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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [18, 54, -100, 64, -15, 11, 28, -28, 2, 4, 2, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 280755374552129536, 'disc_rad': 34, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1], [2, 2]]], [5, [[8, 1], [4, 1]]], [7, [[6, 2]]], [11, [[4, 3]]], [13, [[2, 3], [1, 6]]], [17, [0]], [19, [[3, 2], [2, 2], [1, 2]]], [23, [[4, 2], [2, 2]]], [29, [[4, 2], [2, 2]]], [31, [[6, 2]]], [37, [[8, 1], [4, 1]]], [41, [[12, 1]]], [43, [[4, 1], [2, 1], [1, 6]]], [47, [[6, 1], [3, 2]]], [53, [[6, 1], [4, 1], [2, 1]]], [59, [[6, 1], [2, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [13824, 4224], 'galois_label': '12T260', 'galt': 260, 'grd': 107.39931174612445, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.280755374552129536.1', 'local_algs': ['2.2.2.1', '2.3.0.1', '2.3.0.1', '2.4.11.2', '17.12.11.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 5, 'ramps': [2, 17], 'rd': 28.4464017887, 'regulator': {'__RealLiteral__': 0, 'data': '23296.9609907', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-4.-1.1', '-2.4.-9.4.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{12615601}{1422191069} a^{11} - \\frac{50780525}{1422191069} a^{10} + \\frac{51840453}{1422191069} a^{9} + \\frac{70510948}{1422191069} a^{8} - \\frac{58711529}{1422191069} a^{7} - \\frac{479950585}{1422191069} a^{6} + \\frac{751624175}{1422191069} a^{5} + \\frac{368998160}{1422191069} a^{4} - \\frac{930547090}{1422191069} a^{3} + \\frac{741701583}{1422191069} a^{2} - \\frac{407644685}{1422191069} a + \\frac{533544149}{1422191069} \\)', '\\( \\frac{110261017}{4266573207} a^{11} - \\frac{84711694}{1422191069} a^{10} - \\frac{11647294}{4266573207} a^{9} + \\frac{536419795}{4266573207} a^{8} + \\frac{683883071}{4266573207} a^{7} - \\frac{2883301792}{4266573207} a^{6} + \\frac{452294680}{4266573207} a^{5} + \\frac{2777064065}{4266573207} a^{4} + \\frac{559006150}{1422191069} a^{3} + \\frac{4462154461}{4266573207} a^{2} - \\frac{7096169989}{4266573207} a + \\frac{302560857}{1422191069} \\)', '\\( \\frac{65854454}{1422191069} a^{11} - \\frac{248900160}{1422191069} a^{10} + \\frac{264450274}{1422191069} a^{9} + \\frac{167100822}{1422191069} a^{8} - \\frac{79659883}{1422191069} a^{7} - \\frac{1872546570}{1422191069} a^{6} + \\frac{3047350165}{1422191069} a^{5} - \\frac{970620193}{1422191069} a^{4} - \\frac{1202757984}{1422191069} a^{3} + \\frac{6607378136}{1422191069} a^{2} - \\frac{11075710637}{1422191069} a + \\frac{4050078917}{1422191069} \\)', '\\( \\frac{19970948}{1422191069} a^{11} - \\frac{71872799}{1422191069} a^{10} + \\frac{97433807}{1422191069} a^{9} + \\frac{26958628}{1422191069} a^{8} - \\frac{6994685}{1422191069} a^{7} - \\frac{571208224}{1422191069} a^{6} + \\frac{809131867}{1422191069} a^{5} - \\frac{470885093}{1422191069} a^{4} + \\frac{546279421}{1422191069} a^{3} + \\frac{2393460347}{1422191069} a^{2} - \\frac{4209333813}{1422191069} a + \\frac{2102765053}{1422191069} \\)', '\\( \\frac{174265933}{4266573207} a^{11} - \\frac{73356811}{1422191069} a^{10} - \\frac{275824858}{4266573207} a^{9} + \\frac{574490977}{4266573207} a^{8} + \\frac{1531171334}{4266573207} a^{7} - \\frac{3123019525}{4266573207} a^{6} - \\frac{2009544305}{4266573207} a^{5} + \\frac{2536041323}{4266573207} a^{4} + \\frac{683077724}{1422191069} a^{3} + \\frac{12742103080}{4266573207} a^{2} + \\frac{5227822526}{4266573207} a + \\frac{297545863}{1422191069} \\)', '\\( \\frac{4523141305}{4266573207} a^{11} - \\frac{4846155070}{1422191069} a^{10} + \\frac{12303871469}{4266573207} a^{9} + \\frac{15306608554}{4266573207} a^{8} + \\frac{5226755789}{4266573207} a^{7} - \\frac{126166351861}{4266573207} a^{6} + \\frac{152964669256}{4266573207} a^{5} + \\frac{14604079250}{4266573207} a^{4} - \\frac{23340298324}{1422191069} a^{3} + \\frac{301236197116}{4266573207} a^{2} - \\frac{514883948038}{4266573207} a + \\frac{118756478537}{1422191069} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/4266573207*a^11 - 286872280/1422191069*a^10 - 1037465053/4266573207*a^9 + 986459818/4266573207*a^8 - 1291970911/4266573207*a^7 - 187505560/4266573207*a^6 - 798943634/4266573207*a^5 - 2102552308/4266573207*a^4 - 37826175/1422191069*a^3 + 1337405635/4266573207*a^2 + 798289586/4266573207*a + 695644082/1422191069']}
Number field data - 12.2.280755374552129536.1