Number field data - 8.0.2101386547456.12

Formats: - HTML - YAML - JSON - 2024-12-21T11:51:48.961733

• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [153, 16, -94, 4, 34, -16, 2, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 2101386547456, 'disc_rad': 602, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[7, 1], [1, 1]]], [5, [[6, 1], [2, 1]]], [7, [0]], [11, [[6, 1], [2, 1]]], [13, [[6, 1], [2, 1]]], [17, [[3, 2], [1, 2]]], [19, [[3, 2], [1, 2]]], [23, [[6, 1], [2, 1]]], [29, [[6, 1], [2, 1]]], [31, [[7, 1], [1, 1]]], [37, [[6, 1], [2, 1]]], [41, [[7, 1], [1, 1]]], [43, [0]], [47, [[3, 2], [1, 2]]], [53, [[7, 1], [1, 1]]], [59, [[6, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [186, 112, 112], 'galois_label': '8T36', 'galt': 36, 'grd': 96.75220539252781, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 12, 'label': '8.0.2101386547456.12', 'local_algs': ['2.8.8.13', '7.1.0.1', '7.1.0.1', '7.3.2.3', '7.3.2.3', '43.1.0.1', '43.1.0.1', '43.3.2.1', '43.3.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [2, 7, 43], 'rd': 34.6987031458, 'regulator': {'__RealLiteral__': 0, 'data': '574.051605692', 'prec': 44}, 'res': {'sib': ['1519697613,-562286270,183807904,333635758,-358662996,-3082480,47024200,-58027928,26706834,-6861522,6494086,-2680910,918102,-134568,8470,-73896,47883,-17072,4764,-1652,798,-302,76,-12,1', '17441538898,4170695088,10211926102,-13270842278,-2784910834,-9048529878,-1763440382,-2363805018,-218944340,-129966792,17833820,79398494,5549810,21301016,-3347934,3486238,-1444226,253320,-99208,-36290,20904,-12624,5848,-1930,642,-168,42,-8,1', '1841,-2498,-6297,5994,-3601,-2186,6107,-388,-701,462,-135,22,13,-6,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2421}{40187} a^{7} - \\frac{265}{40187} a^{6} + \\frac{4507}{40187} a^{5} - \\frac{28489}{40187} a^{4} + \\frac{22794}{40187} a^{3} + \\frac{47598}{40187} a^{2} - \\frac{118117}{40187} a - \\frac{185648}{40187} \\)', '\\( a - 2 \\)', '\\( \\frac{34238}{40187} a^{7} - \\frac{65381}{40187} a^{6} - \\frac{6593}{40187} a^{5} - \\frac{81481}{40187} a^{4} + \\frac{412788}{40187} a^{3} + \\frac{150754}{40187} a^{2} - \\frac{2817004}{40187} a + \\frac{2811530}{40187} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/40187*a^7 + 2274/40187*a^6 - 8497/40187*a^5 - 9241/40187*a^4 - 14681/40187*a^3 - 18555/40187*a^2 + 5263/40187*a + 2878/40187']}