Number field data - 8.0.21667237072994304.1

Formats: - HTML - YAML - JSON - 2026-04-22T15:32:41.885093

• 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[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [2, 10, 20], 'class_number': 400, 'cm': True, 'coeffs': [27225, 0, 30492, 0, 4356, 0, 132, 0, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 21667237072994304, 'disc_rad': 66, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 6, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 110.14770224334376, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.21667237072994304.1', 'local_algs': ['2.1.8.24c1.56', '3.2.4.6a1.3', '11.2.4.6a1.3'], 'maximal_cm_subfield': [27225, 0, 30492, 0, 4356, 0, 132, 0, 1], 'monogenic': 0, 'narrow_class_group': [2, 10, 20], 'narrow_class_number': 400, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 11], 'rd': 110.147702243, 'regulator': {'__RealLiteral__': 0, 'data': '267.195532151', 'prec': 44}, 'relative_class_number': 200, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-66.0.1', '-6.0.1', '-11.0.1', '25.0.-34.0.1'], 'torsion_order': 2, 'unit_signature_rank': 0, 'used_grh': False}
• nf_fields_extra •

  Column	Type
  dirichlet_group	bigint[]
  frobs	jsonb
  label	text
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [[2, 4]]], [7, [[4, 2]]], [11, [0]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[1, 8]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[2, 4]]], [47, [[4, 2]]], [53, [[1, 8]]], [59, [[4, 2]]]], 'label': '8.0.21667237072994304.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{8}{8987} a^{6} + \\frac{2956}{26961} a^{4} + \\frac{2385}{817} a^{2} + \\frac{2334}{817} \\)', '\\( \\frac{4}{12255} a^{6} + \\frac{866}{26961} a^{4} + \\frac{1513}{4085} a^{2} - \\frac{288}{817} \\)', '\\( \\frac{23}{134805} a^{6} + \\frac{89}{8987} a^{4} + \\frac{141}{4085} a^{2} - \\frac{2}{817} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/33*a^4', '1/165*a^5 + 2/5*a', '1/134805*a^6 - 166/26961*a^4 + 1427/4085*a^2 + 142/817', '1/134805*a^7 - 13/134805*a^5 + 1427/4085*a^3 - 1741/4085*a']}