Number field data - 8.2.71762455.1

Formats: - HTML - YAML - JSON - 2026-02-23T18:15:39.446940

• 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
  used_grh	boolean
  dirichlet_group	bigint[]
  frobs	jsonb
  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

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -8, -4, 6, 5, 0, -3, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 71762455, 'disc_rad': 216805, 'disc_sign': -1, 'frobs': [[2, [[4, 2]]], [3, [[8, 1]]], [5, [0]], [7, [[8, 1]]], [11, [[4, 2]]], [13, [[4, 1], [2, 2]]], [17, [[3, 2], [1, 2]]], [19, [[3, 2], [2, 1]]], [23, [[2, 2], [1, 4]]], [29, [[8, 1]]], [31, [[6, 1], [1, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[3, 2], [2, 1]]], [47, [[4, 1], [2, 1], [1, 2]]], [53, [[6, 1], [1, 2]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [192, 192, 192], 'galois_label': '8T44', 'galt': 44, 'grd': 465.6232382517007, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.71762455.1', 'local_algs': ['5.1.2.1a1.1', '5.3.1.0a1.1', '5.3.1.0a1.1', '131.1.2.1a1.2', '131.6.1.0a1.1', 'm331.1.1.0', 'm331.1.1.0', 'm331.1.2.0', 'm331.2.2.2'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 3, 'ramps': [5, 131, 331], 'rd': 9.59372269154, 'regulator': {'__RealLiteral__': 0, 'data': '4.87436409009', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.1.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{23} a^{7} + \\frac{1}{23} a^{6} - \\frac{16}{23} a^{5} - \\frac{1}{23} a^{4} + \\frac{20}{23} a^{3} + \\frac{19}{23} a^{2} - \\frac{14}{23} a - \\frac{37}{23} \\)', '\\( \\frac{5}{23} a^{7} - \\frac{9}{23} a^{6} - \\frac{17}{23} a^{5} + \\frac{9}{23} a^{4} + \\frac{27}{23} a^{3} + \\frac{36}{23} a^{2} - \\frac{35}{23} a - \\frac{35}{23} \\)', '\\( \\frac{5}{23} a^{7} - \\frac{9}{23} a^{6} - \\frac{17}{23} a^{5} + \\frac{9}{23} a^{4} + \\frac{27}{23} a^{3} + \\frac{36}{23} a^{2} - \\frac{12}{23} a - \\frac{35}{23} \\)', '\\( \\frac{2}{23} a^{7} + \\frac{1}{23} a^{6} - \\frac{16}{23} a^{5} - \\frac{1}{23} a^{4} + \\frac{20}{23} a^{3} + \\frac{42}{23} a^{2} - \\frac{14}{23} a - \\frac{60}{23} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/23*a^7 - 11/23*a^6 - 8/23*a^5 + 11/23*a^4 + 10/23*a^3 - 2/23*a^2 - 7/23*a - 7/23']}
• 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, [[4, 2]]], [3, [[8, 1]]], [5, [0]], [7, [[8, 1]]], [11, [[4, 2]]], [13, [[4, 1], [2, 2]]], [17, [[3, 2], [1, 2]]], [19, [[3, 2], [2, 1]]], [23, [[2, 2], [1, 4]]], [29, [[8, 1]]], [31, [[6, 1], [1, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[3, 2], [2, 1]]], [47, [[4, 1], [2, 1], [1, 2]]], [53, [[6, 1], [1, 2]]], [59, [[2, 4]]]], 'label': '8.2.71762455.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{2}{23} a^{7} + \\frac{1}{23} a^{6} - \\frac{16}{23} a^{5} - \\frac{1}{23} a^{4} + \\frac{20}{23} a^{3} + \\frac{19}{23} a^{2} - \\frac{14}{23} a - \\frac{37}{23} \\)', '\\( \\frac{5}{23} a^{7} - \\frac{9}{23} a^{6} - \\frac{17}{23} a^{5} + \\frac{9}{23} a^{4} + \\frac{27}{23} a^{3} + \\frac{36}{23} a^{2} - \\frac{35}{23} a - \\frac{35}{23} \\)', '\\( \\frac{5}{23} a^{7} - \\frac{9}{23} a^{6} - \\frac{17}{23} a^{5} + \\frac{9}{23} a^{4} + \\frac{27}{23} a^{3} + \\frac{36}{23} a^{2} - \\frac{12}{23} a - \\frac{35}{23} \\)', '\\( \\frac{2}{23} a^{7} + \\frac{1}{23} a^{6} - \\frac{16}{23} a^{5} - \\frac{1}{23} a^{4} + \\frac{20}{23} a^{3} + \\frac{42}{23} a^{2} - \\frac{14}{23} a - \\frac{60}{23} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/23*a^7 - 11/23*a^6 - 8/23*a^5 + 11/23*a^4 + 10/23*a^3 - 2/23*a^2 - 7/23*a - 7/23']}