Number field data - 8.2.97844723712.2

Formats: - HTML - YAML - JSON - 2026-09-27T03:56:25.694517

• 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[]
  maxp	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': [], 'class_number': 1, 'cm': False, 'coeffs': [-162, 0, 0, 0, 42, 0, -12, 0, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 97844723712, 'disc_rad': 6, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [116, 24], 'galois_label': '8T15', 'galt': 15, 'grd': 28.12384367863563, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '8.2.97844723712.2', 'local_algs': ['2.1.8.27a1.106', '3.1.4.3a1.2', '3.1.4.3a1.2'], 'maxp': 3, 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 3, 'ramps': [2, 3], 'rd': 23.6492393325, 'regulator': {'__RealLiteral__': 0, 'data': '604.358982098', 'prec': 40}, 'subfield_mults': [1, 1], 'subfields': ['-3.0.1', '-2.0.-2.0.1'], 'torsion_order': 2, 'unit_signature_rank': 1, '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, [[8, 1]]], [7, [[8, 1]]], [11, [[4, 2]]], [13, [[2, 3], [1, 2]]], [17, [[4, 2]]], [19, [[2, 4]]], [23, [[2, 3], [1, 2]]], [29, [[8, 1]]], [31, [[8, 1]]], [37, [[2, 3], [1, 2]]], [41, [[4, 2]]], [43, [[2, 4]]], [47, [[2, 3], [1, 2]]], [53, [[8, 1]]], [59, [[2, 2], [1, 4]]]], 'label': '8.2.97844723712.2', 'res': {'ae': ['-162,0,0,0,42,0,12,0,1'], 'gal': ['6561,0,0,0,-52488,0,0,0,158922,0,0,0,-151632,0,0,0,70227,0,0,0,-16848,0,0,0,1962,0,0,0,-72,0,0,0,1'], 'sib': ['324,0,0,0,1620,0,-2160,0,1278,0,-432,0,90,0,-12,0,1', '729,0,-1944,0,2214,0,-1296,0,297,0,0,0,18,0,0,0,1', '729,0,0,0,-756,0,0,0,378,0,0,0,36,0,0,0,1', '81,0,0,0,-432,0,0,0,-378,0,0,0,-48,0,0,0,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{2}{9} a^{6} - \\frac{5}{3} a^{4} + \\frac{4}{3} a^{2} + 11 \\)', '\\( \\frac{1}{3} a^{6} - \\frac{8}{3} a^{4} + 3 a^{2} + 13 \\)', '\\( \\frac{8}{27} a^{7} - \\frac{2}{9} a^{6} - \\frac{20}{9} a^{5} + 2 a^{4} + \\frac{22}{9} a^{3} - \\frac{10}{3} a^{2} + 10 a - 11 \\)', '\\( \\frac{2}{27} a^{7} - \\frac{2}{9} a^{6} - \\frac{20}{9} a^{5} - 2 a^{4} + \\frac{46}{9} a^{3} + \\frac{26}{3} a^{2} + 14 a + 19 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4', '1/3*a^5', '1/9*a^6 - 1/3*a^2', '1/27*a^7 - 1/9*a^5 - 4/9*a^3']}