Number field data - 8.0.29721861554176.1

Formats: - HTML - YAML - JSON - 2026-04-18T01:47:47.270065

• 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': [3, 6], 'class_number': 18, 'cm': True, 'coeffs': [121, 0, 484, 0, 308, 0, 44, 0, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 29721861554176, 'disc_rad': 22, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 48.32084283629789, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.29721861554176.1', 'local_algs': ['2.1.8.24c1.57', '11.2.4.6a1.3'], 'maximal_cm_subfield': [121, 0, 484, 0, 308, 0, 44, 0, 1], 'monogenic': 0, 'narrow_class_group': [3, 6], 'narrow_class_number': 18, 'num_ram': 2, 'r2': 4, 'ramps': [2, 11], 'rd': 48.3208428363, 'regulator': {'__RealLiteral__': 0, 'data': '126.131828435', 'prec': 44}, 'relative_class_number': 18, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-2.0.1', '-22.0.1', '-11.0.1', '25.0.-12.0.1'], '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, [[4, 2]]], [5, [[4, 2]]], [7, [[2, 4]]], [11, [0]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'label': '8.0.29721861554176.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{77} a^{6} + \\frac{6}{11} a^{4} + 3 a^{2} + \\frac{23}{7} \\)', '\\( \\frac{1}{231} a^{6} + \\frac{5}{33} a^{4} - \\frac{5}{21} \\)', '\\( \\frac{9}{77} a^{6} + \\frac{53}{11} a^{4} + 23 a^{2} + \\frac{46}{7} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/33*a^4 - 1/3*a^2 + 1/3', '1/33*a^5 - 1/3*a^3 + 1/3*a', '1/231*a^6 - 1/3*a^2 + 2/21', '1/231*a^7 - 1/3*a^3 + 2/21*a']}