Number field data - 8.0.97844723712.2

Formats: - HTML - YAML - JSON - 2026-09-27T04:39:37.084033

• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [18, 0, 72, 0, 66, 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': '8.0.97844723712.2', 'local_algs': ['2.1.8.27a1.29', '3.2.4.6a1.1'], 'maximal_cm_subfield': [1, 0, 1], 'maxp': 3, 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 23.6492393325, 'regulator': {'__RealLiteral__': 0, 'data': '366.239918759', 'prec': 40}, 'subfield_mults': [1, 1], 'subfields': ['1.0.1', '18.0.-6.0.1'], 'torsion_order': 4, '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, 3], [1, 2]]], [7, [[4, 2]]], [11, [[8, 1]]], [13, [[2, 3], [1, 2]]], [17, [[2, 2], [1, 4]]], [19, [[8, 1]]], [23, [[2, 4]]], [29, [[2, 3], [1, 2]]], [31, [[4, 2]]], [37, [[2, 3], [1, 2]]], [41, [[4, 2]]], [43, [[8, 1]]], [47, [[2, 4]]], [53, [[2, 3], [1, 2]]], [59, [[8, 1]]]], 'label': '8.0.97844723712.2', 'res': {'ae': ['450,0,-288,0,78,0,-12,0,1'], 'gal': ['6561,0,0,0,17496,0,0,0,53946,0,0,0,-15552,0,0,0,13203,0,0,0,1728,0,0,0,666,0,0,0,-24,0,0,0,1'], 'sib': ['2025,0,-3888,0,5292,0,-2592,0,522,0,-144,0,36,0,0,0,1', '324,0,-1296,0,3024,0,-3456,0,2304,0,-936,0,216,0,-24,0,1', '6561,0,0,0,-3888,0,0,0,774,0,0,0,-48,0,0,0,1', '81,0,0,0,216,0,0,0,-90,0,0,0,-24,0,0,0,1']}, 'torsion_gen': '\\( \\frac{2}{3} a^{6} - \\frac{25}{3} a^{4} + 48 a^{2} + 25 \\)', 'units': ['\\( \\frac{6}{5} a^{6} - \\frac{224}{15} a^{4} + \\frac{429}{5} a^{2} + \\frac{243}{5} \\)', '\\( \\frac{2}{3} a^{7} - \\frac{2}{15} a^{6} - \\frac{25}{3} a^{5} + \\frac{26}{15} a^{4} + 48 a^{3} - \\frac{51}{5} a^{2} + 26 a - \\frac{27}{5} \\)', '\\( 654 a^{7} - \\frac{691}{3} a^{6} - \\frac{24503}{3} a^{5} + \\frac{8599}{3} a^{4} + 47156 a^{3} - 16475 a^{2} + 24042 a - 9269 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4', '1/3*a^5', '1/15*a^6 + 2/15*a^4 - 2/5*a^2 + 1/5', '1/15*a^7 + 2/15*a^5 - 2/5*a^3 + 1/5*a']}