} + \\frac{1078}{199} a^{6} + \\frac{165}{199} a^{5} + \\frac{3281}{199} a^{4} - \\frac{988}{199} a^{3} - \\frac{2069}{199} a^{2} - \\frac{1603}{199} a + \\frac{876}{199} \\)', '\\( \\frac{97}{199} a^{11} - \\frac{329}{199} a^{10} + \\frac{305}{199} a^{9} - \\frac{38}{199} a^{8} - \\frac{391}{199} a^{7} + \\frac{574}{199} a^{6} + \\frac{31}{199} a^{5} + \\frac{690}{199} a^{4} - \\frac{738}{199} a^{3} - \\frac{683}{199} a^{2} - \\frac{347}{199} a + \\frac{407}{199} \\)', '\\( \\frac{730}{199} a^{11} - \\frac{1840}{199} a^{10} + \\frac{1286}{199} a^{9} - \\frac{48}{199} a^{8} - \\frac{2243}{199} a^{7} + \\frac{1741}{199} a^{6} + \\frac{301}{199} a^{5} + \\frac{5878}{199} a^{4} - \\frac{2409}{199} a^{3} - \\frac{3345}{199} a^{2} - \\frac{2952}{199} a + \\frac{1750}{199} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/199*a^11 + 52/199*a^10 + 77/199*a^9 + 55/199*a^8 + 37/199*a^7 + 49/199*a^6 - 92/199*a^5 - 77/199*a^4 - 63/199*a^3 - 85/199*a^2 + 99/199*a + 76/199']}
  48. label: 12.2.644204000000.2
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 2, 4, -7, 2, 3, 2, -7, 4, 2, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 644204000000, 'disc_rad': 110, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [0]], [7, [[12, 1]]], [11, [0]], [13, [[12, 1]]], [17, [[12, 1]]], [19, [[2, 5], [1, 2]]], [23, [[2, 6]]], [29, [[6, 1], [3, 2]]], [31, [[2, 6]]], [37, [[6, 2]]], [41, [[3, 2], [2, 3]]], [43, [[12, 1]]], [47, [[6, 2]]], [53, [[6, 2]]], [59, [[2, 4], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [144, 72, 120], 'galois_label': '12T81', 'galt': 81, 'grd': 32.98695556602207, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '12.2.644204000000.2', 'local_algs': ['2.4.0.1', '2.8.8.1', '5.12.6.1', '11.2.0.1', '11.2.0.1', '11.2.0.1', '11.6.5.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 5, 11], 'rd': 9.64018314536, 'regulator': {'__RealLiteral__': 0, 'data': '8.15346214121', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '-1.2.0.-1.1', '1.-4.2.-4.2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - 3 a^{10} + 2 a^{9} + 4 a^{8} - 7 a^{7} + 2 a^{6} + 3 a^{5} + 2 a^{4} - 7 a^{3} + 4 a^{2} + 2 a - 3 \\)', '\\( \\frac{5}{2} a^{11} - 7 a^{10} + 3 a^{9} + 12 a^{8} - 15 a^{7} - a^{6} + 9 a^{5} + 9 a^{4} - 17 a^{3} + 3 a^{2} + \\frac{17}{2} a - 5 \\)', '\\( \\frac{3}{2} a^{11} - \\frac{7}{2} a^{10} + \\frac{1}{2} a^{9} + 7 a^{8} - \\frac{13}{2} a^{7} - 2 a^{6} + \\frac{9}{2} a^{5} + 6 a^{4} - \\frac{13}{2} a^{3} + 5 a - \\frac{3}{2} \\)', '\\( \\frac{1}{2} a^{11} - 2 a^{10} + 2 a^{9} + \\frac{5}{2} a^{8} - 6 a^{7} + \\frac{3}{2} a^{6} + 4 a^{5} + \\frac{1}{2} a^{4} - 7 a^{3} + \\frac{7}{2} a^{2} + \\frac{5}{2} a - \\frac{3}{2} \\)', '\\( \\frac{5}{2} a^{11} - \\frac{13}{2} a^{10} + \\frac{3}{2} a^{9} + \\frac{25}{2} a^{8} - \\frac{25}{2} a^{7} - \\frac{7}{2} a^{6} + \\frac{17}{2} a^{5} + \\frac{19}{2} a^{4} - \\frac{29}{2} a^{3} + \\frac{1}{2} a^{2} + 8 a - 4 \\)', '\\( \\frac{5}{2} a^{11} - \\frac{11}{2} a^{10} + 11 a^{8} - 8 a^{7} - 4 a^{6} + 5 a^{5} + 11 a^{4} - 10 a^{3} - a^{2} + \\frac{11}{2} a - \\frac{3}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8 - 1/2*a^6 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/2*a^9 - 1/2*a^7 - 1/2*a^5 - 1/2*a^3 - 1/2*a', '1/2*a^10 - 1/2', '1/2*a^11 - 1/2*a']}
  49. label: 12.2.659081523200.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 4, 0, 2, -1, 2, 11, -2, 6, -2, 5, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 659081523200, 'disc_rad': 230, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [0]], [7, [[4, 3]]], [11, [[4, 3]]], [13, [[6, 2]]], [17, [[4, 3]]], [19, [[4, 2], [2, 1], [1, 2]]], [23, [0]], [29, [[3, 4]]], [31, [[3, 4]]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[6, 2]]], [53, [[2, 5], [1, 2]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [288, 96, 96], 'galois_label': '12T100', 'galt': 100, 'grd': 30.331501776206203, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.659081523200.1', 'local_algs': ['2.12.12.11', '5.4.0.1', '5.4.0.1', '5.4.2.2', '23.1.0.1', '23.1.0.1', '23.2.1.2', '23.4.2.1', '23.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 5, 23], 'rd': 9.65854249046, 'regulator': {'__RealLiteral__': 0, 'data': '7.95702343355', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.0.0.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{70}{223} a^{11} - \\frac{198}{223} a^{10} + \\frac{393}{223} a^{9} - \\frac{249}{223} a^{8} + \\frac{295}{223} a^{7} - \\frac{257}{223} a^{6} + \\frac{658}{223} a^{5} + \\frac{130}{223} a^{4} - \\frac{337}{223} a^{3} + \\frac{158}{223} a^{2} - \\frac{201}{223} a + \\frac{300}{223} \\)', '\\( \\frac{17}{223} a^{11} + \\frac{22}{223} a^{10} - \\frac{118}{223} a^{9} + \\frac{325}{223} a^{8} - \\frac{231}{223} a^{7} + \\frac{202}{223} a^{6} - \\frac{197}{223} a^{5} + \\frac{605}{223} a^{4} - \\frac{136}{223} a^{3} - \\frac{191}{223} a^{2} + \\frac{171}{223} a - \\frac{182}{223} \\)', '\\( \\frac{74}{223} a^{11} - \\frac{101}{223} a^{10} + \\frac{339}{223} a^{9} - \\frac{2}{223} a^{8} + \\frac{503}{223} a^{7} + \\frac{66}{223} a^{6} + \\frac{874}{223} a^{5} + \\frac{456}{223} a^{4} - \\frac{146}{223} a^{3} - \\frac{5}{223} a^{2} + \\frac{36}{223} a + \\frac{349}{223} \\)', '\\( \\frac{90}{223} a^{11} - \\frac{159}{223} a^{10} + \\frac{346}{223} a^{9} - \\frac{129}{223} a^{8} + \\frac{443}{223} a^{7} - \\frac{426}{223} a^{6} + \\frac{623}{223} a^{5} - \\frac{24}{223} a^{4} - \\frac{274}{223} a^{3} - \\frac{434}{223} a^{2} - \\frac{131}{223} a + \\frac{322}{223} \\)', '\\( \\frac{71}{223} a^{11} - \\frac{118}{223} a^{10} + \\frac{268}{223} a^{9} - \\frac{20}{223} a^{8} + \\frac{347}{223} a^{7} - \\frac{9}{223} a^{6} + \\frac{489}{223} a^{5} + \\frac{546}{223} a^{4} + \\frac{101}{223} a^{3} + \\frac{173}{223} a^{2} - \\frac{309}{223} a + \\frac{145}{223} \\)', '\\( \\frac{44}{223} a^{11} - \\frac{48}{223} a^{10} + \\frac{75}{223} a^{9} + \\frac{41}{223} a^{8} + \\frac{58}{223} a^{7} - \\frac{15}{223} a^{6} - \\frac{77}{223} a^{5} + \\frac{241}{223} a^{4} + \\frac{94}{223} a^{3} + \\frac{437}{223} a^{2} + \\frac{154}{223} a + \\frac{93}{223} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/223*a^11 + 80/223*a^10 + 98/223*a^9 + 6/223*a^8 + 52/223*a^7 + 25/223*a^6 + 54/223*a^5 - 30/223*a^4 - 8/223*a^3 + 15/223*a^2 - 108/223*a + 68/223']}
  50. label: 12.2.713607421387.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 5, 9, 4, -9, -13, -1, 10, 6, -2, -4, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 713607421387, 'disc_rad': 866509, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 1], [3, 2]]], [5, [[6, 1], [3, 2]]], [7, [0]], [11, [[6, 1], [3, 2]]], [13, [[4, 2], [3, 1], [1, 1]]], [17, [[12, 1]]], [19, [[9, 1], [3, 1]]], [23, [[6, 1], [3, 2]]], [29, [[4, 1], [3, 2], [1, 2]]], [31, [[6, 1], [3, 2]]], [37, [[6, 1], [3, 2]]], [41, [[4, 2], [3, 1], [1, 1]]], [43, [[4, 2], [3, 1], [1, 1]]], [47, [[12, 1]]], [53, [[12, 1]]], [59, [[12, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [27648, 20736], 'galois_label': '12T292', 'galt': 292, 'grd': 1287.4673146347911, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.713607421387.1', 'local_algs': ['7.3.2.2', '7.9.6.1', 'm123787.1.1.0', 'm123787.1.1.0', 'm123787.1.1.0', 'm123787.1.1.0', 'm123787.1.1.0', 'm123787.1.1.0', 'm123787.1.1.0', 'm123787.2.1.1', 'm123787.1.3.0'], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [7, 123787], 'rd': 9.72273121475, 'regulator': {'__RealLiteral__': 0, 'data': '8.88769174833', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 7 a^{11} - 3 a^{10} - 27 a^{9} - 2 a^{8} + 44 a^{7} + 50 a^{6} - 31 a^{5} - 78 a^{4} - 26 a^{3} + 42 a^{2} + 44 a + 13 \\)', '\\( a \\)', '\\( 4 a^{11} - a^{10} - 16 a^{9} - 4 a^{8} + 26 a^{7} + 34 a^{6} - 14 a^{5} - 51 a^{4} - 23 a^{3} + 25 a^{2} + 31 a + 11 \\)', '\\( 6 a^{11} - 4 a^{10} - 22 a^{9} + 3 a^{8} + 36 a^{7} + 36 a^{6} - 32 a^{5} - 60 a^{4} - 13 a^{3} + 36 a^{2} + 31 a + 8 \\)', '\\( 2 a^{11} - 3 a^{10} - 6 a^{9} + 7 a^{8} + 10 a^{7} + 2 a^{6} - 18 a^{5} - 9 a^{4} + 9 a^{3} + 11 a^{2} + a - 2 \\)', '\\( 7 a^{11} - 2 a^{10} - 29 a^{9} - 4 a^{8} + 48 a^{7} + 53 a^{6} - 30 a^{5} - 87 a^{4} - 27 a^{3} + 45 a^{2} + 47 a + 13 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  51. label: 12.2.738751981811.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 3, -4, -1, 8, -8, -2, 9, -6, -1, 4, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 738751981811, 'disc_rad': 38789, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[9, 1], [3, 1]]], [5, [[6, 2]]], [7, [[12, 1]]], [11, [[9, 1], [3, 1]]], [13, [[6, 1], [3, 1], [2, 1], [1, 1]]], [17, [[9, 1], [1, 3]]], [19, [[12, 1]]], [23, [[12, 1]]], [29, [[12, 1]]], [31, [[6, 1], [3, 1], [2, 1], [1, 1]]], [37, [[9, 1], [3, 1]]], [41, [[6, 1], [3, 1], [2, 1], [1, 1]]], [43, [[3, 4]]], [47, [[6, 1], [2, 2], [1, 2]]], [53, [[4, 1], [3, 1], [2, 2], [1, 1]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [7776, 7776], 'galois_label': '12T281', 'galt': 281, 'grd': 196.94923203709124, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.738751981811.1', 'local_algs': ['79.2.0.1', '79.2.0.1', '79.2.0.1', '79.2.0.1', '79.4.2.1', 'm491.2.1.1', 'm491.1.3.0', 'm491.1.3.0', 'm491.2.2.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [79, 491], 'rd': 9.75082932818, 'regulator': {'__RealLiteral__': 0, 'data': '8.70585947161', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.3.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( 3 a^{11} - 6 a^{10} + 4 a^{9} + 5 a^{8} - 16 a^{7} + 8 a^{6} + 13 a^{5} - 18 a^{4} + 8 a^{2} - 5 a \\)', '\\( 3 a^{11} - 7 a^{10} + 6 a^{9} + 4 a^{8} - 18 a^{7} + 14 a^{6} + 10 a^{5} - 22 a^{4} + 5 a^{3} + 8 a^{2} - 8 a + 1 \\)', '\\( 4 a^{11} - 9 a^{10} + 8 a^{9} + 4 a^{8} - 22 a^{7} + 17 a^{6} + 11 a^{5} - 26 a^{4} + 8 a^{3} + 7 a^{2} - 10 a + 3 \\)', '\\( 2 a^{11} - 8 a^{10} + 11 a^{9} - 3 a^{8} - 16 a^{7} + 26 a^{6} - 4 a^{5} - 26 a^{4} + 22 a^{3} + 4 a^{2} - 11 a + 6 \\)', '\\( 3 a^{10} - 5 a^{9} + 3 a^{8} + 5 a^{7} - 14 a^{6} + 5 a^{5} + 11 a^{4} - 13 a^{3} - 2 a^{2} + 5 a - 4 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  52. label: 12.2.740225059083.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -3, -7, -5, 0, 6, 5, 2, -4, -2, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 740225059083, 'disc_rad': 21597, 'disc_sign': -1, 'frobs': [[2, [[6, 1], [3, 2]]], [3, [0]], [5, [[4, 3]]], [7, [[4, 2], [2, 2]]], [11, [[4, 3]]], [13, [[6, 2]]], [17, [[4, 1], [2, 4]]], [19, [[4, 2], [2, 2]]], [23, [0]], [29, [[6, 1], [3, 2]]], [31, [[6, 2]]], [37, [[4, 2], [2, 2]]], [41, [[12, 1]]], [43, [[4, 2], [2, 2]]], [47, [[12, 1]]], [53, [[4, 2], [2, 1], [1, 2]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [384, 384, 384], 'galois_label': '12T186', 'galt': 186, 'grd': 146.9591780053223, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.740225059083.1', 'local_algs': ['3.3.0.1', '3.3.0.1', '3.6.3.2', '23.4.0.1', '23.8.4.1', 'm313.2.1.1', 'm313.2.1.1', 'm313.1.4.0', 'm313.1.4.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [3, 23, 313], 'rd': 9.752448118477346, 'regulator': {'__RealLiteral__': 0, 'data': '9.227667082224851', 'prec': 57}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-7.1.9.-1.-3.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{8}{83} a^{11} + \\frac{21}{166} a^{10} - \\frac{165}{166} a^{9} - \\frac{15}{166} a^{8} + \\frac{127}{166} a^{7} + \\frac{327}{166} a^{6} - \\frac{33}{83} a^{5} - \\frac{329}{166} a^{4} - \\frac{91}{83} a^{3} - \\frac{33}{83} a^{2} + \\frac{121}{166} a + \\frac{103}{166} \\)', '\\( -\\frac{43}{332} a^{11} + \\frac{47}{166} a^{10} + \\frac{11}{83} a^{9} + \\frac{1}{83} a^{8} - \\frac{111}{166} a^{7} - \\frac{137}{332} a^{6} + \\frac{167}{332} a^{5} + \\frac{381}{332} a^{4} + \\frac{229}{166} a^{3} - \\frac{165}{332} a^{2} - \\frac{243}{166} a - \\frac{199}{332} \\)', '\\( \\frac{63}{332} a^{11} - \\frac{65}{166} a^{10} - \\frac{47}{83} a^{9} + \\frac{41}{83} a^{8} + \\frac{263}{166} a^{7} + \\frac{193}{332} a^{6} - \\frac{623}{332} a^{5} - \\frac{481}{332} a^{4} - \\frac{73}{166} a^{3} + \\frac{373}{332} a^{2} + \\frac{163}{166} a + \\frac{307}{332} \\)', '\\( -a \\)', '\\( \\frac{30}{83} a^{11} - \\frac{25}{166} a^{10} - \\frac{183}{166} a^{9} - \\frac{243}{166} a^{8} - \\frac{1}{166} a^{7} + \\frac{417}{166} a^{6} + \\frac{146}{83} a^{5} + \\frac{115}{166} a^{4} - \\frac{113}{83} a^{3} - \\frac{186}{83} a^{2} - \\frac{231}{166} a - \\frac{257}{166} \\)', '\\( -\\frac{30}{83} a^{11} + \\frac{25}{166} a^{10} + \\frac{183}{166} a^{9} + \\frac{243}{166} a^{8} + \\frac{1}{166} a^{7} - \\frac{417}{166} a^{6} - \\frac{146}{83} a^{5} - \\frac{115}{166} a^{4} + \\frac{113}{83} a^{3} + \\frac{186}{83} a^{2} + \\frac{231}{166} a + \\frac{91}{166} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/2*a^10 - 1/2*a^9 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 - 1/2*a^4 - 1/2*a - 1/2', '1/332*a^11 + 12/83*a^10 + 13/166*a^9 - 29/166*a^8 + 37/83*a^7 - 47/332*a^6 + 27/332*a^5 - 5/332*a^4 + 41/166*a^3 + 27/332*a^2 - 2/83*a - 61/332']}
  53. label: 12.2.742534191307.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 5, -8, 2, 10, -8, -10, 21, -10, -6, 10, -5, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 742534191307, 'disc_rad': 51223, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[12, 1]]], [7, [[9, 1], [3, 1]]], [11, [[3, 4]]], [13, [[6, 1], [3, 1], [2, 1], [1, 1]]], [17, [[6, 1], [3, 1], [1, 3]]], [19, [[12, 1]]], [23, [[9, 1], [3, 1]]], [29, [[6, 1], [3, 1], [2, 1], [1, 1]]], [31, [[12, 1]]], [37, [[4, 1], [3, 1], [2, 2], [1, 1]]], [41, [[3, 4]]], [43, [[12, 1]]], [47, [[12, 1]]], [53, [[6, 1], [3, 1], [1, 3]]], [59, [[9, 1], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [7776, 7776], 'galois_label': '12T281', 'galt': 281, 'grd': 226.3249875731798, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.742534191307.1', 'local_algs': ['181.2.0.1', '181.2.0.1', '181.4.0.1', '181.4.2.2', 'm283.2.1.1', 'm283.1.3.0', 'm283.1.3.0', 'm283.2.2.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [181, 283], 'rd': 9.75497973121, 'regulator': {'__RealLiteral__': 0, 'data': '8.70536666', 'prec': 34}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - 5 a^{10} + 9 a^{9} - 2 a^{8} - 15 a^{7} + 18 a^{6} + 2 a^{5} - 14 a^{4} + 2 a^{3} + 9 a^{2} - 5 a \\)', '\\( a^{10} - 4 a^{9} + 5 a^{8} + 3 a^{7} - 12 a^{6} + 6 a^{5} + 8 a^{4} - 6 a^{3} - 4 a^{2} + 5 a \\)', '\\( a^{10} - 5 a^{9} + 9 a^{8} - 2 a^{7} - 15 a^{6} + 18 a^{5} + 2 a^{4} - 14 a^{3} + 2 a^{2} + 9 a - 5 \\)', '\\( a^{11} - 3 a^{10} + 2 a^{9} + 5 a^{8} - 8 a^{7} + a^{6} + 7 a^{5} - 3 a^{4} - 2 a^{3} + 3 a^{2} - 1 \\)', '\\( 3 a^{11} - 12 a^{10} + 17 a^{9} + 2 a^{8} - 30 a^{7} + 28 a^{6} + 6 a^{5} - 19 a^{4} + 4 a^{3} + 13 a^{2} - 10 a + 3 \\)', '\\( 2 a^{11} - 8 a^{10} + 12 a^{9} - a^{8} - 18 a^{7} + 22 a^{6} - 3 a^{5} - 11 a^{4} + 8 a^{3} + 6 a^{2} - 9 a + 4 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  54. label: 12.2.780912359375.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -1, 2, 0, -1, -4, 5, -3, 6, -5, 2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 780912359375, 'disc_rad': 297845, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [0]], [7, [[12, 1]]], [11, [[6, 1], [4, 1], [2, 1]]], [13, [[4, 3]]], [17, [[8, 1], [2, 2]]], [19, [[4, 1], [2, 3], [1, 2]]], [23, [[12, 1]]], [29, [[6, 1], [4, 1], [1, 2]]], [31, [[4, 1], [2, 2], [1, 4]]], [37, [[6, 2]]], [41, [[4, 1], [3, 2], [1, 2]]], [43, [[6, 2]]], [47, [[12, 1]]], [53, [[4, 1], [2, 4]]], [59, [[4, 1], [2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 545.7517750772781, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.780912359375.1', 'local_algs': ['5.12.6.1', '71.1.0.1', '71.1.0.1', '71.2.0.1', '71.2.0.1', '71.2.0.1', '71.2.1.2', '71.2.0.1', 'm839.1.1.0', 'm839.1.1.0', 'm839.2.1.1', 'm839.2.1.1', 'm839.1.3.0', 'm839.1.3.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 71, 839], 'rd': 9.79603191501, 'regulator': {'__RealLiteral__': 0, 'data': '8.68760154462', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.1.2.1.-1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{25}{53} a^{11} - \\frac{60}{53} a^{10} + \\frac{74}{53} a^{9} - \\frac{144}{53} a^{8} + \\frac{197}{53} a^{7} - \\frac{122}{53} a^{6} + \\frac{142}{53} a^{5} - \\frac{125}{53} a^{4} - \\frac{28}{53} a^{3} - \\frac{10}{53} a^{2} + \\frac{54}{53} a - \\frac{36}{53} \\)', '\\( a \\)', '\\( \\frac{8}{53} a^{11} + \\frac{2}{53} a^{10} - \\frac{6}{53} a^{9} - \\frac{27}{53} a^{8} - \\frac{26}{53} a^{7} + \\frac{50}{53} a^{6} + \\frac{20}{53} a^{5} + \\frac{66}{53} a^{4} - \\frac{98}{53} a^{3} - \\frac{35}{53} a^{2} - \\frac{23}{53} a + \\frac{33}{53} \\)', '\\( \\frac{2}{53} a^{11} - \\frac{26}{53} a^{10} + \\frac{25}{53} a^{9} - \\frac{20}{53} a^{8} + \\frac{73}{53} a^{7} - \\frac{14}{53} a^{6} - \\frac{48}{53} a^{5} - \\frac{10}{53} a^{4} - \\frac{51}{53} a^{3} + \\frac{84}{53} a^{2} + \\frac{34}{53} a - \\frac{58}{53} \\)', '\\( \\frac{18}{53} a^{11} - \\frac{22}{53} a^{10} + \\frac{13}{53} a^{9} - \\frac{74}{53} a^{8} + \\frac{21}{53} a^{7} + \\frac{33}{53} a^{6} + \\frac{45}{53} a^{5} + \\frac{69}{53} a^{4} - \\frac{88}{53} a^{3} + \\frac{14}{53} a^{2} - \\frac{12}{53} a + \\frac{8}{53} \\)', '\\( \\frac{3}{53} a^{11} - \\frac{39}{53} a^{10} + \\frac{64}{53} a^{9} - \\frac{83}{53} a^{8} + \\frac{189}{53} a^{7} - \\frac{180}{53} a^{6} + \\frac{140}{53} a^{5} - \\frac{227}{53} a^{4} + \\frac{109}{53} a^{3} - \\frac{33}{53} a^{2} + \\frac{51}{53} a - \\frac{34}{53} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/53*a^11 - 13/53*a^10 - 14/53*a^9 - 10/53*a^8 + 10/53*a^7 - 7/53*a^6 - 24/53*a^5 - 5/53*a^4 + 1/53*a^3 - 11/53*a^2 + 17/53*a + 24/53']}
  55. label: 12.2.782479234375.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -1, 4, 4, -10, -1, 13, -7, -5, 7, -1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 782479234375, 'disc_rad': 6355, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[12, 1]]], [5, [0]], [7, [[4, 2], [2, 2]]], [11, [[6, 1], [3, 2]]], [13, [[12, 1]]], [17, [[4, 3]]], [19, [[6, 1], [2, 3]]], [23, [[4, 3]]], [29, [[2, 5], [1, 2]]], [31, [0]], [37, [[4, 3]]], [41, [0]], [43, [[4, 3]]], [47, [[4, 2], [2, 2]]], [53, [[12, 1]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [144, 144, 144], 'galois_label': '12T125', 'galt': 125, 'grd': 79.71825386948713, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.782479234375.1', 'local_algs': ['5.4.2.1', '5.4.2.1', '5.4.2.1', '31.2.1.1', '31.4.2.1', '31.6.0.1', '41.1.0.1', '41.1.0.1', '41.1.0.1', '41.1.0.1', '41.2.0.1', '41.2.1.2', '41.2.0.1', '41.2.1.2'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [5, 31, 41], 'rd': 9.797668361987727, 'regulator': {'__RealLiteral__': 0, 'data': '8.622084220138495', 'prec': 57}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '-1.-3.0.-1.1', '1.0.-5.-2.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( -a \\)', '\\( a^{10} - a^{9} - 2 a^{8} + 4 a^{7} - 6 a^{5} + 4 a^{4} + 4 a^{3} - 4 a^{2} - 2 a + 1 \\)', '\\( a^{9} - a^{8} - 2 a^{7} + 4 a^{6} - 6 a^{4} + 4 a^{3} + 4 a^{2} - 3 a - 2 \\)', '\\( a^{10} - 2 a^{9} - a^{8} + 6 a^{7} - 4 a^{6} - 6 a^{5} + 10 a^{4} - 7 a^{2} + a + 2 \\)', '\\( a^{9} - a^{8} - 2 a^{7} + 4 a^{6} - 6 a^{4} + 4 a^{3} + 3 a^{2} - 3 a - 2 \\)', '\\( -a^{11} + a^{10} + 3 a^{9} - 6 a^{8} - a^{7} + 11 a^{6} - 8 a^{5} - 8 a^{4} + 11 a^{3} + a^{2} - 4 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  56. label: 12.2.803640236800.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 4, -3, 1, 2, 3, -2, -1, -1, -1, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 803640236800, 'disc_rad': 24790, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [0]], [7, [[12, 1]]], [11, [[6, 1], [3, 2]]], [13, [[4, 3]]], [17, [[8, 1], [2, 1], [1, 2]]], [19, [[4, 2], [2, 2]]], [23, [[4, 2], [2, 2]]], [29, [[8, 1], [4, 1]]], [31, [[4, 3]]], [37, [0]], [41, [[6, 1], [3, 2]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[6, 2]]], [53, [[12, 1]]], [59, [[4, 1], [2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2048, 1536, 1536, 1536], 'galois_label': '12T250', 'galt': 250, 'grd': 176.72985833439097, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.803640236800.1', 'local_algs': ['2.12.8.1', '5.4.2.1', '5.8.0.1', '37.2.1.1', '37.2.1.1', '37.2.1.1', '37.2.0.1', '37.2.1.1', '37.2.0.1', '67.1.0.1', '67.1.0.1', '67.2.0.1', '67.2.0.1', '67.2.1.1', '67.4.0.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [2, 5, 37, 67], 'rd': 9.81947961182, 'regulator': {'__RealLiteral__': 0, 'data': '8.96333728062', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-3.-1.1', '1.-1.0.-1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{259}{395} a^{11} - \\frac{162}{395} a^{10} - \\frac{74}{79} a^{9} - \\frac{454}{395} a^{8} - \\frac{336}{395} a^{7} - \\frac{441}{395} a^{6} + \\frac{804}{395} a^{5} + \\frac{205}{79} a^{4} + \\frac{954}{395} a^{3} - \\frac{130}{79} a^{2} + \\frac{576}{395} a - \\frac{773}{395} \\)', '\\( \\frac{234}{395} a^{11} - \\frac{20}{79} a^{10} - \\frac{33}{79} a^{9} - \\frac{369}{395} a^{8} - \\frac{658}{395} a^{7} - \\frac{230}{79} a^{6} + \\frac{34}{395} a^{5} + \\frac{187}{395} a^{4} + \\frac{109}{79} a^{3} - \\frac{11}{79} a^{2} + \\frac{1286}{395} a - \\frac{152}{79} \\)', '\\( \\frac{212}{395} a^{11} - \\frac{254}{395} a^{10} - \\frac{38}{79} a^{9} - \\frac{152}{395} a^{8} - \\frac{17}{79} a^{7} - \\frac{472}{395} a^{6} + \\frac{652}{395} a^{5} + \\frac{347}{395} a^{4} + \\frac{223}{395} a^{3} - \\frac{118}{79} a^{2} + \\frac{1263}{395} a - \\frac{856}{395} \\)', '\\( \\frac{183}{395} a^{11} - \\frac{141}{395} a^{10} - \\frac{41}{79} a^{9} - \\frac{243}{395} a^{8} - \\frac{62}{79} a^{7} - \\frac{318}{395} a^{6} + \\frac{533}{395} a^{5} + \\frac{443}{395} a^{4} + \\frac{172}{395} a^{3} - \\frac{119}{79} a^{2} + \\frac{317}{395} a - \\frac{724}{395} \\)', '\\( \\frac{737}{395} a^{11} - \\frac{371}{395} a^{10} - \\frac{188}{79} a^{9} - \\frac{1147}{395} a^{8} - \\frac{1223}{395} a^{7} - \\frac{2173}{395} a^{6} + \\frac{1022}{395} a^{5} + \\frac{350}{79} a^{4} + \\frac{1307}{395} a^{3} - \\frac{326}{79} a^{2} + \\frac{2548}{395} a - \\frac{1524}{395} \\)', '\\( \\frac{49}{395} a^{11} - \\frac{42}{79} a^{10} - \\frac{14}{79} a^{9} + \\frac{181}{395} a^{8} + \\frac{372}{395} a^{7} + \\frac{70}{79} a^{6} + \\frac{814}{395} a^{5} + \\frac{132}{395} a^{4} - \\frac{95}{79} a^{3} - \\frac{110}{79} a^{2} + \\frac{536}{395} a - \\frac{98}{79} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/5*a^10 - 1/5*a^7 - 2/5*a^6 + 1/5*a^4 - 2/5*a^3 - 1/5', '1/395*a^11 + 7/395*a^10 + 11/79*a^9 + 44/395*a^8 - 44/395*a^7 + 41/395*a^6 - 64/395*a^5 - 23/79*a^4 - 129/395*a^3 + 30/79*a^2 + 19/395*a + 148/395']}
  57. label: 12.2.838790656103.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 5, -7, 6, -3, -2, 4, -4, 2, 1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 838790656103, 'disc_rad': 437, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [[4, 3]]], [7, [[4, 3]]], [11, [[2, 5], [1, 2]]], [13, [[6, 2]]], [17, [[2, 5], [1, 2]]], [19, [0]], [23, [0]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[4, 3]]], [47, [[3, 4]]], [53, [[4, 3]]], [59, [[2, 4], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 24], 'galois_label': '12T22', 'galt': 22, 'grd': 20.904544960366874, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.838790656103.1', 'local_algs': ['19.4.0.1', '19.8.4.1', '23.2.0.1', '23.2.1.1', '23.4.2.1', '23.4.2.1'], 'minimal_sibling': [1, -2, 2, -2, 2, -1, 1], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [19, 23], 'rd': 9.85457272032, 'regulator': {'__RealLiteral__': 0, 'data': '9.60375711012', 'prec': 44}, 'res': {'sib': ['-109,458,-234,-372,473,68,-139,-32,-70,-20,-1,0,1', '-7,2,9,2,-5,-1,1', '1,-1,1,-3,4,-2,1,-2,4,-3,1,-1,1', '1,-1,1,1,-3,1,1,-1,1', '1,-2,2,-2,2,-1,1', '1,2,1,-21,0,21,1,-2,1', '1,5,79,53,15,-2,34,-3,20,-11,10,-3,1', '14641,0,-1089,3564,-830,-1012,221,42,28,26,-12,-3,1', '36,-186,449,-951,1888,-2860,3521,-3690,3364,-2647,1768,-972,435,-154,42,-8,1', '581,-1917,2630,-1519,88,362,-225,80,-14,-9,11,-5,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.-10.0.-2.3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{9} - 2 a^{8} + 4 a^{6} - 4 a^{5} + 2 a^{3} - 4 a^{2} + 4 a - 2 \\)', '\\( a \\)', '\\( a^{11} - 3 a^{10} + 3 a^{9} + 3 a^{8} - 9 a^{7} + 7 a^{6} - 6 a^{4} + 10 a^{3} - 11 a^{2} + 5 a - 1 \\)', '\\( a^{10} - 3 a^{9} + 2 a^{8} + 4 a^{7} - 8 a^{6} + 4 a^{5} + 2 a^{4} - 6 a^{3} + 8 a^{2} - 7 a + 3 \\)', '\\( a^{9} - 2 a^{8} + 4 a^{6} - 4 a^{5} + a^{4} + 2 a^{3} - 5 a^{2} + 5 a - 2 \\)', '\\( 3 a^{11} - 5 a^{10} + 9 a^{8} - 10 a^{7} + 4 a^{6} + 3 a^{5} - 12 a^{4} + 12 a^{3} - 9 a^{2} + 3 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  58. label: 12.2.868902484375.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 9, -12, 9, -4, 1, -4, 9, -12, 9, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 868902484375, 'disc_rad': 331405, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[12, 1]]], [5, [0]], [7, [[12, 1]]], [11, [[6, 1], [4, 1], [1, 2]]], [13, [[8, 1], [4, 1]]], [17, [[8, 1], [2, 2]]], [19, [[4, 1], [2, 3], [1, 2]]], [23, [[6, 2]]], [29, [[6, 1], [4, 1], [2, 1]]], [31, [[4, 1], [2, 3], [1, 2]]], [37, [[12, 1]]], [41, [[6, 1], [4, 1], [2, 1]]], [43, [[12, 1]]], [47, [[12, 1]]], [53, [[4, 1], [2, 4]]], [59, [[4, 1], [2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 575.6778613078673, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.868902484375.1', 'local_algs': ['5.6.3.1', '5.6.3.1', '79.1.0.1', '79.1.0.1', '79.1.0.1', '79.1.0.1', '79.2.0.1', '79.2.1.1', '79.2.0.1', '79.2.0.1', 'm839.1.1.0', 'm839.1.1.0', 'm839.2.1.1', 'm839.2.1.1', 'm839.1.3.0', 'm839.1.3.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 79, 839], 'rd': 9.88357934796, 'regulator': {'__RealLiteral__': 0, 'data': '9.72826881496', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.1.2.1.-1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{3}{2} a^{11} - 5 a^{10} + 10 a^{9} - 11 a^{8} + \\frac{11}{2} a^{7} - \\frac{3}{2} a^{6} - \\frac{1}{2} a^{5} - 5 a^{4} + \\frac{21}{2} a^{3} - \\frac{23}{2} a^{2} + \\frac{11}{2} a - 1 \\)', '\\( \\frac{1}{2} a^{9} - a^{8} + \\frac{3}{2} a^{7} - \\frac{1}{2} a^{6} - \\frac{1}{2} a^{5} - \\frac{1}{2} a^{4} - \\frac{1}{2} a^{3} - a^{2} + \\frac{1}{2} a - 1 \\)', '\\( a^{11} - 3 a^{10} + 6 a^{9} - \\frac{13}{2} a^{8} + 4 a^{7} - \\frac{5}{2} a^{6} + \\frac{1}{2} a^{5} - \\frac{7}{2} a^{4} + \\frac{11}{2} a^{3} - \\frac{15}{2} a^{2} + 4 a - \\frac{5}{2} \\)', '\\( 2 a^{11} - \\frac{13}{2} a^{10} + \\frac{25}{2} a^{9} - \\frac{25}{2} a^{8} + \\frac{9}{2} a^{7} - \\frac{1}{2} a^{6} + \\frac{1}{2} a^{5} - \\frac{17}{2} a^{4} + 12 a^{3} - 12 a^{2} + 4 a - 1 \\)', '\\( \\frac{3}{2} a^{11} - 7 a^{10} + \\frac{33}{2} a^{9} - 23 a^{8} + 17 a^{7} - \\frac{9}{2} a^{6} - \\frac{1}{2} a^{5} - 6 a^{4} + \\frac{35}{2} a^{3} - 23 a^{2} + \\frac{33}{2} a - \\frac{11}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^7 - 1/2', '1/2*a^8 - 1/2*a', '1/2*a^9 - 1/2*a^2', '1/2*a^10 - 1/2*a^3', '1/2*a^11 - 1/2*a^4']}
  59. label: 12.2.884706715067.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 4, -5, 2, -4, 7, -5, 4, -2, 2, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 884706715067, 'disc_rad': 24983, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 2]]], [5, [[12, 1]]], [7, [0]], [11, [[3, 4]]], [13, [[4, 2], [2, 1], [1, 2]]], [17, [[3, 4]]], [19, [[12, 1]]], [23, [[6, 2]]], [29, [[4, 1], [2, 3], [1, 2]]], [31, [[3, 4]]], [37, [[6, 2]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [0]], [47, [[6, 1], [3, 2]]], [53, [[6, 1], [3, 2]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1024, 768, 768], 'galois_label': '12T222', 'galt': 222, 'grd': 218.61097808482216, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.884706715067.1', 'local_algs': ['7.6.4.3', '7.6.4.3', '43.1.0.1', '43.1.0.1', '43.1.0.1', '43.1.0.1', '43.1.0.1', '43.1.0.1', '43.2.0.1', '43.4.2.1', '83.1.0.1', '83.1.0.1', '83.2.1.2', '83.4.0.1', '83.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [7, 43, 83], 'rd': 9.89843670384, 'regulator': {'__RealLiteral__': 0, 'data': '9.52200865587', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.3.2.-2.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{355}{769} a^{11} - \\frac{304}{769} a^{10} + \\frac{636}{769} a^{9} - \\frac{454}{769} a^{8} + \\frac{1097}{769} a^{7} - \\frac{1169}{769} a^{6} + \\frac{1821}{769} a^{5} - \\frac{658}{769} a^{4} - \\frac{290}{769} a^{3} - \\frac{1026}{769} a^{2} + \\frac{978}{769} a - \\frac{918}{769} \\)', '\\( \\frac{774}{769} a^{11} - \\frac{535}{769} a^{10} + \\frac{1352}{769} a^{9} - \\frac{1057}{769} a^{8} + \\frac{2864}{769} a^{7} - \\frac{2930}{769} a^{6} + \\frac{4553}{769} a^{5} - \\frac{1244}{769} a^{4} + \\frac{1144}{769} a^{3} - \\frac{3632}{769} a^{2} + \\frac{2050}{769} a - \\frac{1226}{769} \\)', '\\( \\frac{290}{769} a^{11} - \\frac{270}{769} a^{10} + \\frac{747}{769} a^{9} - \\frac{555}{769} a^{8} + \\frac{1546}{769} a^{7} - \\frac{1529}{769} a^{6} + \\frac{2614}{769} a^{5} - \\frac{1404}{769} a^{4} + \\frac{1756}{769} a^{3} - \\frac{1488}{769} a^{2} + \\frac{1243}{769} a - \\frac{1129}{769} \\)', '\\( \\frac{602}{769} a^{11} - \\frac{587}{769} a^{10} + \\frac{1137}{769} a^{9} - \\frac{993}{769} a^{8} + \\frac{2313}{769} a^{7} - \\frac{2877}{769} a^{6} + \\frac{3883}{769} a^{5} - \\frac{1822}{769} a^{4} + \\frac{548}{769} a^{3} - \\frac{2654}{769} a^{2} + \\frac{2278}{769} a - \\frac{1808}{769} \\)', '\\( \\frac{550}{769} a^{11} - \\frac{406}{769} a^{10} + \\frac{1072}{769} a^{9} - \\frac{920}{769} a^{8} + \\frac{2057}{769} a^{7} - \\frac{2396}{769} a^{6} + \\frac{3287}{769} a^{5} - \\frac{1496}{769} a^{4} + \\frac{493}{769} a^{3} - \\frac{2716}{769} a^{2} + \\frac{952}{769} a - \\frac{1054}{769} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/769*a^11 - 107/769*a^10 - 191/769*a^9 + 250/769*a^8 - 350/769*a^7 + 183/769*a^6 - 166/769*a^5 - 95/769*a^4 + 75/769*a^3 - 265/769*a^2 - 359/769*a + 370/769']}
  60. label: 12.2.984184121123.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 3, 0, 0, 6, -3, -1, 8, -4, 1, 3, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 984184121123, 'disc_rad': 203, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[6, 2]]], [5, [[6, 1], [3, 2]]], [7, [0]], [11, [[12, 1]]], [13, [[2, 5], [1, 2]]], [17, [[6, 2]]], [19, [[6, 2]]], [23, [[6, 2]]], [29, [0]], [31, [[6, 2]]], [37, [[12, 1]]], [41, [[2, 4], [1, 4]]], [43, [[4, 3]]], [47, [[6, 2]]], [53, [[3, 4]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [320, 288], 'galois_label': '12T141', 'galt': 141, 'grd': 63.24800991823296, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.984184121123.1', 'local_algs': ['7.6.4.3', '7.6.5.2', '29.2.0.1', '29.2.0.1', '29.4.3.3', '29.4.0.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [7, 29], 'rd': 9.98672358391, 'regulator': {'__RealLiteral__': 0, 'data': '10.8120129246', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.3.-4.3.1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{95}{41} a^{11} - \\frac{248}{41} a^{10} + \\frac{439}{41} a^{9} - \\frac{170}{41} a^{8} - 7 a^{7} + \\frac{965}{41} a^{6} - \\frac{682}{41} a^{5} + \\frac{118}{41} a^{4} + \\frac{545}{41} a^{3} - \\frac{309}{41} a^{2} + \\frac{177}{41} a + \\frac{186}{41} \\)', '\\( \\frac{67}{41} a^{11} - \\frac{168}{41} a^{10} + \\frac{304}{41} a^{9} - \\frac{135}{41} a^{8} - 3 a^{7} + \\frac{577}{41} a^{6} - \\frac{421}{41} a^{5} + \\frac{154}{41} a^{4} + \\frac{229}{41} a^{3} - \\frac{126}{41} a^{2} + \\frac{108}{41} a + \\frac{126}{41} \\)', '\\( \\frac{58}{41} a^{11} - \\frac{154}{41} a^{10} + \\frac{265}{41} a^{9} - \\frac{93}{41} a^{8} - 5 a^{7} + \\frac{587}{41} a^{6} - \\frac{403}{41} a^{5} + \\frac{25}{41} a^{4} + \\frac{309}{41} a^{3} - \\frac{177}{41} a^{2} + \\frac{99}{41} a + \\frac{95}{41} \\)', '\\( \\frac{39}{41} a^{11} - \\frac{129}{41} a^{10} + \\frac{251}{41} a^{9} - \\frac{182}{41} a^{8} - 2 a^{7} + \\frac{476}{41} a^{6} - \\frac{488}{41} a^{5} + \\frac{190}{41} a^{4} + \\frac{200}{41} a^{3} - \\frac{189}{41} a^{2} + \\frac{80}{41} a + \\frac{25}{41} \\)', '\\( \\frac{1}{41} a^{11} + \\frac{3}{41} a^{10} - \\frac{23}{41} a^{9} + \\frac{50}{41} a^{8} - a^{7} - \\frac{33}{41} a^{6} + \\frac{121}{41} a^{5} - \\frac{136}{41} a^{4} + \\frac{23}{41} a^{3} + \\frac{74}{41} a^{2} - \\frac{81}{41} a + \\frac{8}{41} \\)', '\\( \\frac{73}{41} a^{11} - \\frac{191}{41} a^{10} + \\frac{330}{41} a^{9} - \\frac{122}{41} a^{8} - 6 a^{7} + \\frac{748}{41} a^{6} - \\frac{556}{41} a^{5} + \\frac{76}{41} a^{4} + \\frac{408}{41} a^{3} - \\frac{297}{41} a^{2} + \\frac{155}{41} a + \\frac{133}{41} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/41*a^11 + 3/41*a^10 + 18/41*a^9 + 9/41*a^8 + 8/41*a^6 - 2/41*a^5 - 13/41*a^4 - 18/41*a^3 - 8/41*a^2 + 1/41*a + 8/41']}
  61. label: 12.2.1008394404608.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 4, 0, -11, 24, -29, 24, -11, 0, 4, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1008394404608, 'disc_rad': 166, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[4, 3]]], [7, [[6, 2]]], [11, [[6, 2]]], [13, [[4, 3]]], [17, [[3, 4]]], [19, [[4, 3]]], [23, [[2, 4], [1, 4]]], [29, [[3, 4]]], [31, [[6, 2]]], [37, [[3, 4]]], [41, [[2, 6]]], [43, [[2, 5], [1, 2]]], [47, [[4, 3]]], [53, [[2, 5], [1, 2]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48, 24], 'galois_label': '12T22', 'galt': 22, 'grd': 18.2208671582886, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1008394404608.1', 'local_algs': ['2.4.0.1', '2.8.8.1', '83.1.0.1', '83.1.0.1', '83.2.1.2', '83.4.2.1', '83.4.2.1'], 'minimal_sibling': [1, -1, 0, 2, 0, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 83], 'rd': 10.0069685665, 'regulator': {'__RealLiteral__': 0, 'data': '10.1993004837', 'prec': 44}, 'res': {'sib': ['-2,-4,7,-9,3,-1,1', '1,-1,0,2,0,-1,1', '-67,80,68,-72,28,-28,9,-2,1', '1,-2,1,2,-3,2,1,-2,1']}, 'subfield_mults': [1, 1], 'subfields': ['-2.1.-1.1', '-1.0.2.0.2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( 2 a^{11} - 5 a^{10} + \\frac{9}{2} a^{9} + \\frac{9}{2} a^{8} - \\frac{43}{2} a^{7} + \\frac{69}{2} a^{6} - \\frac{61}{2} a^{5} + \\frac{35}{2} a^{4} - \\frac{3}{2} a^{3} - \\frac{11}{2} a^{2} + \\frac{5}{2} a - \\frac{1}{2} \\)', '\\( a^{11} - a^{10} - \\frac{1}{2} a^{9} + 4 a^{8} - \\frac{13}{2} a^{7} + 4 a^{6} + \\frac{5}{2} a^{5} - 4 a^{4} + \\frac{11}{2} a^{3} - \\frac{3}{2} a + 1 \\)', '\\( \\frac{1}{2} a^{10} - \\frac{1}{2} a^{9} + \\frac{3}{2} a^{7} - 3 a^{6} + \\frac{5}{2} a^{5} - a^{4} + \\frac{3}{2} a^{3} + \\frac{3}{2} a - \\frac{1}{2} \\)', '\\( \\frac{1}{2} a^{11} - \\frac{1}{2} a^{10} - a^{9} + \\frac{7}{2} a^{8} - 4 a^{7} - \\frac{1}{2} a^{6} + 8 a^{5} - \\frac{21}{2} a^{4} + 8 a^{3} - \\frac{5}{2} a^{2} - \\frac{3}{2} a + 2 \\)', '\\( 3 a^{11} - \\frac{15}{2} a^{10} + 8 a^{9} + 5 a^{8} - 32 a^{7} + 56 a^{6} - 55 a^{5} + 36 a^{4} - 6 a^{3} - 8 a^{2} + 9 a - \\frac{7}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8 - 1/2*a^6 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/2*a^9 - 1/2*a^7 - 1/2*a^5 - 1/2*a^3 - 1/2*a', '1/2*a^10 - 1/2', '1/2*a^11 - 1/2*a']}
  62. label: 12.2.1040220487744.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 2, 2, -7, 5, 8, -16, 11, -6, 3, 2, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1040220487744, 'disc_rad': 11086, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 1], [3, 2]]], [5, [[6, 1], [3, 1], [2, 1], [1, 1]]], [7, [[4, 3]]], [11, [[4, 3]]], [13, [[9, 1], [3, 1]]], [17, [[6, 1], [2, 3]]], [19, [[6, 1], [4, 1], [2, 1]]], [23, [0]], [29, [[6, 2]]], [31, [[6, 1], [3, 2]]], [37, [[4, 2], [2, 2]]], [41, [[9, 1], [3, 1]]], [43, [[4, 3]]], [47, [[12, 1]]], [53, [[6, 1], [3, 1], [2, 1], [1, 1]]], [59, [[4, 2], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [20736, 10368, 13824], 'galois_label': '12T283', 'galt': 283, 'grd': 371.45420183662577, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1040220487744.1', 'local_algs': ['2.6.6.5', '2.6.0.1', '23.4.0.1', '23.8.4.1', 'm241.1.1.0', 'm241.1.2.0', 'm241.3.1.2', 'm241.1.6.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 23, 241], 'rd': 10.0329146319, 'regulator': {'__RealLiteral__': 0, 'data': '11.9765407066', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{944}{1233} a^{11} - \\frac{2708}{1233} a^{10} + \\frac{154}{137} a^{9} + \\frac{1043}{411} a^{8} - \\frac{532}{137} a^{7} + \\frac{9358}{1233} a^{6} - \\frac{4712}{411} a^{5} + \\frac{5110}{1233} a^{4} + \\frac{570}{137} a^{3} - \\frac{3395}{1233} a^{2} + \\frac{364}{411} a + \\frac{1300}{1233} \\)', '\\( a \\)', '\\( \\frac{304}{411} a^{11} - \\frac{749}{411} a^{10} + \\frac{242}{411} a^{9} + \\frac{1003}{411} a^{8} - \\frac{1384}{411} a^{7} + \\frac{931}{137} a^{6} - \\frac{1125}{137} a^{5} + \\frac{740}{411} a^{4} + \\frac{1933}{411} a^{3} - \\frac{1841}{411} a^{2} + \\frac{419}{411} a + \\frac{275}{137} \\)', '\\( \\frac{163}{411} a^{11} - \\frac{503}{411} a^{10} + \\frac{365}{411} a^{9} + \\frac{577}{411} a^{8} - \\frac{1099}{411} a^{7} + \\frac{542}{137} a^{6} - \\frac{838}{137} a^{5} + \\frac{1646}{411} a^{4} + \\frac{1246}{411} a^{3} - \\frac{1148}{411} a^{2} - \\frac{331}{411} a + \\frac{147}{137} \\)', '\\( \\frac{1564}{1233} a^{11} - \\frac{3574}{1233} a^{10} + \\frac{272}{411} a^{9} + \\frac{1544}{411} a^{8} - \\frac{1936}{411} a^{7} + \\frac{13787}{1233} a^{6} - \\frac{5494}{411} a^{5} + \\frac{3461}{1233} a^{4} + \\frac{2407}{411} a^{3} - \\frac{5731}{1233} a^{2} + \\frac{343}{411} a + \\frac{1910}{1233} \\)', '\\( \\frac{1157}{1233} a^{11} - \\frac{2861}{1233} a^{10} + \\frac{368}{411} a^{9} + \\frac{425}{137} a^{8} - \\frac{1894}{411} a^{7} + \\frac{10570}{1233} a^{6} - \\frac{4274}{411} a^{5} + \\frac{3925}{1233} a^{4} + \\frac{2773}{411} a^{3} - \\frac{6698}{1233} a^{2} + \\frac{15}{137} a + \\frac{2431}{1233} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/3*a^10 + 1/3*a^9 - 1/3*a^8 + 1/3*a^7 - 1/3*a^6 - 1/3*a^3 + 1/3*a^2 + 1/3*a - 1/3', '1/1233*a^11 - 130/1233*a^10 + 161/411*a^9 + 104/411*a^8 - 58/411*a^7 - 85/1233*a^6 - 106/411*a^5 - 295/1233*a^4 + 160/411*a^3 - 550/1233*a^2 - 143/411*a + 233/1233']}
  63. label: 12.2.1055385022464.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 6, -17, 30, -34, 12, 30, -64, 66, -44, 20, -6, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1055385022464, 'disc_rad': 186, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 2]]], [7, [[3, 4]]], [11, [[4, 2], [2, 1], [1, 2]]], [13, [[4, 3]]], [17, [[4, 3]]], [19, [[3, 4]]], [23, [[4, 3]]], [29, [[4, 3]]], [31, [0]], [37, [[4, 2], [2, 1], [1, 2]]], [41, [[6, 2]]], [43, [[4, 3]]], [47, [[2, 6]]], [53, [[2, 5], [1, 2]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [288, 96, 96], 'galois_label': '12T100', 'galt': 100, 'grd': 27.27636339397171, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1055385022464.1', 'local_algs': ['2.12.12.11', '3.4.0.1', '3.4.0.1', '3.4.2.2', '31.2.1.1', '31.2.0.1', '31.4.2.1', '31.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 31], 'rd': 10.0450224232, 'regulator': {'__RealLiteral__': 0, 'data': '11.1504023923', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.0.1', '-1.0.1.0.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{159}{83} a^{11} - \\frac{881}{83} a^{10} + \\frac{2787}{83} a^{9} - \\frac{5801}{83} a^{8} + \\frac{8088}{83} a^{7} - \\frac{6981}{83} a^{6} + \\frac{2196}{83} a^{5} + \\frac{2567}{83} a^{4} - \\frac{4383}{83} a^{3} + \\frac{3121}{83} a^{2} - \\frac{1434}{83} a + \\frac{352}{83} \\)', '\\( a \\)', '\\( a^{11} - 5 a^{10} + 15 a^{9} - 29 a^{8} + 37 a^{7} - 27 a^{6} + 3 a^{5} + 15 a^{4} - 19 a^{3} + 11 a^{2} - 6 a \\)', '\\( \\frac{78}{83} a^{11} - \\frac{487}{83} a^{10} + \\frac{1635}{83} a^{9} - \\frac{3610}{83} a^{8} + \\frac{5374}{83} a^{7} - \\frac{5022}{83} a^{6} + \\frac{1948}{83} a^{5} + \\frac{1632}{83} a^{4} - \\frac{3107}{83} a^{3} + \\frac{2253}{83} a^{2} - \\frac{882}{83} a + \\frac{204}{83} \\)', '\\( a^{11} - 6 a^{10} + 20 a^{9} - 44 a^{8} + 66 a^{7} - 64 a^{6} + 30 a^{5} + 12 a^{4} - 34 a^{3} + 30 a^{2} - 16 a + 5 \\)', '\\( \\frac{135}{83} a^{11} - \\frac{795}{83} a^{10} + \\frac{2584}{83} a^{9} - \\frac{5533}{83} a^{8} + \\frac{7954}{83} a^{7} - \\frac{7166}{83} a^{6} + \\frac{2599}{83} a^{5} + \\frac{2250}{83} a^{4} - \\frac{4174}{83} a^{3} + \\frac{3245}{83} a^{2} - \\frac{1584}{83} a + \\frac{468}{83} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/83*a^11 + 31/83*a^10 + 5/83*a^9 - 25/83*a^8 - 29/83*a^7 + 25/83*a^6 - 41/83*a^5 - 11/83*a^4 - 26/83*a^3 - 19/83*a^2 + 27/83*a + 9/83']}
  64. label: 12.2.1105886734375.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 6, -2, -6, 14, -17, 14, -6, -2, 6, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1105886734375, 'disc_rad': 234205, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[12, 1]]], [5, [0]], [7, [[6, 2]]], [11, [[6, 1], [4, 1], [2, 1]]], [13, [[4, 1], [2, 4]]], [17, [[12, 1]]], [19, [[6, 2]]], [23, [[8, 1], [2, 2]]], [29, [[6, 1], [4, 1], [2, 1]]], [31, [0]], [37, [[4, 3]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [[8, 1], [2, 2]]], [47, [[4, 2], [2, 2]]], [53, [[4, 3]]], [59, [[4, 1], [2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 483.9473111817029, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1105886734375.1', 'local_algs': ['5.2.1.1', '5.2.1.1', '5.8.4.1', '31.2.1.2', '31.2.0.1', '31.2.0.1', '31.2.0.1', '31.4.0.1', 'm1511.1.1.0', 'm1511.1.1.0', 'm1511.1.2.0', 'm1511.1.2.0', 'm1511.1.2.0', 'm1511.2.1.1', 'm1511.2.1.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 31, 1511], 'rd': 10.08422562507214, 'regulator': {'__RealLiteral__': 0, 'data': '13.15135974710485', 'prec': 57}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.2.2.-4.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{5}{2} a^{11} - \\frac{15}{2} a^{10} + 7 a^{9} + 3 a^{8} - 12 a^{7} + \\frac{43}{2} a^{6} - 20 a^{5} + 13 a^{4} - \\frac{1}{2} a^{3} - \\frac{13}{2} a^{2} + \\frac{15}{2} a - \\frac{3}{2} \\)', '\\( \\frac{1}{2} a^{11} - \\frac{3}{2} a^{10} + \\frac{3}{2} a^{9} + \\frac{1}{2} a^{8} - \\frac{5}{2} a^{7} + \\frac{9}{2} a^{6} - \\frac{9}{2} a^{5} + \\frac{7}{2} a^{4} + \\frac{1}{2} a^{3} - 2 a^{2} + 2 a - 1 \\)', '\\( \\frac{3}{2} a^{11} - 4 a^{10} + \\frac{5}{2} a^{9} + \\frac{7}{2} a^{8} - \\frac{13}{2} a^{7} + 10 a^{6} - \\frac{15}{2} a^{5} + \\frac{7}{2} a^{4} + 2 a^{3} - 5 a^{2} + \\frac{7}{2} a + \\frac{1}{2} \\)', '\\( -3 a^{11} + 11 a^{10} - 14 a^{9} + \\frac{1}{2} a^{8} + \\frac{37}{2} a^{7} - 35 a^{6} + \\frac{77}{2} a^{5} - \\frac{55}{2} a^{4} + 7 a^{3} + \\frac{19}{2} a^{2} - \\frac{29}{2} a + 6 \\)', '\\( a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^3 - 1/2', '1/2*a^7 - 1/2*a^4 - 1/2*a', '1/2*a^8 - 1/2*a^5 - 1/2*a^2', '1/2*a^9 - 1/2', '1/2*a^10 - 1/2*a', '1/2*a^11 - 1/2*a^2']}
  65. label: 12.2.1173531982847.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -4, 6, 8, -3, -17, -1, 13, 8, -5, -4, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1173531982847, 'disc_rad': 9821, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [[8, 1], [2, 2]]], [7, [0]], [11, [[4, 2], [2, 1], [1, 2]]], [13, [[6, 2]]], [17, [[4, 1], [2, 4]]], [19, [[4, 3]]], [23, [0]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[8, 1], [2, 2]]], [41, [[3, 4]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[6, 2]]], [53, [[4, 1], [2, 4]]], [59, [[4, 2], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [768, 1152, 768], 'galois_label': '12T223', 'galt': 223, 'grd': 217.02502480233522, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1173531982847.1', 'local_algs': ['7.2.0.1', '7.2.0.1', '7.4.0.1', '7.4.2.1', '23.4.0.1', '23.4.2.1', '23.4.3.1', '61.2.0.1', '61.2.1.1', '61.2.1.1', '61.2.0.1', '61.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [7, 23, 61], 'rd': 10.1342413791, 'regulator': {'__RealLiteral__': 0, 'data': '11.435150368', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.0.1.-3.4.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{17} a^{11} + \\frac{7}{17} a^{10} - \\frac{7}{17} a^{9} - \\frac{37}{17} a^{8} - 2 a^{7} + \\frac{56}{17} a^{6} + \\frac{105}{17} a^{5} + \\frac{24}{17} a^{4} - \\frac{89}{17} a^{3} - \\frac{42}{17} a^{2} + \\frac{22}{17} a + \\frac{28}{17} \\)', '\\( \\frac{24}{85} a^{11} - \\frac{12}{85} a^{10} - \\frac{18}{17} a^{9} - \\frac{15}{17} a^{8} + \\frac{11}{5} a^{7} + \\frac{261}{85} a^{6} - \\frac{27}{85} a^{5} - \\frac{352}{85} a^{4} - \\frac{151}{85} a^{3} + \\frac{28}{17} a^{2} + \\frac{74}{85} a - \\frac{48}{85} \\)', '\\( \\frac{12}{85} a^{11} - \\frac{6}{85} a^{10} - \\frac{9}{17} a^{9} - \\frac{16}{17} a^{8} + \\frac{8}{5} a^{7} + \\frac{258}{85} a^{6} + \\frac{29}{85} a^{5} - \\frac{516}{85} a^{4} - \\frac{203}{85} a^{3} + \\frac{48}{17} a^{2} + \\frac{292}{85} a - \\frac{109}{85} \\)', '\\( \\frac{2}{85} a^{11} - \\frac{1}{85} a^{10} - \\frac{10}{17} a^{9} + \\frac{3}{17} a^{8} + \\frac{8}{5} a^{7} + \\frac{128}{85} a^{6} - \\frac{236}{85} a^{5} - \\frac{171}{85} a^{4} + \\frac{37}{85} a^{3} + \\frac{25}{17} a^{2} - \\frac{178}{85} a - \\frac{4}{85} \\)', '\\( \\frac{3}{85} a^{11} - \\frac{44}{85} a^{10} + \\frac{2}{17} a^{9} + \\frac{30}{17} a^{8} + \\frac{7}{5} a^{7} - \\frac{318}{85} a^{6} - \\frac{269}{85} a^{5} + \\frac{211}{85} a^{4} + \\frac{268}{85} a^{3} - \\frac{39}{17} a^{2} - \\frac{97}{85} a + \\frac{79}{85} \\)', '\\( \\frac{41}{85} a^{11} + \\frac{22}{85} a^{10} - \\frac{18}{17} a^{9} - \\frac{66}{17} a^{8} - \\frac{1}{5} a^{7} + \\frac{499}{85} a^{6} + \\frac{687}{85} a^{5} - \\frac{233}{85} a^{4} - \\frac{474}{85} a^{3} - \\frac{40}{17} a^{2} + \\frac{261}{85} a + \\frac{3}{85} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/85*a^11 + 42/85*a^10 - 5/17*a^9 - 7/17*a^8 - 1/5*a^7 - 21/85*a^6 - 33/85*a^5 + 42/85*a^4 - 24/85*a^3 + 4/17*a^2 - 4/85*a - 2/85']}
  66. label: 12.2.1188025263792.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -7, 10, 10, -19, -2, 12, -1, -1, -2, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1188025263792, 'disc_rad': 1374, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 1], [3, 2]]], [7, [[8, 1], [4, 1]]], [11, [[6, 1], [3, 2]]], [13, [[8, 1], [4, 1]]], [17, [[6, 1], [3, 2]]], [19, [[6, 2]]], [23, [[4, 2], [2, 1], [1, 2]]], [29, [[2, 5], [1, 2]]], [31, [[8, 1], [4, 1]]], [37, [[4, 2], [2, 2]]], [41, [[8, 1], [2, 2]]], [43, [[6, 2]]], [47, [[2, 5], [1, 2]]], [53, [[2, 5], [1, 2]]], [59, [[8, 1], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [384, 192, 192], 'galois_label': '12T140', 'galt': 140, 'grd': 52.421369688324624, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1188025263792.1', 'local_algs': ['2.4.4.1', '2.8.0.1', '3.6.3.1', '3.6.0.1', 'm229.1.2.0', 'm229.1.2.0', 'm229.2.4.4'], 'minimal_sibling': [-2, 4, 7, -9, -16, 14, 10, -11, -2, 4, 0, -2, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 229], 'rd': 10.1446127416, 'regulator': {'__RealLiteral__': 0, 'data': '13.0090636733', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-4.0.1', '1.0.-1.-1.-1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{46}{53} a^{11} + \\frac{34}{53} a^{10} - \\frac{83}{53} a^{9} - \\frac{82}{53} a^{8} - \\frac{49}{53} a^{7} + \\frac{525}{53} a^{6} + \\frac{273}{53} a^{5} - \\frac{981}{53} a^{4} - \\frac{60}{53} a^{3} + \\frac{812}{53} a^{2} - \\frac{26}{53} a - \\frac{162}{53} \\)', '\\( \\frac{50}{53} a^{11} + \\frac{7}{53} a^{10} - \\frac{81}{53} a^{9} - \\frac{73}{53} a^{8} - \\frac{74}{53} a^{7} + \\frac{596}{53} a^{6} - \\frac{42}{53} a^{5} - \\frac{746}{53} a^{4} + \\frac{156}{53} a^{3} + \\frac{401}{53} a^{2} + \\frac{4}{53} a - \\frac{130}{53} \\)', '\\( \\frac{36}{53} a^{11} + \\frac{75}{53} a^{10} - \\frac{35}{53} a^{9} - \\frac{131}{53} a^{8} - \\frac{172}{53} a^{7} + \\frac{215}{53} a^{6} + \\frac{663}{53} a^{5} - \\frac{535}{53} a^{4} - \\frac{494}{53} a^{3} + \\frac{541}{53} a^{2} + \\frac{111}{53} a - \\frac{136}{53} \\)', '\\( a \\)', '\\( \\frac{28}{53} a^{11} - \\frac{30}{53} a^{10} - \\frac{92}{53} a^{9} + \\frac{10}{53} a^{8} + \\frac{90}{53} a^{7} + \\frac{497}{53} a^{6} - \\frac{297}{53} a^{5} - \\frac{899}{53} a^{4} + \\frac{505}{53} a^{3} + \\frac{621}{53} a^{2} - \\frac{214}{53} a - \\frac{94}{53} \\)', '\\( \\frac{134}{53} a^{11} + \\frac{76}{53} a^{10} - \\frac{198}{53} a^{9} - \\frac{255}{53} a^{8} - \\frac{334}{53} a^{7} + \\frac{1398}{53} a^{6} + \\frac{498}{53} a^{5} - \\frac{1906}{53} a^{4} + \\frac{134}{53} a^{3} + \\frac{939}{53} a^{2} - \\frac{55}{53} a - \\frac{94}{53} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/53*a^11 - 20/53*a^10 - 26/53*a^9 - 11/53*a^8 + 7/53*a^7 - 22/53*a^6 + 14/53*a^5 + 19/53*a^4 + 1/53*a^3 - 10/53*a^2 - 19/53*a + 8/53']}
  67. label: 12.2.1269624859375.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 5, -6, 3, 1, -3, 1, 3, -6, 5, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1269624859375, 'disc_rad': 250945, 'disc_sign': -1, 'frobs': [[2, [[8, 1], [4, 1]]], [3, [[12, 1]]], [5, [0]], [7, [[4, 2], [2, 2]]], [11, [[6, 1], [3, 2]]], [13, [[8, 1], [2, 2]]], [17, [[12, 1]]], [19, [[6, 1], [4, 1], [1, 2]]], [23, [[4, 3]]], [29, [[6, 1], [3, 2]]], [31, [0]], [37, [[4, 1], [2, 4]]], [41, [[4, 2], [2, 2]]], [43, [[12, 1]]], [47, [[4, 2], [2, 2]]], [53, [[12, 1]]], [59, [[2, 4], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2304, 2304, 2304], 'galois_label': '12T260', 'galt': 260, 'grd': 500.9441086588403, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1269624859375.1', 'local_algs': ['5.12.6.1', '31.1.0.1', '31.1.0.1', '31.1.0.1', '31.1.0.1', '31.2.0.1', '31.2.1.2', '31.4.0.1', 'm1619.1.1.0', 'm1619.1.1.0', 'm1619.2.1.1', 'm1619.2.1.1', 'm1619.1.3.0', 'm1619.1.3.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [5, 31, 1619], 'rd': 10.200926493593379, 'regulator': {'__RealLiteral__': 0, 'data': '11.490317164600082', 'prec': 60}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.-3.-1.5.-2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( -a^{10} + 2 a^{9} - 2 a^{8} + a^{7} + 2 a^{6} - 2 a^{5} + 3 a^{3} - 2 a^{2} + a + 1 \\)', '\\( -a^{11} + 3 a^{10} - 5 a^{9} + 6 a^{8} - 3 a^{7} - a^{6} + 3 a^{5} - a^{4} - 3 a^{3} + 6 a^{2} - 4 a + 2 \\)', '\\( -2 a^{10} + 6 a^{9} - 8 a^{8} + 7 a^{7} - 7 a^{5} + 5 a^{4} + 3 a^{3} - 8 a^{2} + 8 a - 4 \\)', '\\( a^{10} - a^{9} - 2 a^{6} + 2 a^{4} - 2 a^{3} - 1 \\)', '\\( a^{11} - 3 a^{10} + 4 a^{9} - 3 a^{8} - a^{7} + 4 a^{6} - 2 a^{5} - 3 a^{4} + 5 a^{3} - 3 a^{2} + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  68. label: 12.2.1291799785472.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 8, -24, 32, -8, -50, 108, -124, 97, -54, 22, -6, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1291799785472, 'disc_rad': 322, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[4, 3]]], [7, [0]], [11, [[4, 3]]], [13, [[6, 2]]], [17, [[4, 3]]], [19, [[4, 2], [2, 1], [1, 2]]], [23, [0]], [29, [[3, 4]]], [31, [[6, 2]]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[2, 5], [1, 2]]], [47, [[6, 2]]], [53, [[4, 2], [2, 1], [1, 2]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [288, 96, 96], 'galois_label': '12T100', 'galt': 100, 'grd': 35.888716889852724, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1291799785472.1', 'local_algs': ['2.6.6.1', '2.6.6.1', '7.4.0.1', '7.4.0.1', '7.4.2.2', '23.2.1.1', '23.2.0.1', '23.4.2.1', '23.4.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 7, 23], 'rd': 10.215656169035022, 'regulator': {'__RealLiteral__': 0, 'data': '12.864501882713615', 'prec': 60}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.0.0.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 3 a^{11} - \\frac{35}{2} a^{10} + 63 a^{9} - 151 a^{8} + 264 a^{7} - \\frac{647}{2} a^{6} + 262 a^{5} - \\frac{193}{2} a^{4} - 48 a^{3} + \\frac{179}{2} a^{2} - 54 a + 11 \\)', '\\( a \\)', '\\( a^{11} - 6 a^{10} + 22 a^{9} - 54 a^{8} + \\frac{193}{2} a^{7} - \\frac{245}{2} a^{6} + \\frac{207}{2} a^{5} - \\frac{87}{2} a^{4} - 16 a^{3} + 35 a^{2} - \\frac{47}{2} a + \\frac{11}{2} \\)', '\\( -3 a^{11} + 18 a^{10} - \\frac{131}{2} a^{9} + \\frac{319}{2} a^{8} - \\frac{565}{2} a^{7} + \\frac{707}{2} a^{6} - 294 a^{5} + 118 a^{4} + \\frac{91}{2} a^{3} - \\frac{197}{2} a^{2} + 64 a - 15 \\)', '\\( -5 a^{11} + 27 a^{10} - 94 a^{9} + 215 a^{8} - 361 a^{7} + \\frac{831}{2} a^{6} - 311 a^{5} + \\frac{173}{2} a^{4} + 77 a^{3} - 113 a^{2} + 59 a - \\frac{21}{2} \\)', '\\( -\\frac{1}{2} a^{11} + \\frac{5}{2} a^{10} - 8 a^{9} + 16 a^{8} - 22 a^{7} + \\frac{31}{2} a^{6} + 2 a^{5} - \\frac{37}{2} a^{4} + \\frac{31}{2} a^{3} - \\frac{7}{2} a^{2} - \\frac{9}{2} a + 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^4 - 1/2', '1/2*a^7 - 1/2*a^5 - 1/2*a', '1/2*a^8 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/2*a^9 - 1/2*a^5 - 1/2*a^3 - 1/2*a', '1/2*a^10 - 1/2*a^2 - 1/2', '1/2*a^11 - 1/2*a^3 - 1/2*a']}
  69. label: 12.2.1297480511488.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, 3, -8, -5, -12, -11, -16, 1, -4, 5, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1297480511488, 'disc_rad': 434, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[4, 3]]], [5, [[6, 1], [3, 2]]], [7, [0]], [11, [[4, 2], [2, 2]]], [13, [[4, 3]]], [17, [[4, 3]]], [19, [[6, 1], [3, 2]]], [23, [[4, 2], [2, 2]]], [29, [[4, 2], [2, 2]]], [31, [0]], [37, [[2, 4], [1, 4]]], [41, [[6, 1], [3, 2]]], [43, [[4, 2], [2, 2]]], [47, [[4, 2], [2, 1], [1, 2]]], [53, [[4, 2], [2, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [288, 96, 96], 'galois_label': '12T110', 'galt': 110, 'grd': 41.66533331199932, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1297480511488.1', 'local_algs': ['2.6.6.1', '2.6.6.1', '7.3.0.1', '7.3.0.1', '7.6.3.2', '31.1.0.1', '31.1.0.1', '31.2.0.1', '31.8.4.1'], 'minimal_sibling': [1, -2, 7, -5, 6, -2, 3, -1, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 7, 31], 'rd': 10.2193922811, 'regulator': {'__RealLiteral__': 0, 'data': '12.6508432833', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.0.1', '-1.0.1.0.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2766}{17131} a^{11} - \\frac{12835}{34262} a^{10} + \\frac{9924}{17131} a^{9} - \\frac{42413}{17131} a^{8} + \\frac{21969}{34262} a^{7} - \\frac{63239}{34262} a^{6} + \\frac{146929}{34262} a^{5} + \\frac{190079}{34262} a^{4} + \\frac{88663}{17131} a^{3} + \\frac{67401}{34262} a^{2} + \\frac{90751}{34262} a - \\frac{8347}{17131} \\)', '\\( \\frac{33429}{34262} a^{11} + \\frac{11133}{34262} a^{10} + \\frac{77063}{17131} a^{9} - \\frac{85337}{34262} a^{8} - \\frac{34202}{17131} a^{7} - \\frac{252707}{17131} a^{6} - \\frac{246680}{17131} a^{5} - \\frac{335193}{34262} a^{4} - \\frac{58963}{34262} a^{3} - \\frac{93289}{17131} a^{2} + \\frac{13589}{34262} a + \\frac{1613}{17131} \\)', '\\( \\frac{4369}{34262} a^{11} + \\frac{14331}{17131} a^{10} + \\frac{11851}{17131} a^{9} + \\frac{114753}{34262} a^{8} - \\frac{103765}{34262} a^{7} - \\frac{97457}{34262} a^{6} - \\frac{469037}{34262} a^{5} - \\frac{187116}{17131} a^{4} - \\frac{213765}{34262} a^{3} - \\frac{71303}{34262} a^{2} - \\frac{73919}{17131} a + \\frac{32095}{17131} \\)', '\\( \\frac{27203}{34262} a^{11} - \\frac{3224}{17131} a^{10} + \\frac{61955}{17131} a^{9} - \\frac{143875}{34262} a^{8} - \\frac{2253}{34262} a^{7} - \\frac{401435}{34262} a^{6} - \\frac{176347}{34262} a^{5} - \\frac{33960}{17131} a^{4} + \\frac{86451}{34262} a^{3} - \\frac{102217}{34262} a^{2} + \\frac{71367}{17131} a + \\frac{980}{17131} \\)', '\\( \\frac{4073}{34262} a^{11} - \\frac{10570}{17131} a^{10} + \\frac{11529}{34262} a^{9} - \\frac{120567}{34262} a^{8} + \\frac{47269}{34262} a^{7} - \\frac{21848}{17131} a^{6} + \\frac{146193}{17131} a^{5} + \\frac{314079}{34262} a^{4} + \\frac{150064}{17131} a^{3} + \\frac{126129}{34262} a^{2} + \\frac{160557}{34262} a - \\frac{10365}{34262} \\)', '\\( \\frac{15827}{34262} a^{11} - \\frac{5955}{34262} a^{10} + \\frac{69531}{34262} a^{9} - \\frac{91697}{34262} a^{8} - \\frac{1140}{17131} a^{7} - \\frac{213197}{34262} a^{6} - \\frac{65341}{34262} a^{5} + \\frac{6533}{17131} a^{4} + \\frac{37653}{17131} a^{3} - \\frac{43395}{17131} a^{2} + \\frac{16518}{17131} a - \\frac{44163}{34262} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a - 1/2', '1/2*a^10 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^2 - 1/2*a', '1/34262*a^11 + 1673/34262*a^10 + 6581/34262*a^9 + 11907/34262*a^8 + 7095/17131*a^7 + 13419/34262*a^6 - 8765/34262*a^5 - 8426/17131*a^4 - 6453/17131*a^3 - 3343/17131*a^2 + 434/17131*a - 3973/34262']}
  70. label: 12.2.1297573185143.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, -2, 8, -4, -12, 21, -12, -4, 8, -2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1297573185143, 'disc_rad': 10327, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [[4, 3]]], [7, [[4, 3]]], [11, [[4, 2], [2, 1], [1, 2]]], [13, [[6, 2]]], [17, [[4, 3]]], [19, [[4, 2], [2, 1], [1, 2]]], [23, [0]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[6, 2]]], [53, [[4, 3]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [192, 192], 'galois_label': '12T148', 'galt': 148, 'grd': 101.62184804460112, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1297573185143.1', 'local_algs': ['23.1.0.1', '23.1.0.1', '23.2.1.2', '23.4.2.1', '23.4.2.1', 'm449.1.2.0', 'm449.1.2.0', 'm449.1.2.0', 'm449.1.2.0', 'm449.2.1.1', 'm449.2.1.1'], 'minimal_sibling': [1, 1, -2, -4, 1, 5, 1, -5, 1, 4, -2, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [23, 449], 'rd': 10.2194531065, 'regulator': {'__RealLiteral__': 0, 'data': '12.4021804922', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-8.12.-6.1.2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 2 a^{11} - 3 a^{10} - 6 a^{9} + \\frac{27}{2} a^{8} + \\frac{1}{2} a^{7} - 26 a^{6} + \\frac{55}{2} a^{5} - \\frac{11}{2} a^{4} - 14 a^{3} + \\frac{19}{2} a^{2} + \\frac{3}{2} a - 3 \\)', '\\( a^{11} - 2 a^{10} - 2 a^{9} + 8 a^{8} - 4 a^{7} - 12 a^{6} + 21 a^{5} - 12 a^{4} - 4 a^{3} + 8 a^{2} - 2 a - 2 \\)', '\\( \\frac{3}{2} a^{11} - \\frac{5}{2} a^{10} - \\frac{9}{2} a^{9} + 11 a^{8} - \\frac{41}{2} a^{6} + 23 a^{5} - 4 a^{4} - \\frac{25}{2} a^{3} + \\frac{15}{2} a^{2} + \\frac{5}{2} a - 3 \\)', '\\( a^{11} - a^{10} - \\frac{7}{2} a^{9} + 5 a^{8} + \\frac{5}{2} a^{7} - \\frac{23}{2} a^{6} + 9 a^{5} + \\frac{1}{2} a^{4} - \\frac{15}{2} a^{3} + 4 a^{2} + \\frac{1}{2} a - 1 \\)', '\\( \\frac{1}{2} a^{11} + \\frac{1}{2} a^{10} - 2 a^{9} - \\frac{3}{2} a^{8} + \\frac{7}{2} a^{7} - \\frac{1}{2} a^{6} - \\frac{9}{2} a^{5} + \\frac{3}{2} a^{4} + \\frac{3}{2} a^{3} - 3 a^{2} - a + \\frac{1}{2} \\)', '\\( \\frac{5}{2} a^{11} - 3 a^{10} - \\frac{15}{2} a^{9} + 14 a^{8} + \\frac{3}{2} a^{7} - 29 a^{6} + 29 a^{5} - \\frac{11}{2} a^{4} - 15 a^{3} + \\frac{15}{2} a^{2} + \\frac{5}{2} a - \\frac{7}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^3 - 1/2', '1/2*a^7 - 1/2*a^4 - 1/2*a', '1/2*a^8 - 1/2*a^5 - 1/2*a^2', '1/2*a^9 - 1/2', '1/2*a^10 - 1/2*a', '1/2*a^11 - 1/2*a^2']}
  71. label: 12.2.1297573185143.2
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 0, -4, 0, -8, -3, -8, 0, -4, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1297573185143, 'disc_rad': 10327, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [[4, 2], [2, 1], [1, 2]]], [7, [[4, 3]]], [11, [[4, 3]]], [13, [[6, 2]]], [17, [[4, 3]]], [19, [[4, 1], [2, 4]]], [23, [0]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[6, 2]]], [53, [[4, 3]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [192, 192], 'galois_label': '12T148', 'galt': 148, 'grd': 101.62184804460112, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '12.2.1297573185143.2', 'local_algs': ['23.2.1.1', '23.2.0.1', '23.4.2.1', '23.4.2.1', 'm449.1.1.0', 'm449.1.1.0', 'm449.1.1.0', 'm449.1.1.0', 'm449.1.2.0', 'm449.1.2.0', 'm449.2.2.2'], 'minimal_sibling': [1, 1, -2, -4, 1, 5, 1, -5, 1, 4, -2, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [23, 449], 'rd': 10.2194531065, 'regulator': {'__RealLiteral__': 0, 'data': '14.5178310466', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-5.-7.3.7.-1.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{11} + \\frac{1}{2} a^{10} - 2 a^{8} - \\frac{5}{2} a^{7} - 4 a^{6} - 5 a^{5} - \\frac{7}{2} a^{4} - 4 a^{3} - \\frac{1}{2} a^{2} - a + 1 \\)', '\\( a \\)', '\\( \\frac{4}{5} a^{11} - \\frac{1}{5} a^{10} + \\frac{3}{10} a^{9} - \\frac{29}{10} a^{8} + \\frac{1}{10} a^{7} - \\frac{39}{5} a^{6} - \\frac{17}{10} a^{5} - \\frac{51}{10} a^{4} - \\frac{3}{5} a^{3} - \\frac{23}{10} a^{2} + \\frac{7}{10} a + \\frac{17}{10} \\)', '\\( \\frac{1}{5} a^{11} - \\frac{3}{10} a^{10} - \\frac{4}{5} a^{9} - \\frac{11}{10} a^{8} + \\frac{19}{10} a^{7} + \\frac{23}{10} a^{6} + \\frac{27}{10} a^{5} + \\frac{21}{10} a^{4} + \\frac{41}{10} a^{3} + \\frac{23}{10} a^{2} - \\frac{1}{5} a - \\frac{7}{10} \\)', '\\( \\frac{13}{10} a^{11} - \\frac{1}{5} a^{10} - \\frac{7}{10} a^{9} - \\frac{27}{5} a^{8} + \\frac{11}{10} a^{7} - \\frac{34}{5} a^{6} - \\frac{6}{5} a^{5} - \\frac{61}{10} a^{4} + \\frac{7}{5} a^{3} - \\frac{23}{10} a^{2} - \\frac{13}{10} a - \\frac{3}{10} \\)', '\\( \\frac{4}{5} a^{11} + \\frac{3}{10} a^{10} - \\frac{7}{10} a^{9} - \\frac{39}{10} a^{8} - \\frac{9}{10} a^{7} - \\frac{14}{5} a^{6} - \\frac{17}{10} a^{5} - \\frac{31}{10} a^{4} + \\frac{7}{5} a^{3} + \\frac{7}{10} a^{2} - \\frac{4}{5} a - \\frac{13}{10} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^3 - 1/2', '1/2*a^7 - 1/2*a^4 - 1/2*a', '1/2*a^8 - 1/2*a^5 - 1/2*a^2', '1/2*a^9 - 1/2', '1/2*a^10 - 1/2*a', '1/10*a^11 + 1/10*a^10 + 1/10*a^9 + 1/5*a^8 + 1/5*a^7 - 1/10*a^6 - 2/5*a^5 - 1/5*a^4 + 3/10*a^3 - 1/10*a^2 - 1/10*a + 2/5']}
  72. label: 12.2.1379382496000.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 4, -2, -9, 3, 8, 3, -8, -7, 11, -1, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1379382496000, 'disc_rad': 8510, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [0]], [7, [[6, 2]]], [11, [[6, 1], [3, 2]]], [13, [[4, 1], [2, 4]]], [17, [[8, 1], [2, 1], [1, 2]]], [19, [[4, 3]]], [23, [0]], [29, [[4, 2], [2, 2]]], [31, [[4, 2], [2, 2]]], [37, [0]], [41, [[6, 2]]], [43, [[8, 1], [2, 1], [1, 2]]], [47, [[12, 1]]], [53, [[6, 2]]], [59, [[4, 1], [2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2048, 2304, 1536, 1536], 'galois_label': '12T250', 'galt': 250, 'grd': 154.8384970181677, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1379382496000.1', 'local_algs': ['2.12.8.1', '5.4.0.1', '5.4.0.1', '5.4.3.3', '23.2.0.1', '23.2.1.2', '23.4.0.1', '23.4.0.1', '37.2.0.1', '37.2.0.1', '37.4.2.1', '37.4.2.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [2, 5, 23, 37], 'rd': 10.2716542545, 'regulator': {'__RealLiteral__': 0, 'data': '13.7389817612', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-3.-1.1', '1.-1.0.-1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{4}{13} a^{11} - \\frac{30}{13} a^{10} + \\frac{40}{13} a^{9} + \\frac{72}{13} a^{8} - \\frac{170}{13} a^{7} + \\frac{31}{13} a^{6} + \\frac{61}{13} a^{5} + \\frac{76}{13} a^{4} - \\frac{57}{13} a^{3} - \\frac{85}{13} a^{2} + \\frac{43}{13} a + \\frac{24}{13} \\)', '\\( \\frac{2}{13} a^{11} - \\frac{15}{13} a^{10} + \\frac{20}{13} a^{9} + \\frac{36}{13} a^{8} - \\frac{85}{13} a^{7} + \\frac{22}{13} a^{6} + \\frac{24}{13} a^{5} + \\frac{25}{13} a^{4} - \\frac{9}{13} a^{3} - \\frac{49}{13} a^{2} + \\frac{28}{13} a - \\frac{1}{13} \\)', '\\( \\frac{15}{13} a^{11} - \\frac{54}{13} a^{10} + \\frac{7}{13} a^{9} + \\frac{166}{13} a^{8} - \\frac{163}{13} a^{7} - \\frac{43}{13} a^{6} + \\frac{24}{13} a^{5} + \\frac{103}{13} a^{4} + \\frac{17}{13} a^{3} - \\frac{114}{13} a^{2} + \\frac{15}{13} a + \\frac{25}{13} \\)', '\\( \\frac{4}{13} a^{11} - \\frac{4}{13} a^{10} - \\frac{25}{13} a^{9} + \\frac{33}{13} a^{8} + \\frac{38}{13} a^{7} - \\frac{60}{13} a^{6} - \\frac{4}{13} a^{5} - \\frac{2}{13} a^{4} + \\frac{34}{13} a^{3} - \\frac{7}{13} a^{2} - \\frac{22}{13} a + \\frac{11}{13} \\)', '\\( \\frac{5}{13} a^{11} - \\frac{18}{13} a^{10} + \\frac{11}{13} a^{9} + \\frac{38}{13} a^{8} - \\frac{76}{13} a^{7} + \\frac{42}{13} a^{6} + \\frac{8}{13} a^{5} + \\frac{17}{13} a^{4} - \\frac{29}{13} a^{3} - \\frac{25}{13} a^{2} + \\frac{31}{13} a + \\frac{4}{13} \\)', '\\( \\frac{4}{13} a^{11} - \\frac{17}{13} a^{10} + \\frac{14}{13} a^{9} + \\frac{33}{13} a^{8} - \\frac{66}{13} a^{7} + \\frac{44}{13} a^{6} - \\frac{30}{13} a^{5} + \\frac{24}{13} a^{4} - \\frac{5}{13} a^{3} - \\frac{7}{13} a^{2} + \\frac{17}{13} a - \\frac{2}{13} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/13*a^11 - 1/13*a^10 - 3/13*a^9 + 5/13*a^8 + 3/13*a^7 - 2/13*a^6 - 1/13*a^5 + 6/13*a^4 + 2/13*a^3 - 5/13*a^2 + 1/13*a + 6/13']}
  73. label: 12.2.1384093442864.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 5, -10, 15, -14, 5, 3, -3, 1, -3, 5, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1384093442864, 'disc_rad': 1298, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[3, 4]]], [7, [[6, 2]]], [11, [0]], [13, [[4, 2], [2, 1], [1, 2]]], [17, [[4, 2], [2, 2]]], [19, [[3, 4]]], [23, [[4, 1], [2, 4]]], [29, [[6, 2]]], [31, [[4, 2], [2, 1], [1, 2]]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[4, 3]]], [47, [[4, 2], [2, 1], [1, 2]]], [53, [[3, 4]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1536, 768, 1152], 'galois_label': '12T223', 'galt': 223, 'grd': 141.20996551754735, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1384093442864.1', 'local_algs': ['2.4.4.1', '2.8.0.1', '11.2.0.1', '11.2.0.1', '11.4.0.1', '11.4.2.1', '59.4.2.1', '59.4.0.1', '59.4.3.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 11, 59], 'rd': 10.274573050748863, 'regulator': {'__RealLiteral__': 0, 'data': '14.586348633597444', 'prec': 60}, 'subfield_mults': [1, 1], 'subfields': ['-1.2.0.1', '2.-4.-1.5.-2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{393}{425} a^{11} - \\frac{908}{425} a^{10} + \\frac{1314}{425} a^{9} - \\frac{13}{25} a^{8} + \\frac{206}{425} a^{7} - \\frac{1197}{425} a^{6} + \\frac{109}{85} a^{5} + \\frac{466}{85} a^{4} - \\frac{4117}{425} a^{3} + \\frac{2896}{425} a^{2} - \\frac{1468}{425} a + \\frac{744}{425} \\)', '\\( -\\frac{508}{425} a^{11} + \\frac{1268}{425} a^{10} - \\frac{1814}{425} a^{9} + \\frac{28}{25} a^{8} - \\frac{151}{425} a^{7} + \\frac{1642}{425} a^{6} - \\frac{146}{85} a^{5} - \\frac{121}{17} a^{4} + \\frac{5437}{425} a^{3} - \\frac{4261}{425} a^{2} + \\frac{2578}{425} a - \\frac{1194}{425} \\)', '\\( \\frac{362}{425} a^{11} - \\frac{1012}{425} a^{10} + \\frac{1636}{425} a^{9} - \\frac{42}{25} a^{8} + \\frac{209}{425} a^{7} - \\frac{893}{425} a^{6} + \\frac{46}{17} a^{5} + \\frac{417}{85} a^{4} - \\frac{4623}{425} a^{3} + \\frac{4384}{425} a^{2} - \\frac{2327}{425} a + \\frac{806}{425} \\)', '\\( -\\frac{362}{425} a^{11} + \\frac{1012}{425} a^{10} - \\frac{1636}{425} a^{9} + \\frac{42}{25} a^{8} - \\frac{209}{425} a^{7} + \\frac{893}{425} a^{6} - \\frac{46}{17} a^{5} - \\frac{417}{85} a^{4} + \\frac{4623}{425} a^{3} - \\frac{4384}{425} a^{2} + \\frac{2752}{425} a - \\frac{1231}{425} \\)', '\\( -\\frac{517}{425} a^{11} + \\frac{1427}{425} a^{10} - \\frac{2066}{425} a^{9} + \\frac{47}{25} a^{8} + \\frac{61}{425} a^{7} + \\frac{1818}{425} a^{6} - \\frac{186}{85} a^{5} - \\frac{594}{85} a^{4} + \\frac{6598}{425} a^{3} - \\frac{5274}{425} a^{2} + \\frac{2792}{425} a - \\frac{1261}{425} \\)', '\\( -a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/5*a^10 + 1/5*a^9 - 2/5*a^7 - 2/5*a^6 + 2/5*a^5 - 1/5*a^4 - 2/5*a^3 + 2/5*a^2 + 1/5*a + 1/5', '1/425*a^11 + 39/425*a^10 - 57/425*a^9 + 9/25*a^8 + 52/425*a^7 + 56/425*a^6 - 39/85*a^5 - 22/85*a^4 + 41/425*a^3 + 37/425*a^2 - 156/425*a - 172/425']}
  74. label: 12.2.1481617269811.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 2, 2, 6, 4, 9, 0, 10, 2, 1, 4, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1481617269811, 'disc_rad': 41839, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[6, 2]]], [7, [0]], [11, [[6, 2]]], [13, [[4, 1], [2, 3], [1, 2]]], [17, [[6, 1], [3, 2]]], [19, [[12, 1]]], [23, [[6, 1], [3, 2]]], [29, [[4, 1], [2, 1], [1, 6]]], [31, [[6, 2]]], [37, [[6, 2]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [0]], [47, [[3, 4]]], [53, [[6, 1], [3, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1024, 768, 768], 'galois_label': '12T222', 'galt': 222, 'grd': 282.90480334560243, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1481617269811.1', 'local_algs': ['7.6.4.3', '7.6.4.3', '43.1.0.1', '43.1.0.1', '43.2.0.1', '43.2.0.1', '43.2.0.1', '43.4.2.1', '139.1.0.1', '139.1.0.1', '139.2.0.1', '139.2.0.1', '139.2.0.1', '139.2.1.2', '139.2.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [7, 43, 139], 'rd': 10.3330374315, 'regulator': {'__RealLiteral__': 0, 'data': '12.8298526818', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.3.2.-2.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{13} a^{11} - \\frac{3}{13} a^{10} - \\frac{5}{13} a^{8} - \\frac{20}{13} a^{7} - \\frac{10}{13} a^{6} - \\frac{35}{13} a^{5} - \\frac{45}{13} a^{4} - \\frac{31}{13} a^{3} - \\frac{36}{13} a^{2} - \\frac{32}{13} a - \\frac{18}{13} \\)', '\\( a \\)', '\\( \\frac{9}{13} a^{11} - \\frac{2}{13} a^{10} + \\frac{28}{13} a^{9} + \\frac{35}{13} a^{8} + \\frac{22}{13} a^{7} + \\frac{93}{13} a^{6} + \\frac{60}{13} a^{5} + \\frac{57}{13} a^{4} + \\frac{72}{13} a^{3} + \\frac{58}{13} a^{2} + 2 a + \\frac{15}{13} \\)', '\\( \\frac{4}{13} a^{11} - \\frac{1}{13} a^{10} + \\frac{17}{13} a^{9} + \\frac{10}{13} a^{8} + \\frac{25}{13} a^{7} + \\frac{40}{13} a^{6} + \\frac{25}{13} a^{5} + \\frac{55}{13} a^{4} + \\frac{6}{13} a^{3} + \\frac{48}{13} a^{2} + \\frac{6}{13} a + \\frac{9}{13} \\)', '\\( \\frac{3}{13} a^{11} - \\frac{3}{13} a^{10} + \\frac{14}{13} a^{9} - \\frac{1}{13} a^{8} + \\frac{15}{13} a^{7} + \\frac{29}{13} a^{6} - \\frac{2}{13} a^{5} + \\frac{44}{13} a^{4} - \\frac{2}{13} a^{3} + \\frac{31}{13} a^{2} - \\frac{4}{13} a + \\frac{2}{13} \\)', '\\( \\frac{4}{13} a^{11} - \\frac{3}{13} a^{10} + \\frac{8}{13} a^{9} + \\frac{14}{13} a^{8} - a^{7} + \\frac{29}{13} a^{6} + \\frac{8}{13} a^{5} - \\frac{22}{13} a^{4} + \\frac{19}{13} a^{3} - \\frac{7}{13} a^{2} - \\frac{3}{13} a - \\frac{14}{13} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/13*a^10 - 2/13*a^9 - 2/13*a^8 + 6/13*a^7 - 1/13*a^6 + 2/13*a^5 + 6/13*a^4 - 5/13*a^2 - 2/13*a + 5/13', '1/13*a^11 - 6/13*a^9 + 2/13*a^8 - 2/13*a^7 - 3/13*a^5 - 1/13*a^4 - 5/13*a^3 + 1/13*a^2 + 1/13*a - 3/13']}
  75. label: 12.2.1676496367616.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 6, -10, 12, -22, 32, -30, 20, -8, 2, 1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1676496367616, 'disc_rad': 994, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[6, 2]]], [7, [0]], [11, [[6, 1], [3, 2]]], [13, [[4, 2], [2, 1], [1, 2]]], [17, [[6, 1], [3, 2]]], [19, [[3, 4]]], [23, [[6, 1], [3, 2]]], [29, [[4, 1], [2, 3], [1, 2]]], [31, [[6, 1], [3, 2]]], [37, [[3, 4]]], [41, [[4, 1], [2, 4]]], [43, [[4, 2], [2, 2]]], [47, [[6, 1], [3, 2]]], [53, [[6, 1], [3, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1152, 512, 384], 'galois_label': '12T188', 'galt': 188, 'grd': 87.21132026694137, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1676496367616.1', 'local_algs': ['2.12.12.11', '7.3.2.2', '7.3.2.2', '7.6.4.3', '71.1.0.1', '71.1.0.1', '71.2.1.2', '71.4.0.1', '71.4.0.1'], 'minimal_sibling': [1, 0, -2, 0, -5, 0, 4, 0, 2, 0, -2, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 7, 71], 'rd': 10.4399932547, 'regulator': {'__RealLiteral__': 0, 'data': '15.7319845938', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.0.-2.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{38772}{41917} a^{11} - \\frac{60209}{41917} a^{10} + \\frac{14978}{41917} a^{9} + \\frac{78154}{41917} a^{8} - \\frac{271871}{41917} a^{7} + \\frac{665399}{41917} a^{6} - \\frac{895322}{41917} a^{5} + \\frac{899773}{41917} a^{4} - \\frac{527790}{41917} a^{3} + \\frac{314128}{41917} a^{2} - \\frac{259161}{41917} a + \\frac{97317}{41917} \\)', '\\( \\frac{26334}{41917} a^{11} - \\frac{45545}{41917} a^{10} + \\frac{10212}{41917} a^{9} + \\frac{65420}{41917} a^{8} - \\frac{193276}{41917} a^{7} + \\frac{459977}{41917} a^{6} - \\frac{631028}{41917} a^{5} + \\frac{595851}{41917} a^{4} - \\frac{308152}{41917} a^{3} + \\frac{159841}{41917} a^{2} - \\frac{177015}{41917} a + \\frac{99900}{41917} \\)', '\\( \\frac{23088}{41917} a^{11} - \\frac{50150}{41917} a^{10} + \\frac{16288}{41917} a^{9} + \\frac{49095}{41917} a^{8} - \\frac{187283}{41917} a^{7} + \\frac{464784}{41917} a^{6} - \\frac{695691}{41917} a^{5} + \\frac{703453}{41917} a^{4} - \\frac{497097}{41917} a^{3} + \\frac{226704}{41917} a^{2} - \\frac{300315}{41917} a + \\frac{128357}{41917} \\)', '\\( \\frac{7022}{41917} a^{11} - \\frac{2435}{41917} a^{10} + \\frac{3850}{41917} a^{9} + \\frac{6751}{41917} a^{8} - \\frac{40341}{41917} a^{7} + \\frac{85238}{41917} a^{6} - \\frac{86850}{41917} a^{5} + \\frac{149697}{41917} a^{4} - \\frac{68824}{41917} a^{3} + \\frac{90562}{41917} a^{2} - \\frac{47994}{41917} a + \\frac{41308}{41917} \\)', '\\( \\frac{65005}{41917} a^{11} - \\frac{92067}{41917} a^{10} + \\frac{16288}{41917} a^{9} + \\frac{132929}{41917} a^{8} - \\frac{438785}{41917} a^{7} + \\frac{1051622}{41917} a^{6} - \\frac{1366363}{41917} a^{5} + \\frac{1374125}{41917} a^{4} - \\frac{748599}{41917} a^{3} + \\frac{478206}{41917} a^{2} - \\frac{467983}{41917} a + \\frac{170274}{41917} \\)', '\\( \\frac{7625}{41917} a^{11} + \\frac{9229}{41917} a^{10} - \\frac{18121}{41917} a^{9} + \\frac{11372}{41917} a^{8} - \\frac{9726}{41917} a^{7} - \\frac{4409}{41917} a^{6} + \\frac{108830}{41917} a^{5} - \\frac{133416}{41917} a^{4} + \\frac{177914}{41917} a^{3} + \\frac{5503}{41917} a^{2} - \\frac{30745}{41917} a - \\frac{22360}{41917} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/41917*a^11 + 10655/41917*a^10 - 2817/41917*a^9 - 8195/41917*a^8 + 20905/41917*a^7 - 4250/41917*a^6 + 19997/41917*a^5 + 2033/41917*a^4 - 5430/41917*a^3 + 19879/41917*a^2 + 1975/41917*a + 5247/41917']}
  76. label: 12.2.1687248699392.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 10, -16, 19, -28, 28, -28, 19, -16, 10, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1687248699392, 'disc_rad': 46, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[3, 4]]], [5, [[4, 3]]], [7, [[4, 3]]], [11, [[4, 3]]], [13, [[3, 4]]], [17, [[4, 3]]], [19, [[2, 5], [1, 2]]], [23, [0]], [29, [[3, 4]]], [31, [[3, 4]]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[2, 5], [1, 2]]], [47, [[3, 4]]], [53, [[2, 5], [1, 2]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 12], 'galois_label': '12T8', 'galt': 8, 'grd': 13.564659966250536, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1687248699392.1', 'local_algs': ['2.12.18.59', '23.2.1.1', '23.2.0.1', '23.4.2.1', '23.4.2.1'], 'minimal_sibling': [-2, 0, 2, -2, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 23], 'rd': 10.4455567243, 'regulator': {'__RealLiteral__': 0, 'data': '14.3102205078', 'prec': 44}, 'res': {'gal': ['1,-2,8,-22,60,-132,248,-460,826,-1326,1778,-2000,1982,-1758,1308,-690,157,88,-102,50,-18,4,2,-2,1'], 'sib': ['-1,0,0,0,1,0,1', '-2,0,2,-2,1', '1,0,3,0,5,0,5,0,5,0,3,0,1', '23,0,8,0,3,0,1', '26,-32,42,-22,17,-10,8,-4,1']}, 'subfield_mults': [1, 2, 1], 'subfields': ['1.0.-1.1', '-2.0.2.-2.1', '-1.0.0.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{11} - \\frac{3}{2} a^{10} + \\frac{17}{4} a^{9} - 8 a^{8} + 10 a^{7} - \\frac{23}{2} a^{6} + 14 a^{5} - 11 a^{4} + \\frac{39}{4} a^{3} - 4 a^{2} + \\frac{15}{4} a - 1 \\)', '\\( a \\)', '\\( \\frac{1}{4} a^{11} - a^{10} + \\frac{5}{2} a^{9} - \\frac{17}{4} a^{8} + \\frac{11}{2} a^{7} - \\frac{17}{2} a^{6} + \\frac{17}{2} a^{5} - \\frac{15}{2} a^{4} + \\frac{25}{4} a^{3} - \\frac{7}{2} a^{2} + 3 a - \\frac{1}{4} \\)', '\\( 2 a^{11} - 7 a^{10} + \\frac{63}{4} a^{9} - \\frac{85}{4} a^{8} + \\frac{41}{2} a^{7} - \\frac{71}{2} a^{6} + \\frac{55}{2} a^{5} - \\frac{53}{2} a^{4} + \\frac{23}{2} a^{3} - \\frac{29}{2} a^{2} + \\frac{27}{4} a - \\frac{1}{4} \\)', '\\( \\frac{1}{4} a^{11} - a^{10} + \\frac{9}{4} a^{9} - \\frac{13}{4} a^{8} + 3 a^{7} - \\frac{9}{2} a^{6} + 4 a^{5} - \\frac{3}{2} a^{4} + \\frac{7}{4} a^{3} + \\frac{1}{2} a^{2} - \\frac{1}{4} a + \\frac{3}{4} \\)', '\\( \\frac{5}{4} a^{11} - 5 a^{10} + \\frac{49}{4} a^{9} - \\frac{77}{4} a^{8} + 22 a^{7} - \\frac{65}{2} a^{6} + 32 a^{5} - \\frac{59}{2} a^{4} + \\frac{83}{4} a^{3} - \\frac{31}{2} a^{2} + \\frac{43}{4} a - \\frac{13}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/2*a^5 - 1/2*a', '1/2*a^6 - 1/2*a^2', '1/2*a^7 - 1/2*a^3', '1/4*a^8 - 1/4', '1/4*a^9 - 1/4*a', '1/4*a^10 - 1/4*a^2', '1/4*a^11 - 1/4*a^3']}
  77. label: 12.2.1687248699392.2
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 2, 10, -30, 12, 14, -2, -4, -11, 10, 2, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1687248699392, 'disc_rad': 46, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[4, 3]]], [7, [[4, 3]]], [11, [[4, 3]]], [13, [[3, 4]]], [17, [[4, 3]]], [19, [[2, 5], [1, 2]]], [23, [0]], [29, [[3, 4]]], [31, [[6, 2]]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[2, 5], [1, 2]]], [47, [[6, 2]]], [53, [[2, 5], [1, 2]]], [59, [[2, 4], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [84, 24], 'galois_label': '12T22', 'galt': 22, 'grd': 16.131190144457708, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '12.2.1687248699392.2', 'local_algs': ['2.12.18.31', '23.1.0.1', '23.1.0.1', '23.2.1.2', '23.4.2.1', '23.4.2.1'], 'minimal_sibling': [1, 0, 0, 0, -1, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 23], 'rd': 10.4455567243, 'regulator': {'__RealLiteral__': 0, 'data': '14.2298934051', 'prec': 44}, 'res': {'sib': ['-23,0,8,0,-3,0,1', '1,0,0,0,-1,0,1', '1,-2,2,2,-4,2,2,-2,1', '2,12,16,-16,-8,12,-4,-2,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.0.0.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{377}{449} a^{11} - \\frac{1501}{449} a^{10} + \\frac{532}{449} a^{9} + \\frac{4292}{449} a^{8} - \\frac{3791}{449} a^{7} - \\frac{2792}{449} a^{6} - \\frac{1181}{449} a^{5} + \\frac{5873}{449} a^{4} + \\frac{6541}{449} a^{3} - \\frac{11578}{449} a^{2} + \\frac{1366}{449} a + \\frac{933}{449} \\)', '\\( \\frac{338}{449} a^{11} - \\frac{1098}{449} a^{10} - \\frac{3}{449} a^{9} + \\frac{2950}{449} a^{8} - \\frac{1448}{449} a^{7} - \\frac{1760}{449} a^{6} - \\frac{2251}{449} a^{5} + \\frac{2974}{449} a^{4} + \\frac{5276}{449} a^{3} - \\frac{5240}{449} a^{2} + \\frac{48}{449} a - \\frac{77}{449} \\)', '\\( \\frac{17}{449} a^{11} - \\frac{26}{449} a^{10} + \\frac{49}{449} a^{9} - \\frac{290}{449} a^{8} + \\frac{153}{449} a^{7} + \\frac{759}{449} a^{6} - \\frac{351}{449} a^{5} - \\frac{682}{449} a^{4} - \\frac{715}{449} a^{3} + \\frac{1025}{449} a^{2} + \\frac{1012}{449} a - \\frac{688}{449} \\)', '\\( \\frac{7}{449} a^{11} - \\frac{222}{449} a^{10} + \\frac{522}{449} a^{9} + \\frac{356}{449} a^{8} - \\frac{1284}{449} a^{7} - \\frac{427}{449} a^{6} + \\frac{595}{449} a^{5} + \\frac{2017}{449} a^{4} - \\frac{268}{449} a^{3} - \\frac{2404}{449} a^{2} + \\frac{179}{449} a + \\frac{377}{449} \\)', '\\( \\frac{494}{449} a^{11} - \\frac{1812}{449} a^{10} + \\frac{341}{449} a^{9} + \\frac{5175}{449} a^{8} - \\frac{3636}{449} a^{7} - \\frac{3643}{449} a^{6} - \\frac{2012}{449} a^{5} + \\frac{6488}{449} a^{4} + \\frac{8540}{449} a^{3} - \\frac{12183}{449} a^{2} - \\frac{517}{449} a + \\frac{1718}{449} \\)', '\\( \\frac{645}{449} a^{11} - \\frac{2175}{449} a^{10} - \\frac{201}{449} a^{9} + \\frac{6825}{449} a^{8} - \\frac{3175}{449} a^{7} - \\frac{5221}{449} a^{6} - \\frac{3994}{449} a^{5} + \\frac{6637}{449} a^{4} + \\frac{13150}{449} a^{3} - \\frac{12983}{449} a^{2} - \\frac{1723}{449} a + \\frac{1127}{449} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/449*a^11 - 160/449*a^10 - 182/449*a^9 + 115/449*a^8 + 9/449*a^7 - 61/449*a^6 + 85/449*a^5 + 224/449*a^4 + 90/449*a^3 - 151/449*a^2 + 218/449*a + 118/449']}
  78. label: 12.2.1687248699392.3
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 10, -35, 56, -34, -20, 42, -14, -11, 10, -1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1687248699392, 'disc_rad': 46, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[4, 3]]], [7, [[2, 5], [1, 2]]], [11, [[4, 3]]], [13, [[6, 2]]], [17, [[2, 5], [1, 2]]], [19, [[4, 3]]], [23, [0]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[4, 3]]], [47, [[3, 4]]], [53, [[4, 3]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 12], 'galois_label': '12T13', 'galt': 13, 'grd': 13.564659966250536, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '12.2.1687248699392.3', 'local_algs': ['2.12.18.23', '23.2.1.1', '23.2.0.1', '23.4.2.1', '23.4.2.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 23], 'rd': 10.4455567243, 'regulator': {'__RealLiteral__': 0, 'data': '15.4837872745', 'prec': 44}, 'res': {'gal': ['1,0,6,-18,70,-226,509,-916,1470,-2218,3213,-4384,5234,-5126,4098,-2870,1935,-1208,579,-166,20,-10,13,-6,1'], 'sib': ['1,-5,14,-26,37,-39,30,-19,14,-12,9,-4,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-2.0.1', '1.0.-1.1', '-1.-2.3.-2.1', '-8.0.8.0.-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{18232}{2423} a^{11} - \\frac{26262}{2423} a^{10} - \\frac{32880}{2423} a^{9} + \\frac{163560}{2423} a^{8} - \\frac{109106}{2423} a^{7} - \\frac{315047}{2423} a^{6} + \\frac{587338}{2423} a^{5} - \\frac{37511}{2423} a^{4} - \\frac{634036}{2423} a^{3} + \\frac{663275}{2423} a^{2} - \\frac{274506}{2423} a + \\frac{35726}{2423} \\)', '\\( \\frac{12577}{2423} a^{11} - \\frac{21194}{2423} a^{10} - \\frac{20130}{2423} a^{9} + \\frac{120068}{2423} a^{8} - \\frac{98469}{2423} a^{7} - \\frac{213239}{2423} a^{6} + \\frac{461646}{2423} a^{5} - \\frac{90723}{2423} a^{4} - \\frac{471767}{2423} a^{3} + \\frac{545010}{2423} a^{2} - \\frac{247077}{2423} a + \\frac{35672}{2423} \\)', '\\( \\frac{5601}{2423} a^{11} - \\frac{8192}{2423} a^{10} - \\frac{10051}{2423} a^{9} + \\frac{50856}{2423} a^{8} - \\frac{34151}{2423} a^{7} - \\frac{97684}{2423} a^{6} + \\frac{184041}{2423} a^{5} - \\frac{10825}{2423} a^{4} - \\frac{201530}{2423} a^{3} + \\frac{207243}{2423} a^{2} - \\frac{78383}{2423} a + \\frac{7559}{2423} \\)', '\\( \\frac{19135}{2423} a^{11} - \\frac{27597}{2423} a^{10} - \\frac{33457}{2423} a^{9} + \\frac{171798}{2423} a^{8} - \\frac{117310}{2423} a^{7} - \\frac{325319}{2423} a^{6} + \\frac{621331}{2423} a^{5} - \\frac{56347}{2423} a^{4} - \\frac{660387}{2423} a^{3} + \\frac{717470}{2423} a^{2} - \\frac{298491}{2423} a + \\frac{39587}{2423} \\)', '\\( \\frac{16492}{2423} a^{11} - \\frac{24889}{2423} a^{10} - \\frac{28025}{2423} a^{9} + \\frac{150737}{2423} a^{8} - \\frac{109188}{2423} a^{7} - \\frac{279621}{2423} a^{6} + \\frac{555187}{2423} a^{5} - \\frac{69913}{2423} a^{4} - \\frac{582616}{2423} a^{3} + \\frac{645897}{2423} a^{2} - \\frac{277063}{2423} a + \\frac{40369}{2423} \\)', '\\( \\frac{14484}{2423} a^{11} - \\frac{20085}{2423} a^{10} - \\frac{26377}{2423} a^{9} + \\frac{128514}{2423} a^{8} - \\frac{81666}{2423} a^{7} - \\frac{250291}{2423} a^{6} + \\frac{455721}{2423} a^{5} - \\frac{18000}{2423} a^{4} - \\frac{499631}{2423} a^{3} + \\frac{513003}{2423} a^{2} - \\frac{201180}{2423} a + \\frac{22043}{2423} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/2423*a^11 + 1045/2423*a^10 - 1082/2423*a^9 + 1120/2423*a^8 - 103/2423*a^7 + 1180/2423*a^6 - 228/2423*a^5 + 1141/2423*a^4 + 54/2423*a^3 + 865/2423*a^2 - 582/2423*a - 1171/2423']}
  79. label: 12.2.1744787927040.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -4, -7, -4, 3, 8, 8, 2, -3, -6, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1744787927040, 'disc_rad': 2190, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[6, 1], [3, 2]]], [11, [[5, 2], [2, 1]]], [13, [[5, 2], [2, 1]]], [17, [[3, 4]]], [19, [[6, 2]]], [23, [[10, 1], [2, 1]]], [29, [[6, 1], [3, 2]]], [31, [[4, 1], [2, 3], [1, 2]]], [37, [[6, 1], [3, 2]]], [41, [[4, 2], [2, 1], [1, 2]]], [43, [[6, 1], [3, 2]]], [47, [[3, 4]]], [53, [[3, 4]]], [59, [[4, 1], [2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [5760, 1920, 1920, 1920], 'galois_label': '12T255', 'galt': 255, 'grd': 93.59487165438073, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.1744787927040.1', 'local_algs': ['2.12.12.11', '3.2.1.1', '3.5.0.1', '3.5.0.1', '5.2.1.1', '5.10.0.1', '73.1.0.1', '73.1.0.1', '73.2.1.2', '73.2.1.2', '73.2.0.1', '73.4.2.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [2, 3, 5, 73], 'rd': 10.4747874842, 'regulator': {'__RealLiteral__': 0, 'data': '19.965236689', 'prec': 40}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-2.3.-4.4.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{207}{73} a^{11} - \\frac{99}{73} a^{10} + \\frac{41}{73} a^{9} - \\frac{1214}{73} a^{8} - \\frac{15}{73} a^{7} + \\frac{491}{73} a^{6} + \\frac{1199}{73} a^{5} + \\frac{835}{73} a^{4} + \\frac{82}{73} a^{3} - \\frac{772}{73} a^{2} - \\frac{810}{73} a - \\frac{174}{73} \\)', '\\( a \\)', '\\( \\frac{97}{73} a^{11} - \\frac{21}{73} a^{10} - \\frac{9}{73} a^{9} - \\frac{565}{73} a^{8} - \\frac{189}{73} a^{7} + \\frac{332}{73} a^{6} + \\frac{668}{73} a^{5} + \\frac{666}{73} a^{4} + \\frac{55}{73} a^{3} - \\frac{500}{73} a^{2} - \\frac{570}{73} a - \\frac{236}{73} \\)', '\\( \\frac{167}{73} a^{11} - \\frac{64}{73} a^{10} - \\frac{17}{73} a^{9} - \\frac{978}{73} a^{8} - \\frac{138}{73} a^{7} + \\frac{619}{73} a^{6} + \\frac{1132}{73} a^{5} + \\frac{820}{73} a^{4} + \\frac{39}{73} a^{3} - \\frac{912}{73} a^{2} - \\frac{882}{73} a - \\frac{243}{73} \\)', '\\( \\frac{36}{73} a^{11} - \\frac{68}{73} a^{10} + \\frac{23}{73} a^{9} - \\frac{227}{73} a^{8} + \\frac{264}{73} a^{7} + \\frac{133}{73} a^{6} + \\frac{126}{73} a^{5} - \\frac{23}{73} a^{4} - \\frac{173}{73} a^{3} - \\frac{239}{73} a^{2} + \\frac{21}{73} a + \\frac{84}{73} \\)', '\\( \\frac{32}{73} a^{11} - \\frac{28}{73} a^{10} - \\frac{12}{73} a^{9} - \\frac{145}{73} a^{8} + \\frac{40}{73} a^{7} + \\frac{248}{73} a^{6} - \\frac{34}{73} a^{5} + \\frac{85}{73} a^{4} - \\frac{170}{73} a^{3} - \\frac{107}{73} a^{2} - \\frac{30}{73} a + \\frac{99}{73} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/73*a^11 - 10/73*a^10 + 27/73*a^9 + 16/73*a^8 - 17/73*a^7 + 26/73*a^6 - 33/73*a^5 - 27/73*a^4 - 19/73*a^3 - 33/73*a^2 + 31/73*a - 22/73']}
  80. label: 12.2.1815232161643.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 10, -21, 34, -46, 51, -46, 34, -21, 10, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1815232161643, 'disc_rad': 283, 'disc_sign': -1, 'frobs': [[2, [[4, 3]]], [3, [[4, 3]]], [5, [[4, 3]]], [7, [[3, 4]]], [11, [[3, 4]]], [13, [[3, 4]]], [17, [[2, 5], [1, 2]]], [19, [[4, 3]]], [23, [[3, 4]]], [29, [[3, 4]]], [31, [[4, 3]]], [37, [[2, 5], [1, 2]]], [41, [[3, 4]]], [43, [[4, 3]]], [47, [[4, 3]]], [53, [[2, 5], [1, 2]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '12T8', 'galt': 8, 'grd': 16.822603841260722, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1815232161643.1', 'local_algs': ['m283.1.1.0', 'm283.1.1.0', 'm283.2.1.1', 'm283.2.1.1', 'm283.2.1.1', 'm283.2.1.1', 'm283.2.1.1'], 'minimal_sibling': [-1, -1, 0, 0, 1], 'monogenic': 1, 'num_ram': 1, 'r2': 5, 'ramps': [283], 'rd': 10.5093941769, 'regulator': {'__RealLiteral__': 0, 'data': '14.3846253035', 'prec': 44}, 'res': {'gal': ['1,0,16,0,98,0,238,0,249,0,149,0,297,0,85,0,138,0,31,0,22,0,3,0,1'], 'sib': ['-1,-1,0,0,1', '-1,0,-1,-1,1,0,1', '343,297,147,36,-29,-18,-4,0,1', '36,-66,47,-32,24,-34,22,1,10,-10,2,0,1', '6,-7,10,-7,6,-3,1']}, 'subfield_mults': [1, 2, 1], 'subfields': ['-1.4.0.1', '-1.-1.0.0.1', '-1.0.-1.-1.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{9} - 3 a^{8} + 6 a^{7} - 11 a^{6} + 14 a^{5} - 15 a^{4} + 11 a^{3} - 6 a^{2} + 2 a - 1 \\)', '\\( a^{10} - 3 a^{9} + 6 a^{8} - 12 a^{7} + 16 a^{6} - 18 a^{5} + 17 a^{4} - 11 a^{3} + 6 a^{2} - 3 a \\)', '\\( a^{10} - 4 a^{9} + 9 a^{8} - 18 a^{7} + 28 a^{6} - 34 a^{5} + 35 a^{4} - 28 a^{3} + 17 a^{2} - 9 a + 3 \\)', '\\( 2 a^{9} - 6 a^{8} + 12 a^{7} - 23 a^{6} + 30 a^{5} - 33 a^{4} + 27 a^{3} - 16 a^{2} + 7 a - 4 \\)', '\\( a^{11} - 5 a^{10} + 13 a^{9} - 26 a^{8} + 43 a^{7} - 56 a^{6} + 58 a^{5} - 49 a^{4} + 30 a^{3} - 16 a^{2} + 7 a - 2 \\)', '\\( a^{11} - 3 a^{10} + 8 a^{9} - 18 a^{8} + 28 a^{7} - 41 a^{6} + 47 a^{5} - 44 a^{4} + 33 a^{3} - 20 a^{2} + 8 a - 4 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  81. label: 12.2.1815232161643.2
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 5, 0, 3, 5, -11, 14, -16, 12, -8, 5, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1815232161643, 'disc_rad': 283, 'disc_sign': -1, 'frobs': [[2, [[4, 3]]], [3, [[8, 1], [2, 2]]], [5, [[4, 3]]], [7, [[6, 2]]], [11, [[6, 2]]], [13, [[3, 4]]], [17, [[4, 1], [2, 4]]], [19, [[4, 3]]], [23, [[3, 4]]], [29, [[6, 2]]], [31, [[4, 3]]], [37, [[4, 1], [2, 4]]], [41, [[6, 2]]], [43, [[8, 1], [2, 2]]], [47, [[8, 1], [2, 2]]], [53, [[4, 2], [2, 1], [1, 2]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [576], 'galois_label': '12T190', 'galt': 190, 'grd': 68.99852815152498, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '12.2.1815232161643.2', 'local_algs': ['m283.1.1.0', 'm283.1.1.0', 'm283.1.2.0', 'm283.2.1.1', 'm283.2.1.1', 'm283.4.1.3'], 'minimal_sibling': [-107, -11, 196, -196, 30, 25, -38, 26, -12, 3, 2, -2, 1], 'monogenic': 0, 'num_ram': 1, 'r2': 5, 'ramps': [283], 'rd': 10.5093941769, 'regulator': {'__RealLiteral__': 0, 'data': '15.4665830352', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.4.0.1', '-1.0.-1.-1.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{51} a^{11} - \\frac{31}{102} a^{10} + \\frac{61}{102} a^{9} - \\frac{115}{102} a^{8} + \\frac{97}{51} a^{7} - \\frac{245}{102} a^{6} + \\frac{97}{34} a^{5} - \\frac{88}{51} a^{4} + \\frac{12}{17} a^{3} + \\frac{11}{34} a^{2} - \\frac{26}{17} a + \\frac{59}{102} \\)', '\\( \\frac{10}{51} a^{11} - \\frac{35}{102} a^{10} + \\frac{101}{102} a^{9} - \\frac{173}{102} a^{8} + \\frac{152}{51} a^{7} - \\frac{439}{102} a^{6} + \\frac{159}{34} a^{5} - \\frac{260}{51} a^{4} + \\frac{70}{17} a^{3} - \\frac{73}{34} a^{2} + \\frac{15}{17} a + \\frac{139}{102} \\)', '\\( \\frac{16}{51} a^{11} - \\frac{89}{102} a^{10} + \\frac{233}{102} a^{9} - \\frac{395}{102} a^{8} + \\frac{308}{51} a^{7} - \\frac{865}{102} a^{6} + \\frac{299}{34} a^{5} - \\frac{389}{51} a^{4} + \\frac{71}{17} a^{3} - \\frac{1}{2} a^{2} - \\frac{1}{17} a + \\frac{199}{102} \\)', '\\( \\frac{2}{17} a^{11} + \\frac{3}{34} a^{10} - \\frac{7}{34} a^{9} + \\frac{21}{34} a^{8} - \\frac{22}{17} a^{7} + \\frac{61}{34} a^{6} - \\frac{117}{34} a^{5} + \\frac{48}{17} a^{4} - \\frac{32}{17} a^{3} + \\frac{67}{34} a^{2} + \\frac{7}{17} a + \\frac{25}{34} \\)', '\\( \\frac{11}{51} a^{11} - \\frac{49}{102} a^{10} + \\frac{157}{102} a^{9} - \\frac{265}{102} a^{8} + \\frac{211}{51} a^{7} - \\frac{581}{102} a^{6} + \\frac{203}{34} a^{5} - \\frac{17}{3} a^{4} + \\frac{40}{17} a^{3} + \\frac{21}{34} a^{2} - \\frac{10}{17} a + \\frac{215}{102} \\)', '\\( \\frac{8}{51} a^{11} - \\frac{43}{102} a^{10} + \\frac{91}{102} a^{9} - \\frac{181}{102} a^{8} + \\frac{139}{51} a^{7} - \\frac{401}{102} a^{6} + \\frac{145}{34} a^{5} - \\frac{205}{51} a^{4} + \\frac{59}{17} a^{3} - \\frac{39}{34} a^{2} + \\frac{13}{17} a + \\frac{95}{102} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/34*a^10 - 1/2*a^9 + 11/34*a^8 + 7/17*a^7 - 13/34*a^6 - 9/34*a^5 - 7/17*a^4 - 4/17*a^3 + 7/34*a^2 - 7/17*a - 3/34', '1/102*a^11 - 1/102*a^10 - 23/102*a^9 + 10/51*a^8 + 41/102*a^7 - 47/102*a^6 + 2/17*a^5 + 20/51*a^4 + 5/34*a^3 + 5/17*a^2 + 15/34*a + 10/51']}
  82. label: 12.2.1931707442875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 5, 1, -15, 32, -39, 32, -15, 1, 5, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1931707442875, 'disc_rad': 805, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [0]], [11, [[8, 1], [2, 2]]], [13, [[12, 1]]], [17, [[4, 2], [2, 2]]], [19, [[2, 5], [1, 2]]], [23, [0]], [29, [[3, 4]]], [31, [[3, 4]]], [37, [[4, 2], [2, 2]]], [41, [[6, 2]]], [43, [[8, 1], [2, 1], [1, 2]]], [47, [[12, 1]]], [53, [[8, 1], [2, 1], [1, 2]]], [59, [[4, 1], [2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1152, 768, 1152], 'galois_label': '12T225', 'galt': 225, 'grd': 92.91212656206241, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1931707442875.1', 'local_algs': ['5.4.3.4', '5.4.0.1', '5.4.0.1', '7.2.0.1', '7.2.0.1', '7.8.4.1', '23.2.1.2', '23.2.0.1', '23.2.0.1', '23.2.1.2', '23.4.3.1'], 'minimal_sibling': [1, -2, 3, -2, 4, -7, 11, -7, 4, -2, 3, -2, 1], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [5, 7, 23], 'rd': 10.5640013028, 'regulator': {'__RealLiteral__': 0, 'data': '16.4962180483', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.-5.4.-8.4.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 4 a^{11} - 13 a^{10} + 10 a^{9} + 11 a^{8} - 48 a^{7} + 89 a^{6} - 94 a^{5} + 70 a^{4} - 24 a^{3} - 3 a^{2} + 15 a - 8 \\)', '\\( a^{11} - 4 a^{10} + 5 a^{9} + a^{8} - 15 a^{7} + 32 a^{6} - 39 a^{5} + 32 a^{4} - 15 a^{3} + a^{2} + 5 a - 4 \\)', '\\( a^{11} - 3 a^{10} + 3 a^{9} - a^{8} - 9 a^{7} + 27 a^{6} - 36 a^{5} + 34 a^{4} - 17 a^{3} + 2 a^{2} + 7 a - 4 \\)', '\\( 2 a^{11} - 7 a^{10} + 7 a^{9} + 4 a^{8} - 28 a^{7} + 54 a^{6} - 57 a^{5} + 40 a^{4} - 10 a^{3} - 6 a^{2} + 11 a - 4 \\)', '\\( 2 a^{11} - 6 a^{10} + 4 a^{9} + 5 a^{8} - 22 a^{7} + 41 a^{6} - 43 a^{5} + 34 a^{4} - 10 a^{3} - 2 a^{2} + 8 a - 4 \\)', '\\( 4 a^{11} - 13 a^{10} + 12 a^{9} + 6 a^{8} - 49 a^{7} + 101 a^{6} - 112 a^{5} + 87 a^{4} - 28 a^{3} - 5 a^{2} + 20 a - 8 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  83. label: 12.2.1965200244736.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-4, 0, 12, 0, -12, 0, 4, 0, 4, 0, -4, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1965200244736, 'disc_rad': 74, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 1], [3, 2]]], [5, [[8, 1], [4, 1]]], [7, [[6, 1], [3, 2]]], [11, [[6, 1], [3, 2]]], [13, [[8, 1], [4, 1]]], [17, [[8, 1], [4, 1]]], [19, [[8, 1], [2, 2]]], [23, [[4, 2], [2, 1], [1, 2]]], [29, [[4, 2], [2, 2]]], [31, [[2, 5], [1, 2]]], [37, [0]], [41, [[3, 4]]], [43, [[8, 1], [2, 2]]], [47, [[6, 1], [3, 2]]], [53, [[3, 4]]], [59, [[4, 2], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [412, 96], 'galois_label': '12T114', 'galt': 114, 'grd': 26.919132557278957, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1965200244736.1', 'local_algs': ['2.12.20.59', '37.2.0.1', '37.2.0.1', '37.8.4.1'], 'minimal_sibling': [-34, -60, 0, 48, 72, -16, -22, -36, 20, 0, 8, -6, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 37], 'rd': 10.5791449454, 'regulator': {'__RealLiteral__': 0, 'data': '25.049194178', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-3.-1.1', '1.0.-1.-2.-1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{10} - 2 a^{8} + \\frac{3}{2} a^{6} + 3 a^{4} - 6 a^{2} + 4 \\)', '\\( \\frac{1}{4} a^{11} - a^{9} + a^{7} + \\frac{3}{2} a^{5} - 3 a^{3} + 2 a \\)', '\\( \\frac{1}{2} a^{11} - \\frac{1}{4} a^{10} - \\frac{7}{4} a^{9} + a^{8} + a^{7} - a^{6} + 3 a^{5} - a^{4} - \\frac{9}{2} a^{3} + 3 a^{2} + 3 a - 3 \\)', '\\( \\frac{1}{2} a^{10} - \\frac{3}{2} a^{8} + a^{6} + 2 a^{4} - 4 a^{2} + 3 \\)', '\\( \\frac{1}{2} a^{11} - \\frac{1}{4} a^{10} - \\frac{7}{4} a^{9} + \\frac{1}{2} a^{8} + a^{7} + \\frac{1}{2} a^{6} + 3 a^{5} - a^{4} - \\frac{9}{2} a^{3} + 3 a \\)', '\\( \\frac{1}{4} a^{11} - \\frac{1}{4} a^{10} - a^{9} + \\frac{1}{2} a^{8} + a^{7} + a^{5} - \\frac{1}{2} a^{4} - 3 a^{3} + a^{2} + 3 a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6', '1/2*a^7', '1/2*a^8', '1/4*a^9 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3', '1/4*a^10 - 1/2*a^5 - 1/2*a^4', '1/4*a^11 - 1/2*a^5']}
  84. label: 12.2.1980683255808.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -6, -14, -24, -21, -16, 0, -4, 2, -6, 2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1980683255808, 'disc_rad': 138, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 3]]], [7, [[4, 2], [2, 2]]], [11, [[4, 3]]], [13, [[3, 4]]], [17, [[4, 3]]], [19, [[4, 2], [2, 2]]], [23, [0]], [29, [[6, 1], [3, 2]]], [31, [[3, 4]]], [37, [[4, 2], [2, 2]]], [41, [[6, 1], [3, 2]]], [43, [[2, 4], [1, 4]]], [47, [[6, 1], [3, 2]]], [53, [[4, 2], [2, 1], [1, 2]]], [59, [[4, 2], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [360, 96, 96], 'galois_label': '12T110', 'galt': 110, 'grd': 30.468830670705117, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1980683255808.1', 'local_algs': ['2.12.18.33', '3.3.0.1', '3.3.0.1', '3.6.3.2', '23.1.0.1', '23.1.0.1', '23.2.0.1', '23.8.4.1'], 'minimal_sibling': [3, -6, 4, -4, 11, -12, 6, -2, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 23], 'rd': 10.5860657204, 'regulator': {'__RealLiteral__': 0, 'data': '15.2996347166', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.0.0.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{55}{9} a^{11} - 13 a^{10} + \\frac{92}{9} a^{9} - \\frac{245}{9} a^{8} + \\frac{7}{9} a^{7} + \\frac{37}{9} a^{6} - \\frac{223}{9} a^{5} - \\frac{229}{3} a^{4} - 120 a^{3} - \\frac{251}{3} a^{2} - \\frac{386}{9} a - \\frac{58}{9} \\)', '\\( \\frac{155}{9} a^{11} - \\frac{122}{3} a^{10} + \\frac{370}{9} a^{9} - \\frac{859}{9} a^{8} + \\frac{350}{9} a^{7} - \\frac{214}{9} a^{6} - \\frac{344}{9} a^{5} - \\frac{682}{3} a^{4} - \\frac{838}{3} a^{3} - 206 a^{2} - \\frac{784}{9} a - \\frac{110}{9} \\)', '\\( \\frac{56}{9} a^{11} - \\frac{40}{3} a^{10} + \\frac{97}{9} a^{9} - \\frac{256}{9} a^{8} + \\frac{20}{9} a^{7} + \\frac{20}{9} a^{6} - \\frac{206}{9} a^{5} - 80 a^{4} - \\frac{356}{3} a^{3} - \\frac{260}{3} a^{2} - \\frac{382}{9} a - \\frac{68}{9} \\)', '\\( \\frac{113}{9} a^{11} - \\frac{118}{3} a^{10} + \\frac{526}{9} a^{9} - \\frac{982}{9} a^{8} + \\frac{941}{9} a^{7} - \\frac{742}{9} a^{6} + \\frac{196}{9} a^{5} - 171 a^{4} - \\frac{224}{3} a^{3} - \\frac{200}{3} a^{2} + \\frac{26}{9} a + \\frac{28}{9} \\)', '\\( \\frac{7}{9} a^{11} - \\frac{14}{3} a^{10} + \\frac{83}{9} a^{9} - \\frac{113}{9} a^{8} + \\frac{169}{9} a^{7} - \\frac{101}{9} a^{6} + \\frac{35}{9} a^{5} - 6 a^{4} + \\frac{77}{3} a^{3} + \\frac{74}{3} a^{2} + \\frac{166}{9} a + \\frac{41}{9} \\)', '\\( \\frac{13}{9} a^{11} - \\frac{5}{3} a^{10} - \\frac{4}{9} a^{9} - \\frac{44}{9} a^{8} - \\frac{41}{9} a^{7} - \\frac{5}{9} a^{6} - \\frac{25}{9} a^{5} - 24 a^{4} - \\frac{142}{3} a^{3} - \\frac{139}{3} a^{2} - \\frac{224}{9} a - \\frac{55}{9} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/3*a^10 - 1/3*a^9 + 1/3*a^7 + 1/3*a^5 + 1/3*a^4 - 1/3*a^3 + 1/3*a^2 - 1/3*a - 1/3', '1/9*a^11 + 2/9*a^9 - 2/9*a^8 - 2/9*a^7 + 1/9*a^6 + 2/9*a^5 - 1/3*a^4 + 1/3*a^2 + 1/9*a - 4/9']}
  85. label: 12.2.1980683255808.2
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 4, -24, -1, -22, 20, -6, 12, -8, 2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1980683255808, 'disc_rad': 138, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 3]]], [7, [[4, 2], [2, 2]]], [11, [[4, 3]]], [13, [[3, 4]]], [17, [[4, 3]]], [19, [[4, 2], [1, 4]]], [23, [0]], [29, [[6, 1], [3, 2]]], [31, [[6, 2]]], [37, [[4, 2], [2, 2]]], [41, [[6, 1], [3, 2]]], [43, [[2, 6]]], [47, [[6, 1], [3, 2]]], [53, [[4, 2], [2, 1], [1, 2]]], [59, [[4, 2], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [744, 192, 192], 'galois_label': '12T137', 'galt': 137, 'grd': 31.81780105063763, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '12.2.1980683255808.2', 'local_algs': ['2.12.18.47', '3.6.0.1', '3.6.3.1', '23.1.0.1', '23.1.0.1', '23.2.0.1', '23.8.4.1'], 'minimal_sibling': [1, 0, 4, 0, 6, 0, 0, 0, -4, 0, -1, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 23], 'rd': 10.5860657204, 'regulator': {'__RealLiteral__': 0, 'data': '15.9146900417', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.0.0.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3709}{12899} a^{11} - \\frac{6000}{12899} a^{10} + \\frac{2954}{12899} a^{9} - \\frac{25204}{12899} a^{8} + \\frac{36385}{12899} a^{7} - \\frac{2407}{12899} a^{6} + \\frac{59387}{12899} a^{5} - \\frac{74460}{12899} a^{4} - \\frac{23506}{12899} a^{3} - \\frac{81532}{12899} a^{2} + \\frac{18568}{12899} a - \\frac{6927}{12899} \\)', '\\( \\frac{5778}{12899} a^{11} - \\frac{12004}{12899} a^{10} + \\frac{10674}{12899} a^{9} - \\frac{40140}{12899} a^{8} + \\frac{63206}{12899} a^{7} - \\frac{28094}{12899} a^{6} + \\frac{90324}{12899} a^{5} - \\frac{105629}{12899} a^{4} - \\frac{11822}{12899} a^{3} - \\frac{105778}{12899} a^{2} + \\frac{13655}{12899} a + \\frac{1388}{12899} \\)', '\\( \\frac{6150}{12899} a^{11} - \\frac{12884}{12899} a^{10} + \\frac{14375}{12899} a^{9} - \\frac{51404}{12899} a^{8} + \\frac{74562}{12899} a^{7} - \\frac{41690}{12899} a^{6} + \\frac{126036}{12899} a^{5} - \\frac{126869}{12899} a^{4} - \\frac{9422}{12899} a^{3} - \\frac{143878}{12899} a^{2} + \\frac{7435}{12899} a + \\frac{13787}{12899} \\)', '\\( \\frac{747}{12899} a^{11} - \\frac{1351}{12899} a^{10} + \\frac{3791}{12899} a^{9} - \\frac{14713}{12899} a^{8} + \\frac{20307}{12899} a^{7} - \\frac{20228}{12899} a^{6} + \\frac{45914}{12899} a^{5} - \\frac{41403}{12899} a^{4} + \\frac{11893}{12899} a^{3} - \\frac{45300}{12899} a^{2} + \\frac{18301}{12899} a - \\frac{5165}{12899} \\)', '\\( \\frac{4209}{12899} a^{11} - \\frac{6628}{12899} a^{10} + \\frac{3074}{12899} a^{9} - \\frac{25503}{12899} a^{8} + \\frac{31121}{12899} a^{7} + \\frac{5949}{12899} a^{6} + \\frac{55791}{12899} a^{5} - \\frac{49748}{12899} a^{4} - \\frac{45246}{12899} a^{3} - \\frac{91132}{12899} a^{2} - \\frac{17532}{12899} a - \\frac{248}{12899} \\)', '\\( \\frac{5165}{12899} a^{11} - \\frac{9583}{12899} a^{10} + \\frac{8979}{12899} a^{9} - \\frac{37529}{12899} a^{8} + \\frac{47267}{12899} a^{7} - \\frac{10683}{12899} a^{6} + \\frac{83072}{12899} a^{5} - \\frac{67716}{12899} a^{4} - \\frac{46568}{12899} a^{3} - \\frac{112067}{12899} a^{2} - \\frac{24640}{12899} a + \\frac{18301}{12899} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/12899*a^11 + 4436/12899*a^10 + 3096/12899*a^9 + 2605/12899*a^8 + 3498/12899*a^7 - 6278/12899*a^6 + 96/12899*a^5 + 359/12899*a^4 - 6235/12899*a^3 - 2599/12899*a^2 - 2652/12899*a - 5688/12899']}
  86. label: 12.2.1985706421875.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 1, 1, -3, -6, 4, 5, -6, 1, 1, 1, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1985706421875, 'disc_rad': 16995, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [0]], [5, [0]], [7, [[12, 1]]], [11, [0]], [13, [[12, 1]]], [17, [[12, 1]]], [19, [[3, 2], [2, 3]]], [23, [[4, 2], [2, 2]]], [29, [[4, 1], [3, 1], [2, 2], [1, 1]]], [31, [[4, 2], [2, 2]]], [37, [[6, 1], [2, 3]]], [41, [[4, 1], [3, 1], [2, 2], [1, 1]]], [43, [[12, 1]]], [47, [[4, 2], [2, 2]]], [53, [[4, 2], [2, 2]]], [59, [[3, 1], [2, 2], [1, 5]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2592, 2592, 2592, 2592], 'galois_label': '12T267', 'galt': 267, 'grd': 130.3648725692623, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.1985706421875.1', 'local_algs': ['3.2.0.1', '3.2.0.1', '3.4.0.1', '3.4.2.2', '5.12.6.1', '11.2.1.1', '11.4.2.1', '11.6.0.1', '103.2.0.1', '103.2.0.1', '103.4.0.1', '103.4.2.2'], 'minimal_sibling': [1264, 3324, 999, -3502, -1771, 1790, 609, -547, -21, 79, -12, -4, 1], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [3, 5, 11, 103], 'rd': 10.5883003809, 'regulator': {'__RealLiteral__': 0, 'data': '16.9493563775', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.2.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{20}{69} a^{11} - \\frac{7}{69} a^{10} - \\frac{41}{69} a^{9} + \\frac{19}{23} a^{8} + \\frac{37}{69} a^{7} - \\frac{30}{23} a^{6} - \\frac{20}{23} a^{5} + \\frac{78}{23} a^{4} - \\frac{26}{69} a^{3} - \\frac{78}{23} a^{2} + \\frac{6}{23} a + \\frac{2}{23} \\)', '\\( \\frac{9}{23} a^{11} - \\frac{52}{69} a^{10} + \\frac{8}{23} a^{9} + \\frac{13}{23} a^{8} + \\frac{4}{23} a^{7} - \\frac{52}{23} a^{6} + \\frac{149}{69} a^{5} + \\frac{125}{69} a^{4} - \\frac{60}{23} a^{3} - \\frac{56}{69} a^{2} + \\frac{68}{69} a - \\frac{31}{69} \\)', '\\( \\frac{26}{69} a^{11} - \\frac{62}{69} a^{10} + \\frac{64}{69} a^{9} - \\frac{11}{69} a^{8} + \\frac{32}{69} a^{7} - \\frac{163}{69} a^{6} + \\frac{221}{69} a^{5} - \\frac{50}{69} a^{4} - \\frac{89}{69} a^{3} + \\frac{4}{69} a^{2} + \\frac{5}{69} a - \\frac{29}{69} \\)', '\\( \\frac{50}{69} a^{11} - \\frac{52}{69} a^{10} - \\frac{22}{69} a^{9} + \\frac{85}{69} a^{8} + \\frac{27}{23} a^{7} - \\frac{75}{23} a^{6} + \\frac{11}{69} a^{5} + \\frac{126}{23} a^{4} - \\frac{134}{69} a^{3} - \\frac{103}{23} a^{2} - \\frac{70}{69} a + \\frac{5}{23} \\)', '\\( \\frac{4}{23} a^{11} - \\frac{41}{69} a^{10} + \\frac{26}{69} a^{9} + \\frac{2}{69} a^{8} + \\frac{13}{69} a^{7} - \\frac{41}{23} a^{6} + \\frac{125}{69} a^{5} + \\frac{7}{69} a^{4} - \\frac{42}{23} a^{3} - \\frac{76}{69} a^{2} + \\frac{89}{69} a + \\frac{91}{69} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/3*a^8 + 1/3*a^7 - 1/3*a^6 - 1/3*a^4 - 1/3', '1/3*a^9 + 1/3*a^7 + 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a + 1/3', '1/3*a^10 + 1/3*a^5 + 1/3*a^4 - 1/3*a^2 + 1/3*a + 1/3', '1/69*a^11 + 10/69*a^10 + 2/23*a^9 + 4/69*a^8 - 20/69*a^7 + 10/23*a^6 + 20/69*a^5 - 3/23*a^4 - 22/69*a^3 + 3/23*a^2 + 17/69*a + 7/23']}
  87. label: 12.2.2200087036903.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -3, 5, 10, -25, 13, 9, -13, 2, 3, 0, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2200087036903, 'disc_rad': 1981, 'disc_sign': -1, 'frobs': [[2, [[8, 1], [4, 1]]], [3, [[8, 1], [2, 2]]], [5, [[8, 1], [2, 2]]], [7, [0]], [11, [[3, 4]]], [13, [[6, 1], [3, 2]]], [17, [[2, 5], [1, 2]]], [19, [[8, 1], [2, 2]]], [23, [[3, 4]]], [29, [[3, 4]]], [31, [[8, 1], [2, 2]]], [37, [[4, 2], [2, 2]]], [41, [[6, 1], [3, 2]]], [43, [[8, 1], [4, 1]]], [47, [[8, 1], [2, 2]]], [53, [[4, 2], [2, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [96, 96], 'galois_label': '12T114', 'galt': 114, 'grd': 44.50842616853577, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.2200087036903.1', 'local_algs': ['7.3.0.1', '7.3.0.1', '7.6.3.2', 'm283.1.1.0', 'm283.1.1.0', 'm283.1.2.0', 'm283.2.1.1', 'm283.2.1.1', 'm283.2.2.2'], 'minimal_sibling': [16, -19, 180, -1, 757, -238, 624, -141, 188, -18, 23, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [7, 283], 'rd': 10.6791492254, 'regulator': {'__RealLiteral__': 0, 'data': '17.3507619158', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.4.0.1', '-1.0.-1.-1.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - \\frac{77}{51} a^{10} - \\frac{6}{17} a^{9} + \\frac{112}{51} a^{8} + \\frac{143}{51} a^{7} - \\frac{542}{51} a^{6} + \\frac{84}{17} a^{5} + \\frac{565}{51} a^{4} - 18 a^{3} + \\frac{117}{17} a^{2} + \\frac{73}{51} a - \\frac{44}{51} \\)', '\\( \\frac{44}{51} a^{11} - \\frac{139}{51} a^{10} + \\frac{77}{51} a^{9} + \\frac{50}{17} a^{8} - \\frac{8}{17} a^{7} - \\frac{715}{51} a^{6} + \\frac{938}{51} a^{5} + \\frac{320}{51} a^{4} - \\frac{555}{17} a^{3} + \\frac{1358}{51} a^{2} - \\frac{131}{51} a - \\frac{205}{51} \\)', '\\( \\frac{46}{51} a^{11} - \\frac{86}{51} a^{10} + \\frac{16}{51} a^{9} + \\frac{37}{17} a^{8} + \\frac{27}{17} a^{7} - \\frac{542}{51} a^{6} + \\frac{451}{51} a^{5} + \\frac{421}{51} a^{4} - \\frac{360}{17} a^{3} + \\frac{634}{51} a^{2} + \\frac{14}{51} a - \\frac{143}{51} \\)', '\\( \\frac{46}{51} a^{11} - \\frac{86}{51} a^{10} + \\frac{16}{51} a^{9} + \\frac{37}{17} a^{8} + \\frac{27}{17} a^{7} - \\frac{542}{51} a^{6} + \\frac{451}{51} a^{5} + \\frac{421}{51} a^{4} - \\frac{360}{17} a^{3} + \\frac{634}{51} a^{2} + \\frac{14}{51} a - \\frac{92}{51} \\)', '\\( \\frac{22}{51} a^{11} - \\frac{43}{51} a^{10} - \\frac{2}{51} a^{9} + \\frac{55}{51} a^{8} + \\frac{59}{51} a^{7} - \\frac{268}{51} a^{6} + \\frac{169}{51} a^{5} + \\frac{254}{51} a^{4} - \\frac{150}{17} a^{3} + \\frac{232}{51} a^{2} - \\frac{11}{17} a + \\frac{11}{51} \\)', '\\( \\frac{19}{51} a^{11} - \\frac{2}{3} a^{10} - \\frac{14}{51} a^{9} + \\frac{52}{51} a^{8} + \\frac{65}{51} a^{7} - \\frac{244}{51} a^{6} + \\frac{79}{51} a^{5} + \\frac{287}{51} a^{4} - \\frac{111}{17} a^{3} + \\frac{2}{3} a^{2} + \\frac{21}{17} a + \\frac{56}{51} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/51*a^10 - 5/17*a^9 - 20/51*a^8 + 20/51*a^7 + 13/51*a^6 + 2/17*a^5 - 8/51*a^4 + 4/17*a^2 + 7/51*a - 14/51', '1/51*a^11 + 10/51*a^9 - 25/51*a^8 + 7/51*a^7 - 1/17*a^6 - 20/51*a^5 - 6/17*a^4 + 4/17*a^3 - 1/3*a^2 - 11/51*a - 2/17']}
  88. label: 12.2.2233584845312.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 6, -16, 20, -6, -4, 0, 2, -1, 2, 0, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2233584845312, 'disc_rad': 514, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1], [4, 1]]], [5, [[8, 1], [2, 2]]], [7, [[8, 1], [2, 2]]], [11, [[3, 4]]], [13, [[6, 1], [3, 2]]], [17, [[3, 4]]], [19, [[4, 2], [2, 2]]], [23, [[6, 1], [3, 2]]], [29, [[6, 1], [3, 2]]], [31, [[6, 1], [3, 2]]], [37, [[8, 1], [2, 2]]], [41, [[4, 2], [2, 2]]], [43, [[8, 1], [4, 1]]], [47, [[4, 2], [2, 1], [1, 2]]], [53, [[8, 1], [2, 2]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [288, 96], 'galois_label': '12T114', 'galt': 114, 'grd': 45.34313619501854, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.2233584845312.1', 'local_algs': ['2.3.0.1', '2.3.0.1', '2.6.9.5', 'm257.1.2.0', 'm257.1.2.0', 'm257.2.4.4'], 'minimal_sibling': [875, -1738, 1591, -840, 739, -554, 405, -162, -161, 132, -21, -2, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 5, 'ramps': [2, 257], 'rd': 10.6926053494, 'regulator': {'__RealLiteral__': 0, 'data': '18.2043751513', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['3.-4.-1.1', '1.-1.-1.1.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - \\frac{5}{4} a^{10} - a^{9} + \\frac{3}{2} a^{8} + \\frac{1}{4} a^{7} + 2 a^{6} + \\frac{5}{4} a^{5} - \\frac{7}{2} a^{4} - \\frac{17}{2} a^{3} + \\frac{59}{4} a^{2} - \\frac{17}{4} a + \\frac{5}{4} \\)', '\\( \\frac{1}{4} a^{11} - \\frac{1}{4} a^{10} - \\frac{3}{4} a^{9} + \\frac{1}{2} a^{8} + a^{7} + \\frac{3}{4} a^{6} + \\frac{1}{4} a^{5} - \\frac{7}{4} a^{4} - 4 a^{3} + \\frac{13}{4} a^{2} + \\frac{9}{2} a - \\frac{3}{2} \\)', '\\( \\frac{3}{2} a^{11} - \\frac{11}{4} a^{10} - a^{9} + 3 a^{8} - \\frac{1}{4} a^{7} + 3 a^{6} + \\frac{3}{4} a^{5} - 7 a^{4} - 12 a^{3} + \\frac{111}{4} a^{2} - \\frac{61}{4} a + \\frac{13}{4} \\)', '\\( \\frac{3}{4} a^{11} - a^{10} - \\frac{1}{4} a^{9} + a^{8} - \\frac{3}{4} a^{7} + \\frac{5}{4} a^{6} + a^{5} - \\frac{7}{4} a^{4} - \\frac{9}{2} a^{3} + \\frac{23}{2} a^{2} - \\frac{31}{4} a + \\frac{11}{4} \\)', '\\( \\frac{3}{2} a^{11} - \\frac{11}{4} a^{10} - a^{9} + 3 a^{8} - \\frac{1}{4} a^{7} + 3 a^{6} + \\frac{3}{4} a^{5} - 7 a^{4} - 12 a^{3} + \\frac{111}{4} a^{2} - \\frac{61}{4} a + \\frac{17}{4} \\)', '\\( a^{11} - 2 a^{10} + 2 a^{8} - a^{7} + 2 a^{6} - 4 a^{4} - 6 a^{3} + 20 a^{2} - 16 a + 5 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^4 - 1/2', '1/2*a^7 - 1/2*a^5 - 1/2*a', '1/2*a^8 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/4*a^9 - 1/4*a^8 - 1/4*a^7 - 1/4*a^4 - 1/4*a^3 - 1/4*a^2 - 1/2*a - 1/4', '1/4*a^10 - 1/4*a^7 - 1/4*a^5 - 1/2*a^3 - 1/4*a^2 + 1/4*a + 1/4', '1/4*a^11 - 1/4*a^8 - 1/4*a^6 - 1/2*a^4 - 1/4*a^3 + 1/4*a^2 + 1/4*a']}
  89. label: 12.2.2334026173504.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, -7, 0, 3, 0, -9, 0, 5, 0, -3, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2334026173504, 'disc_rad': 874, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 1], [3, 2]]], [5, [[4, 2], [2, 2]]], [7, [[4, 3]]], [11, [[4, 2], [2, 1], [1, 2]]], [13, [[6, 2]]], [17, [[4, 2], [2, 2]]], [19, [0]], [23, [0]], [29, [[6, 2]]], [31, [[6, 1], [3, 2]]], [37, [[4, 2], [2, 2]]], [41, [[6, 2]]], [43, [[4, 3]]], [47, [[6, 1], [3, 2]]], [53, [[4, 2], [2, 2]]], [59, [[4, 2], [2, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [384, 192, 192], 'galois_label': '12T137', 'galt': 137, 'grd': 41.80908992073375, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.2334026173504.1', 'local_algs': ['2.6.6.5', '2.6.0.1', '19.4.0.1', '19.4.2.2', '19.4.2.2', '23.1.0.1', '23.1.0.1', '23.2.0.1', '23.8.4.1'], 'minimal_sibling': [1, -6, 17, -34, 53, -64, 62, -46, 27, -14, 8, -4, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 19, 23], 'rd': 10.7318718186, 'regulator': {'__RealLiteral__': 0, 'data': '18.1806291049', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.-10.0.-2.3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{9} a^{10} - \\frac{4}{9} a^{8} + a^{6} - 2 a^{4} + \\frac{4}{3} a^{2} - \\frac{10}{9} \\)', '\\( a \\)', '\\( \\frac{5}{18} a^{11} + \\frac{2}{9} a^{10} - \\frac{7}{9} a^{9} - \\frac{8}{9} a^{8} + \\frac{4}{3} a^{7} + \\frac{3}{2} a^{6} - \\frac{17}{6} a^{5} - 2 a^{4} + \\frac{7}{6} a^{3} + \\frac{7}{6} a^{2} - \\frac{47}{18} a - \\frac{13}{18} \\)', '\\( \\frac{5}{18} a^{11} - \\frac{2}{9} a^{10} - \\frac{7}{9} a^{9} + \\frac{8}{9} a^{8} + \\frac{4}{3} a^{7} - \\frac{3}{2} a^{6} - \\frac{17}{6} a^{5} + 2 a^{4} + \\frac{7}{6} a^{3} - \\frac{7}{6} a^{2} - \\frac{47}{18} a + \\frac{13}{18} \\)', '\\( \\frac{5}{18} a^{11} + \\frac{1}{9} a^{10} - \\frac{17}{18} a^{9} - \\frac{11}{18} a^{8} + \\frac{5}{3} a^{7} + \\frac{4}{3} a^{6} - \\frac{8}{3} a^{5} - \\frac{11}{6} a^{4} + a^{3} + \\frac{7}{6} a^{2} - \\frac{35}{18} a - \\frac{4}{9} \\)', '\\( \\frac{2}{9} a^{11} + \\frac{1}{6} a^{10} - \\frac{8}{9} a^{9} - \\frac{1}{2} a^{8} + \\frac{3}{2} a^{7} + \\frac{2}{3} a^{6} - 2 a^{5} - \\frac{2}{3} a^{4} + \\frac{7}{6} a^{3} - \\frac{1}{3} a^{2} - \\frac{13}{18} a - \\frac{5}{6} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/3*a^8 + 1/3*a^6 - 1/3*a^4 + 1/3*a^2 - 1/3', '1/6*a^9 - 1/6*a^8 - 1/3*a^7 - 1/6*a^6 - 1/6*a^5 + 1/6*a^4 + 1/6*a^3 + 1/3*a^2 + 1/3*a + 1/6', '1/18*a^10 - 1/18*a^8 - 1/2*a^7 - 1/3*a^6 + 1/3*a^4 - 1/2*a^3 + 1/3*a^2 - 1/2*a + 5/18', '1/18*a^11 - 1/18*a^9 - 1/6*a^8 - 1/3*a^7 + 1/3*a^6 + 1/3*a^5 + 1/6*a^4 + 1/3*a^3 - 1/6*a^2 + 5/18*a - 1/3']}
  90. label: 12.2.2408586330112.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, 2, -4, 9, -16, 18, -16, 9, -4, 2, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2408586330112, 'disc_rad': 86, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[4, 3]]], [5, [[4, 3]]], [7, [[4, 3]]], [11, [[3, 4]]], [13, [[3, 4]]], [17, [[3, 4]]], [19, [[2, 5], [1, 2]]], [23, [[3, 4]]], [29, [[4, 3]]], [31, [[3, 4]]], [37, [[2, 5], [1, 2]]], [41, [[3, 4]]], [43, [0]], [47, [[2, 6]]], [53, [[3, 4]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [28, 12], 'galois_label': '12T8', 'galt': 8, 'grd': 14.720951755301632, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.2408586330112.1', 'local_algs': ['2.12.14.1', '43.1.0.1', '43.1.0.1', '43.2.1.2', '43.2.1.2', '43.2.1.2', '43.2.1.2', '43.2.1.2'], 'minimal_sibling': [-1, -2, 0, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 43], 'rd': 10.7600308898, 'regulator': {'__RealLiteral__': 0, 'data': '28.1348461967', 'prec': 44}, 'res': {'gal': ['16,0,48,0,96,0,128,0,16,0,-80,0,-8,0,-84,0,36,0,-12,0,16,0,0,0,1'], 'sib': ['-1,-2,0,0,1', '10,-2,0,10,4,-2,1', '1,-2,3,-6,3,-2,1', '1,0,3,0,10,0,15,0,10,0,3,0,1', '13,-6,10,-8,7,-4,4,0,1']}, 'subfield_mults': [1, 2, 1], 'subfields': ['3.-1.-1.1', '-1.-2.0.0.1', '1.-2.3.-6.3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{11} - \\frac{5}{3} a^{10} + \\frac{2}{3} a^{9} - 3 a^{8} + \\frac{23}{3} a^{7} - 11 a^{6} + \\frac{29}{3} a^{5} - 6 a^{4} + \\frac{5}{3} a^{3} + a^{2} + \\frac{2}{3} a - \\frac{1}{3} \\)', '\\( a^{11} - \\frac{4}{3} a^{10} + \\frac{2}{3} a^{9} - 3 a^{8} + \\frac{20}{3} a^{7} - 10 a^{6} + \\frac{26}{3} a^{5} - 6 a^{4} + \\frac{2}{3} a^{3} - a^{2} + \\frac{5}{3} a - \\frac{5}{3} \\)', '\\( \\frac{1}{3} a^{10} + \\frac{1}{3} a^{9} - \\frac{1}{3} a^{8} - \\frac{2}{3} a^{7} - \\frac{1}{3} a^{6} + \\frac{1}{3} a^{5} - \\frac{10}{3} a^{4} + \\frac{7}{3} a^{3} - \\frac{10}{3} a^{2} + \\frac{1}{3} a - \\frac{2}{3} \\)', '\\( \\frac{2}{3} a^{10} - 2 a^{7} + 2 a^{6} - 3 a^{5} - 2 a^{3} - a^{2} - a - \\frac{2}{3} \\)', '\\( \\frac{1}{3} a^{10} - a^{7} + a^{6} - 2 a^{5} - a^{3} + a^{2} - 2 a + \\frac{2}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/3*a^8 + 1/3*a^6 + 1/3*a^4 + 1/3*a^2 + 1/3', '1/3*a^9 + 1/3*a^7 + 1/3*a^5 + 1/3*a^3 + 1/3*a', '1/3*a^10 - 1/3', '1/3*a^11 - 1/3*a']}
  91. label: 12.2.2443693379099.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -2, -1, 1, 5, 2, -7, -4, 6, 3, -3, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2443693379099, 'disc_rad': 60557, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[9, 1], [3, 1]]], [5, [[9, 1], [3, 1]]], [7, [0]], [11, [[6, 1], [3, 2]]], [13, [[4, 1], [3, 2], [1, 2]]], [17, [[9, 1], [3, 1]]], [19, [[12, 1]]], [23, [[12, 1]]], [29, [[4, 2], [2, 2]]], [31, [[12, 1]]], [37, [[9, 1], [3, 1]]], [41, [0]], [43, [[4, 2], [3, 1], [1, 1]]], [47, [[6, 1], [3, 2]]], [53, [[12, 1]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36864, 20736, 20736], 'galois_label': '12T292', 'galt': 292, 'grd': 524.4829973100741, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.2443693379099.1', 'local_algs': ['7.3.2.2', '7.9.8.2', '41.1.0.1', '41.1.0.1', '41.1.0.1', '41.2.1.1', '41.3.0.1', '41.4.0.1', 'm211.1.1.0', 'm211.1.1.0', 'm211.1.1.0', 'm211.1.1.0', 'm211.1.1.0', 'm211.1.2.0', 'm211.2.1.1', 'm211.1.3.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 5, 'ramps': [7, 41, 211], 'rd': 10.773014044220586, 'regulator': {'__RealLiteral__': 0, 'data': '19.50697542079606', 'prec': 57}, 'subfield_mults': [1], 'subfields': ['1.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - a^{10} - 3 a^{9} + 3 a^{8} + 6 a^{7} - 4 a^{6} - 7 a^{5} + 2 a^{4} + 5 a^{3} + a^{2} - a - 2 \\)', '\\( 2 a^{11} - 3 a^{10} - 4 a^{9} + 8 a^{8} + 6 a^{7} - 11 a^{6} - 5 a^{5} + 7 a^{4} + 3 a^{3} - a^{2} - a - 3 \\)', '\\( -a^{11} + a^{10} + 2 a^{9} - 2 a^{8} - 4 a^{7} + 2 a^{6} + 4 a^{5} - a^{4} - 3 a^{3} + a + 1 \\)', '\\( -a^{7} + a^{6} + a^{5} - a^{4} - 2 a^{3} + a^{2} \\)', '\\( a^{9} - a^{8} - 2 a^{7} + 2 a^{6} + 3 a^{5} - 2 a^{4} - 2 a^{3} + a^{2} - 1 \\)', '\\( -a^{4} + a^{2} - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  92. label: 12.2.2458624000000.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, 0, 0, -5, 0, -16, 0, 5, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2458624000000, 'disc_rad': 70, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [0]], [7, [0]], [11, [[6, 1], [3, 2]]], [13, [[6, 2]]], [17, [[6, 2]]], [19, [[2, 5], [1, 2]]], [23, [[4, 3]]], [29, [[3, 4]]], [31, [[2, 5], [1, 2]]], [37, [[2, 6]]], [41, [[2, 6]]], [43, [[4, 3]]], [47, [[12, 1]]], [53, [[2, 6]]], [59, [[2, 5], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [80, 24, 24], 'galois_label': '12T28', 'galt': 28, 'grd': 18.782382542440256, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.2458624000000.1', 'local_algs': ['2.12.16.2', '5.4.2.1', '5.4.2.1', '5.4.2.1', '7.4.0.1', '7.8.4.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 5, 7], 'rd': 10.7784838763, 'regulator': {'__RealLiteral__': 0, 'data': '19.8761373413', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '-2.2.0.1', '-1.0.-1.0.1', '1.-1.-2.5.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{11} - \\frac{1}{8} a^{9} + \\frac{5}{2} a^{7} - \\frac{35}{4} a^{5} - \\frac{1}{2} a^{3} + \\frac{3}{8} a \\)', '\\( \\frac{1}{8} a^{8} + \\frac{3}{4} a^{4} - \\frac{3}{2} a^{2} - \\frac{3}{8} \\)', '\\( \\frac{1}{4} a^{10} + \\frac{1}{8} a^{8} + \\frac{5}{4} a^{6} - \\frac{7}{2} a^{4} - 3 a^{2} - \\frac{1}{8} \\)', '\\( \\frac{3}{16} a^{11} - \\frac{3}{16} a^{10} - \\frac{1}{16} a^{9} + \\frac{1}{16} a^{8} + \\frac{7}{8} a^{7} - \\frac{7}{8} a^{6} - \\frac{27}{8} a^{5} + \\frac{27}{8} a^{4} - \\frac{1}{16} a^{3} + \\frac{1}{16} a^{2} + \\frac{23}{16} a - \\frac{7}{16} \\)', '\\( \\frac{7}{16} a^{11} - \\frac{3}{16} a^{10} + \\frac{3}{16} a^{9} + \\frac{1}{16} a^{8} + \\frac{17}{8} a^{7} - \\frac{7}{8} a^{6} - \\frac{49}{8} a^{5} + \\frac{27}{8} a^{4} - \\frac{89}{16} a^{3} + \\frac{1}{16} a^{2} - \\frac{1}{16} a - \\frac{7}{16} \\)', '\\( \\frac{5}{8} a^{11} - \\frac{1}{2} a^{10} + \\frac{1}{4} a^{9} + 3 a^{7} - \\frac{5}{2} a^{6} - \\frac{35}{4} a^{5} + 8 a^{4} - \\frac{61}{8} a^{3} + \\frac{5}{2} a^{2} + \\frac{1}{2} a - \\frac{1}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^4 - 1/2', '1/2*a^5 - 1/2*a', '1/4*a^6 - 1/4*a^4 - 1/4*a^2 + 1/4', '1/4*a^7 - 1/4*a^5 - 1/4*a^3 + 1/4*a', '1/8*a^8 - 1/4*a^4 - 1/2*a^2 - 3/8', '1/8*a^9 - 1/4*a^5 - 1/2*a^2 + 1/8*a - 1/2', '1/8*a^10 - 1/4*a^4 + 3/8*a^2 - 1/4', '1/16*a^11 - 1/16*a^10 - 1/16*a^9 - 1/16*a^8 - 1/8*a^7 - 1/8*a^6 - 1/8*a^5 + 1/8*a^4 + 1/16*a^3 - 5/16*a^2 + 3/16*a + 7/16']}
  93. label: 12.2.2458729426447.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 1, -1, 0, 0, -1, 0, 0, -1, 1, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2458729426447, 'disc_rad': 4148627, 'disc_sign': -1, 'frobs': [[2, [[6, 2]]], [3, [[12, 1]]], [5, [[4, 3]]], [7, [0]], [11, [[8, 1], [4, 1]]], [13, [[10, 1], [1, 2]]], [17, [[12, 1]]], [19, [[12, 1]]], [23, [[6, 2]]], [29, [[6, 2]]], [31, [[4, 2], [2, 1], [1, 2]]], [37, [[6, 1], [2, 3]]], [41, [[12, 1]]], [43, [[5, 2], [1, 2]]], [47, [[6, 1], [2, 2], [1, 2]]], [53, [[5, 2], [1, 2]]], [59, [[6, 1], [2, 2], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [23040, 23040], 'galois_label': '12T293', 'galt': 293, 'grd': 2036.8178612728238, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.2458729426447.1', 'local_algs': ['7.2.0.1', '7.2.0.1', '7.2.1.2', '7.3.0.1', '7.3.0.1', 'm592661.1.2.0', 'm592661.1.2.0', 'm592661.2.1.1', 'm592661.2.1.1', 'm592661.1.4.0'], 'monogenic': 1, 'num_ram': 2, 'r2': 5, 'ramps': [7, 592661], 'rd': 10.7785223909, 'regulator': {'__RealLiteral__': 0, 'data': '18.0616925439', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-2.5.4.-5.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{10} - a^{6} - a^{3} - a \\)', '\\( a^{7} - a^{3} - a \\)', '\\( a^{10} - a^{9} + a^{8} - a^{6} - a^{4} - a^{3} - a + 1 \\)', '\\( a^{9} - a^{8} - a^{3} - 1 \\)', '\\( a^{11} - a^{10} + a^{9} - a^{8} - a^{5} + a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11']}
  94. label: 12.2.2512782950976.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -7, 19, -29, 28, -18, 10, -9, 11, -12, 8, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2512782950976, 'disc_rad': 1542, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1], [4, 1]]], [7, [[8, 1], [2, 2]]], [11, [[6, 1], [3, 2]]], [13, [[3, 4]]], [17, [[6, 2]]], [19, [[2, 5], [1, 2]]], [23, [[6, 1], [3, 2]]], [29, [[6, 2]]], [31, [[6, 1], [3, 2]]], [37, [[8, 1], [4, 1]]], [41, [[4, 2], [1, 4]]], [43, [[8, 1], [2, 2]]], [47, [[2, 5], [1, 2]]], [53, [[8, 1], [4, 1]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [384, 192, 192], 'galois_label': '12T140', 'galt': 140, 'grd': 55.53377350765928, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.2512782950976.1', 'local_algs': ['2.6.6.5', '2.6.0.1', '3.4.2.1', '3.8.0.1', 'm257.1.1.0', 'm257.1.1.0', 'm257.1.1.0', 'm257.1.1.0', 'm257.2.4.4'], 'minimal_sibling': [1, -6, 22, -54, 90, -122, 139, -122, 90, -54, 22, -6, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 257], 'rd': 10.7980727236, 'regulator': {'__RealLiteral__': 0, 'data': '18.3189409677', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['3.-4.-1.1', '1.-1.-1.1.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{154}{67} a^{11} - \\frac{564}{67} a^{10} + \\frac{1052}{67} a^{9} - \\frac{1498}{67} a^{8} + \\frac{1176}{67} a^{7} - \\frac{995}{67} a^{6} + \\frac{1164}{67} a^{5} - \\frac{2439}{67} a^{4} + \\frac{3478}{67} a^{3} - \\frac{3289}{67} a^{2} + \\frac{1758}{67} a - \\frac{420}{67} \\)', '\\( \\frac{241}{67} a^{11} - \\frac{793}{67} a^{10} + \\frac{1367}{67} a^{9} - \\frac{1924}{67} a^{8} + \\frac{1280}{67} a^{7} - \\frac{1253}{67} a^{6} + \\frac{1524}{67} a^{5} - \\frac{3270}{67} a^{4} + \\frac{4410}{67} a^{3} - \\frac{3831}{67} a^{2} + \\frac{1841}{67} a - \\frac{371}{67} \\)', '\\( \\frac{52}{67} a^{11} - \\frac{180}{67} a^{10} + \\frac{350}{67} a^{9} - \\frac{518}{67} a^{8} + \\frac{391}{67} a^{7} - \\frac{376}{67} a^{6} + \\frac{333}{67} a^{5} - \\frac{834}{67} a^{4} + \\frac{1177}{67} a^{3} - \\frac{1168}{67} a^{2} + \\frac{658}{67} a - \\frac{87}{67} \\)', '\\( \\frac{49}{67} a^{11} - \\frac{283}{67} a^{10} + \\frac{621}{67} a^{9} - \\frac{903}{67} a^{8} + \\frac{965}{67} a^{7} - \\frac{545}{67} a^{6} + \\frac{748}{67} a^{5} - \\frac{1242}{67} a^{4} + \\frac{2203}{67} a^{3} - \\frac{2353}{67} a^{2} + \\frac{1473}{67} a - \\frac{359}{67} \\)', '\\( \\frac{160}{67} a^{11} - \\frac{626}{67} a^{10} + \\frac{1180}{67} a^{9} - \\frac{1666}{67} a^{8} + \\frac{1368}{67} a^{7} - \\frac{992}{67} a^{6} + \\frac{1339}{67} a^{5} - \\frac{2628}{67} a^{4} + \\frac{3972}{67} a^{3} - \\frac{3733}{67} a^{2} + \\frac{1870}{67} a - \\frac{412}{67} \\)', '\\( \\frac{154}{67} a^{11} - \\frac{564}{67} a^{10} + \\frac{1052}{67} a^{9} - \\frac{1498}{67} a^{8} + \\frac{1176}{67} a^{7} - \\frac{995}{67} a^{6} + \\frac{1164}{67} a^{5} - \\frac{2439}{67} a^{4} + \\frac{3478}{67} a^{3} - \\frac{3289}{67} a^{2} + \\frac{1758}{67} a - \\frac{353}{67} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/67*a^11 + 12/67*a^10 - 1/67*a^9 - 28/67*a^8 + 32/67*a^7 - 33/67*a^6 + 18/67*a^5 + 2/67*a^4 - 7/67*a^3 - 7/67*a^2 - 26/67*a - 21/67']}
  95. label: 12.2.2558708740096.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 2, -3, 4, -7, 10, -12, 8, 1, -8, 8, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2558708740096, 'disc_rad': 4154, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[5, 2], [2, 1]]], [5, [[4, 2], [2, 2]]], [7, [[10, 1], [2, 1]]], [11, [[4, 3]]], [13, [[5, 2], [2, 1]]], [17, [[10, 1], [1, 2]]], [19, [[5, 2], [1, 2]]], [23, [[8, 1], [2, 2]]], [29, [[5, 2], [2, 1]]], [31, [0]], [37, [[4, 3]]], [41, [[10, 1], [2, 1]]], [43, [[6, 1], [3, 2]]], [47, [[8, 1], [4, 1]]], [53, [[4, 3]]], [59, [[5, 2], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [34560, 11520, 15360], 'galois_label': '12T286', 'galt': 286, 'grd': 259.78199174886123, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.2558708740096.1', 'local_algs': ['2.12.12.11', '31.1.0.1', '31.1.0.1', '31.2.1.2', '31.4.0.1', '31.4.0.1', '67.6.4.3', '67.6.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 31, 67], 'rd': 10.8143827839, 'regulator': {'__RealLiteral__': 0, 'data': '18.2745114334', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-2.1.0.-2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{8}{5} a^{11} - 5 a^{10} + \\frac{39}{5} a^{9} - \\frac{23}{5} a^{8} - \\frac{19}{5} a^{7} + \\frac{43}{5} a^{6} - \\frac{44}{5} a^{5} + \\frac{34}{5} a^{4} - 6 a^{3} + \\frac{12}{5} a^{2} - \\frac{11}{5} a + \\frac{7}{5} \\)', '\\( \\frac{7}{5} a^{11} - 5 a^{10} + \\frac{41}{5} a^{9} - \\frac{27}{5} a^{8} - \\frac{21}{5} a^{7} + \\frac{52}{5} a^{6} - \\frac{46}{5} a^{5} + \\frac{26}{5} a^{4} - 4 a^{3} + \\frac{13}{5} a^{2} - \\frac{14}{5} a + \\frac{8}{5} \\)', '\\( a^{11} - 4 a^{10} + 7 a^{9} - 5 a^{8} - 3 a^{7} + 9 a^{6} - 8 a^{5} + 5 a^{4} - 4 a^{3} + 2 a^{2} - a + 2 \\)', '\\( \\frac{3}{5} a^{11} - 2 a^{10} + \\frac{19}{5} a^{9} - \\frac{13}{5} a^{8} - \\frac{9}{5} a^{7} + \\frac{28}{5} a^{6} - \\frac{24}{5} a^{5} + \\frac{4}{5} a^{4} - a^{3} + \\frac{7}{5} a^{2} - \\frac{6}{5} a + \\frac{2}{5} \\)', '\\( \\frac{1}{5} a^{11} - a^{10} + \\frac{13}{5} a^{9} - \\frac{16}{5} a^{8} + \\frac{7}{5} a^{7} + \\frac{11}{5} a^{6} - \\frac{23}{5} a^{5} + \\frac{18}{5} a^{4} - 3 a^{3} + \\frac{4}{5} a^{2} - \\frac{2}{5} a + \\frac{4}{5} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/5*a^11 - 2/5*a^9 - 1/5*a^8 + 2/5*a^7 + 1/5*a^6 + 2/5*a^5 - 2/5*a^4 - 1/5*a^2 - 2/5*a - 1/5']}
  96. label: 12.2.2928329928704.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, -2, 8, -8, -1, 7, -4, 1, -1, 1, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2928329928704, 'disc_rad': 118, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[3, 4]]], [5, [[6, 2]]], [7, [[6, 2]]], [11, [[4, 3]]], [13, [[2, 5], [1, 2]]], [17, [[2, 6]]], [19, [[3, 4]]], [23, [[4, 3]]], [29, [[6, 2]]], [31, [[4, 3]]], [37, [[4, 3]]], [41, [[3, 4]]], [43, [[4, 3]]], [47, [[2, 5], [1, 2]]], [53, [[6, 2]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 24], 'galois_label': '12T22', 'galt': 22, 'grd': 21.72556098240043, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.2928329928704.1', 'local_algs': ['2.4.0.1', '2.8.12.2', '59.2.1.1', '59.2.0.1', '59.4.2.1', '59.4.2.1'], 'minimal_sibling': [1, -1, 2, 0, 2, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 59], 'rd': 10.9366672924, 'regulator': {'__RealLiteral__': 0, 'data': '19.2003177427', 'prec': 44}, 'res': {'sib': ['-11,19,-16,8,-2,-1,1', '1,-1,2,0,2,-1,1', '1,-2,1,0,1,0,1,-2,1', '3,16,-62,62,-38,16,5,-2,1']}, 'subfield_mults': [1, 1], 'subfields': ['-1.2.0.1', '-4.0.-2.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{363}{509} a^{11} - \\frac{306}{509} a^{10} + \\frac{92}{509} a^{9} - \\frac{378}{509} a^{8} + \\frac{148}{509} a^{7} - \\frac{1454}{509} a^{6} + \\frac{2258}{509} a^{5} + \\frac{652}{509} a^{4} - \\frac{3298}{509} a^{3} + \\frac{1284}{509} a^{2} + \\frac{990}{509} a - \\frac{624}{509} \\)', '\\( a \\)', '\\( \\frac{119}{509} a^{11} - \\frac{155}{509} a^{10} + \\frac{183}{509} a^{9} + \\frac{78}{509} a^{8} + \\frac{228}{509} a^{7} - \\frac{314}{509} a^{6} + \\frac{851}{509} a^{5} - \\frac{385}{509} a^{4} - \\frac{1614}{509} a^{3} + \\frac{1868}{509} a^{2} + \\frac{232}{509} a - \\frac{865}{509} \\)', '\\( \\frac{9}{509} a^{11} - \\frac{16}{509} a^{10} + \\frac{78}{509} a^{9} + \\frac{100}{509} a^{8} + \\frac{214}{509} a^{7} + \\frac{250}{509} a^{6} + \\frac{321}{509} a^{5} - \\frac{89}{509} a^{4} - \\frac{229}{509} a^{3} + \\frac{137}{509} a^{2} - \\frac{577}{509} a + \\frac{157}{509} \\)', '\\( \\frac{452}{509} a^{11} - \\frac{238}{509} a^{10} + \\frac{524}{509} a^{9} - \\frac{294}{509} a^{8} + \\frac{511}{509} a^{7} - \\frac{1753}{509} a^{6} + \\frac{2548}{509} a^{5} - \\frac{115}{509} a^{4} - \\frac{2452}{509} a^{3} + \\frac{2356}{509} a^{2} - \\frac{757}{509} a - \\frac{146}{509} \\)', '\\( \\frac{166}{509} a^{11} - \\frac{182}{509} a^{10} + \\frac{251}{509} a^{9} - \\frac{135}{509} a^{8} + \\frac{271}{509} a^{7} - \\frac{592}{509} a^{6} + \\frac{1170}{509} a^{5} - \\frac{567}{509} a^{4} - \\frac{1396}{509} a^{3} + \\frac{1622}{509} a^{2} - \\frac{519}{509} a + \\frac{68}{509} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/509*a^11 - 228/509*a^10 - 161/509*a^9 - 102/509*a^8 + 250/509*a^7 + 254/509*a^6 - 134/509*a^5 - 123/509*a^4 - 82/509*a^3 - 211/509*a^2 + 49/509*a + 74/509']}
  97. label: 12.2.2938402978819.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 5, -1, -10, 11, 0, -11, 14, -6, -2, 4, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2938402978819, 'disc_rad': 1771, 'disc_sign': -1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [[4, 2], [2, 2]]], [7, [0]], [11, [0]], [13, [[3, 4]]], [17, [[8, 1], [2, 2]]], [19, [[8, 1], [2, 2]]], [23, [0]], [29, [[12, 1]]], [31, [[12, 1]]], [37, [[8, 1], [2, 2]]], [41, [[6, 2]]], [43, [[8, 1], [2, 1], [1, 2]]], [47, [[12, 1]]], [53, [[2, 5], [1, 2]]], [59, [[4, 1], [2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [288, 288, 192], 'galois_label': '12T151', 'galt': 151, 'grd': 124.66138909089473, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.2938402978819.1', 'local_algs': ['7.2.0.1', '7.2.0.1', '7.2.0.1', '7.2.0.1', '7.4.3.2', '11.4.3.2', '11.8.0.1', '23.2.0.1', '23.2.1.1', '23.8.4.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [7, 11, 23], 'rd': 10.9397974125, 'regulator': {'__RealLiteral__': 0, 'data': '19.8237670654', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.0.-1.1', '-1.3.-3.-2.3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{132}{421} a^{11} - \\frac{442}{421} a^{10} + \\frac{631}{421} a^{9} - \\frac{452}{421} a^{8} - \\frac{660}{421} a^{7} + \\frac{2078}{421} a^{6} - \\frac{1921}{421} a^{5} + \\frac{561}{421} a^{4} + \\frac{1046}{421} a^{3} - \\frac{1659}{421} a^{2} + \\frac{6}{421} a + \\frac{390}{421} \\)', '\\( \\frac{131}{421} a^{11} - \\frac{394}{421} a^{10} + \\frac{572}{421} a^{9} - \\frac{321}{421} a^{8} - \\frac{655}{421} a^{7} + \\frac{1839}{421} a^{6} - \\frac{1680}{421} a^{5} + \\frac{241}{421} a^{4} + \\frac{1121}{421} a^{3} - \\frac{1235}{421} a^{2} - \\frac{128}{421} a + \\frac{521}{421} \\)', '\\( \\frac{352}{421} a^{11} - \\frac{898}{421} a^{10} + \\frac{981}{421} a^{9} - \\frac{223}{421} a^{8} - \\frac{2181}{421} a^{7} + \\frac{3717}{421} a^{6} - \\frac{1895}{421} a^{5} - \\frac{1030}{421} a^{4} + \\frac{3070}{421} a^{3} - \\frac{1477}{421} a^{2} - \\frac{1247}{421} a + \\frac{1040}{421} \\)', '\\( \\frac{194}{421} a^{11} - \\frac{471}{421} a^{10} + \\frac{500}{421} a^{9} - \\frac{154}{421} a^{8} - \\frac{970}{421} a^{7} + \\frac{1740}{421} a^{6} - \\frac{865}{421} a^{5} - \\frac{228}{421} a^{4} + \\frac{1027}{421} a^{3} - \\frac{582}{421} a^{2} - \\frac{527}{421} a + \\frac{267}{421} \\)', '\\( \\frac{198}{421} a^{11} - \\frac{663}{421} a^{10} + \\frac{736}{421} a^{9} - \\frac{257}{421} a^{8} - \\frac{1411}{421} a^{7} + \\frac{3117}{421} a^{6} - \\frac{1829}{421} a^{5} - \\frac{632}{421} a^{4} + \\frac{2411}{421} a^{3} - \\frac{2278}{421} a^{2} - \\frac{833}{421} a + \\frac{1006}{421} \\)', '\\( \\frac{398}{421} a^{11} - \\frac{1001}{421} a^{10} + \\frac{1169}{421} a^{9} - \\frac{355}{421} a^{8} - \\frac{2411}{421} a^{7} + \\frac{4186}{421} a^{6} - \\frac{2456}{421} a^{5} - \\frac{624}{421} a^{4} + \\frac{3409}{421} a^{3} - \\frac{1615}{421} a^{2} - \\frac{977}{421} a + \\frac{908}{421} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/421*a^11 - 48/421*a^10 + 59/421*a^9 - 131/421*a^8 - 5/421*a^7 - 182/421*a^6 + 180/421*a^5 - 101/421*a^4 - 75/421*a^3 - 3/421*a^2 + 134/421*a - 131/421']}
  98. label: 12.2.2998803361792.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -2, 3, 6, -6, -14, -20, -12, -4, -2, 2, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2998803361792, 'disc_rad': 1778, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 1], [3, 2]]], [5, [[6, 1], [3, 2]]], [7, [0]], [11, [[3, 4]]], [13, [[4, 1], [2, 3], [1, 2]]], [17, [[6, 2]]], [19, [[3, 4]]], [23, [[6, 1], [3, 2]]], [29, [[4, 1], [2, 4]]], [31, [[6, 2]]], [37, [[3, 4]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[6, 2]]], [53, [[6, 1], [3, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1152, 512, 384], 'galois_label': '12T188', 'galt': 188, 'grd': 116.63947261487952, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.2998803361792.1', 'local_algs': ['2.12.12.11', '7.3.2.2', '7.3.2.2', '7.6.4.3', '127.1.0.1', '127.1.0.1', '127.2.0.1', '127.2.0.1', '127.2.1.2', '127.2.0.1', '127.2.0.1'], 'minimal_sibling': [1, 0, 7, 0, 10, 0, -7, 0, -4, 0, 0, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 7, 127], 'rd': 10.9583625772, 'regulator': {'__RealLiteral__': 0, 'data': '21.9786876084', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-2.-1.1', '-1.0.-2.0.1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{5}{7} a^{11} - \\frac{27}{91} a^{10} + \\frac{158}{91} a^{9} - \\frac{192}{91} a^{8} - \\frac{152}{91} a^{7} - \\frac{733}{91} a^{6} - \\frac{1080}{91} a^{5} - \\frac{674}{91} a^{4} - \\frac{66}{13} a^{3} + \\frac{249}{91} a^{2} - \\frac{25}{91} a - \\frac{88}{91} \\)', '\\( \\frac{122}{91} a^{11} - \\frac{57}{91} a^{10} + \\frac{274}{91} a^{9} - \\frac{360}{91} a^{8} - \\frac{320}{91} a^{7} - \\frac{1296}{91} a^{6} - \\frac{1877}{91} a^{5} - \\frac{911}{91} a^{4} - \\frac{495}{91} a^{3} + \\frac{765}{91} a^{2} - \\frac{150}{91} a - \\frac{30}{13} \\)', '\\( a \\)', '\\( \\frac{16}{91} a^{11} - \\frac{6}{91} a^{10} + \\frac{30}{91} a^{9} - \\frac{51}{91} a^{8} - \\frac{9}{13} a^{7} - \\frac{166}{91} a^{6} - \\frac{253}{91} a^{5} - \\frac{5}{91} a^{4} + \\frac{14}{13} a^{3} + \\frac{46}{13} a^{2} + \\frac{21}{13} a - \\frac{1}{7} \\)', '\\( \\frac{110}{91} a^{11} - \\frac{4}{13} a^{10} + \\frac{235}{91} a^{9} - \\frac{275}{91} a^{8} - \\frac{361}{91} a^{7} - \\frac{1231}{91} a^{6} - \\frac{1952}{91} a^{5} - \\frac{1135}{91} a^{4} - \\frac{579}{91} a^{3} + \\frac{52}{7} a^{2} + \\frac{128}{91} a - \\frac{173}{91} \\)', '\\( \\frac{1}{91} a^{11} - \\frac{1}{13} a^{10} + \\frac{1}{13} a^{9} - \\frac{4}{13} a^{8} + \\frac{25}{91} a^{7} - \\frac{11}{91} a^{6} + \\frac{58}{91} a^{5} + \\frac{21}{13} a^{4} + \\frac{41}{91} a^{3} + \\frac{191}{91} a^{2} - \\frac{89}{91} a + \\frac{15}{91} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/7*a^9 + 3/7*a^8 + 1/7*a^7 + 3/7*a^5 - 2/7*a^4 + 2/7*a^2 - 2/7*a + 1/7', '1/91*a^10 - 2/91*a^9 - 6/13*a^8 + 9/91*a^7 + 31/91*a^6 - 38/91*a^5 + 24/91*a^4 - 19/91*a^3 + 37/91*a^2 + 25/91*a + 23/91', '1/91*a^11 + 6/91*a^9 - 10/91*a^8 + 10/91*a^7 + 24/91*a^6 + 1/7*a^5 + 16/91*a^4 - 1/91*a^3 + 3/13*a^2 - 31/91*a + 1/13']}
  99. label: 12.2.3017909078784.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, -2, 7, -7, 6, 1, -8, 11, -11, 7, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 3017909078784, 'disc_rad': 2622, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[3, 4]]], [7, [[6, 2]]], [11, [[3, 4]]], [13, [[4, 2], [2, 1], [1, 2]]], [17, [[6, 2]]], [19, [0]], [23, [0]], [29, [[8, 1], [2, 2]]], [31, [[4, 3]]], [37, [[4, 1], [2, 4]]], [41, [[4, 1], [2, 4]]], [43, [[6, 2]]], [47, [[6, 2]]], [53, [[4, 3]]], [59, [[4, 1], [2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1024, 768, 1152, 768], 'galois_label': '12T223', 'galt': 223, 'grd': 119.99866371920555, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.3017909078784.1', 'local_algs': ['2.12.8.1', '3.4.2.1', '3.8.0.1', '19.4.3.1', '19.4.0.1', '19.4.2.1', '23.1.0.1', '23.1.0.1', '23.2.1.2', '23.2.1.2', '23.2.0.1', '23.4.0.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 5, 'ramps': [2, 3, 19, 23], 'rd': 10.964163737799463, 'regulator': {'__RealLiteral__': 0, 'data': '20.75361161902643', 'prec': 57}, 'subfield_mults': [1, 1], 'subfields': ['-2.-2.0.1', '-3.9.-8.1.4.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{47}{23} a^{11} - \\frac{112}{23} a^{10} + \\frac{255}{23} a^{9} - \\frac{344}{23} a^{8} + \\frac{270}{23} a^{7} - \\frac{159}{23} a^{6} - \\frac{102}{23} a^{5} + \\frac{245}{23} a^{4} - \\frac{170}{23} a^{3} + \\frac{183}{23} a^{2} + \\frac{61}{23} a - \\frac{73}{23} \\)', '\\( -\\frac{5}{23} a^{11} + \\frac{8}{23} a^{10} - \\frac{10}{23} a^{9} - \\frac{5}{23} a^{8} + \\frac{53}{23} a^{7} - \\frac{79}{23} a^{6} + \\frac{96}{23} a^{5} - \\frac{75}{23} a^{4} - \\frac{1}{23} a^{3} + \\frac{5}{23} a^{2} - \\frac{52}{23} a + \\frac{43}{23} \\)', '\\( -\\frac{36}{23} a^{11} + \\frac{99}{23} a^{10} - \\frac{233}{23} a^{9} + \\frac{355}{23} a^{8} - \\frac{336}{23} a^{7} + \\frac{250}{23} a^{6} - \\frac{8}{23} a^{5} - \\frac{195}{23} a^{4} + \\frac{186}{23} a^{3} - \\frac{217}{23} a^{2} + \\frac{35}{23} a + \\frac{75}{23} \\)', '\\( -\\frac{18}{23} a^{11} + \\frac{38}{23} a^{10} - \\frac{82}{23} a^{9} + \\frac{97}{23} a^{8} - \\frac{53}{23} a^{7} + \\frac{10}{23} a^{6} + \\frac{65}{23} a^{5} - \\frac{86}{23} a^{4} + \\frac{24}{23} a^{3} - \\frac{28}{23} a^{2} - \\frac{40}{23} a + \\frac{26}{23} \\)', '\\( \\frac{29}{23} a^{11} - \\frac{74}{23} a^{10} + \\frac{173}{23} a^{9} - \\frac{247}{23} a^{8} + \\frac{217}{23} a^{7} - \\frac{149}{23} a^{6} - \\frac{37}{23} a^{5} + \\frac{159}{23} a^{4} - \\frac{146}{23} a^{3} + \\frac{155}{23} a^{2} - \\frac{2}{23} a - \\frac{47}{23} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/23*a^11 + 3/23*a^10 + 2/23*a^9 + 1/23*a^8 - 6/23*a^7 + 2/23*a^6 - 10/23*a^5 - 8/23*a^4 - 9/23*a^3 - 1/23*a^2 - 8/23*a - 4/23']}
  100. label: 12.2.3110228525056.1
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 0, -5, 0, -12, 0, -5, 0, 0, 0, -1, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 3110228525056, 'disc_rad': 166, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[6, 1], [3, 2]]], [5, [[8, 1], [4, 1]]], [7, [[6, 1], [3, 2]]], [11, [[6, 1], [3, 2]]], [13, [[8, 1], [4, 1]]], [17, [[3, 4]]], [19, [[8, 1], [2, 2]]], [23, [[2, 5], [1, 2]]], [29, [[3, 4]]], [31, [[6, 1], [3, 2]]], [37, [[3, 4]]], [41, [[4, 2], [2, 2]]], [43, [[4, 2], [2, 1], [1, 2]]], [47, [[8, 1], [2, 2]]], [53, [[4, 2], [2, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [336, 96], 'galois_label': '12T114', 'galt': 114, 'grd': 30.643723752438035, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.2.3110228525056.1', 'local_algs': ['2.4.4.4', '2.8.12.19', '83.1.0.1', '83.1.0.1', '83.2.0.1', '83.4.2.1', '83.4.2.1'], 'minimal_sibling': [25, 0, 51, 0, 12, 0, -6, 0, 4, 0, 5, 0, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 5, 'ramps': [2, 83], 'rd': 10.9917293202, 'regulator': {'__RealLiteral__': 0, 'data': '26.7827438496', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-2.1.-1.1', '-1.0.2.0.2.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{4} a^{11} - \\frac{5}{4} a^{9} + \\frac{3}{4} a^{7} - \\frac{17}{4} a^{5} - \\frac{25}{4} a^{3} + \\frac{3}{4} a \\)', '\\( \\frac{1}{2} a^{10} - \\frac{3}{4} a^{8} + \\frac{1}{2} a^{6} - \\frac{11}{4} a^{4} - \\frac{9}{2} a^{2} - \\frac{3}{4} \\)', '\\( \\frac{1}{4} a^{10} - \\frac{1}{4} a^{8} - \\frac{1}{4} a^{6} - \\frac{3}{4} a^{4} - \\frac{13}{4} a^{2} - \\frac{1}{4} \\)', '\\( \\frac{1}{4} a^{11} + \\frac{1}{8} a^{10} - \\frac{1}{8} a^{9} - \\frac{1}{8} a^{8} - \\frac{1}{4} a^{7} - \\frac{1}{8} a^{6} - \\frac{7}{8} a^{5} - \\frac{5}{8} a^{4} - 4 a^{3} - \\frac{11}{8} a^{2} - \\frac{19}{8} a + \\frac{1}{8} \\)', '\\( a^{11} - \\frac{1}{8} a^{10} - \\frac{11}{8} a^{9} + \\frac{3}{8} a^{8} + \\frac{1}{2} a^{7} - \\frac{3}{8} a^{6} - \\frac{41}{8} a^{5} + \\frac{7}{8} a^{4} - \\frac{41}{4} a^{3} + \\frac{3}{8} a^{2} - \\frac{5}{8} a - \\frac{11}{8} \\)', '\\( a^{11} - \\frac{1}{8} a^{10} - \\frac{11}{8} a^{9} + \\frac{3}{8} a^{8} + \\frac{1}{2} a^{7} - \\frac{3}{8} a^{6} - \\frac{41}{8} a^{5} + \\frac{7}{8} a^{4} - \\frac{41}{4} a^{3} + \\frac{3}{8} a^{2} - \\frac{13}{8} a - \\frac{11}{8} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^2 - 1/2', '1/2*a^5 - 1/2*a^3 - 1/2*a', '1/2*a^6 - 1/2', '1/2*a^7 - 1/2*a', '1/4*a^8 - 1/4*a^4 - 1/2*a^2 - 1/4', '1/4*a^9 - 1/4*a^5 - 1/2*a^3 - 1/4*a', '1/8*a^10 - 1/8*a^9 - 1/8*a^8 - 1/8*a^6 + 1/8*a^5 - 1/8*a^4 - 1/4*a^3 + 1/8*a^2 + 1/8*a - 3/8', '1/8*a^11 - 1/8*a^8 - 1/8*a^7 - 1/4*a^5 + 1/8*a^4 + 3/8*a^3 - 1/4*a^2 - 1/2*a + 1/8']}