Number field data - 8.0.49213429281.1

Formats: - HTML - YAML - JSON - 2026-01-07T18:50:58.905283

• 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
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [4], 'class_number': 4, 'cm': False, 'coeffs': [729, 0, -189, 0, 76, 0, 7, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 49213429281, 'disc_rad': 471, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [[4, 2]]], [7, [[2, 4]]], [11, [[2, 4]]], [13, [[1, 8]]], [17, [[2, 4]]], [19, [[2, 4]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[2, 4]]], [37, [[2, 4]]], [41, [[4, 2]]], [43, [[2, 4]]], [47, [[2, 4]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '8T4', 'galt': 4, 'grd': 21.702534414210707, 'inessentialp': [3], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.0.49213429281.1', 'local_algs': ['3.1.2.1a1.1', '3.1.2.1a1.1', '3.1.2.1a1.1', '3.1.2.1a1.1', '157.1.2.1a1.1', '157.1.2.1a1.1', '157.1.2.1a1.1', '157.1.2.1a1.1'], 'maximal_cm_subfield': [1521, 39, 40, -1, 1], 'minimal_sibling': [9, -3, 7, -1, 1], 'monogenic': -1, 'narrow_class_group': [4], 'narrow_class_number': 4, 'num_ram': 2, 'r2': 4, 'ramps': [3, 157], 'rd': 21.7025344142, 'regulator': {'__RealLiteral__': 0, 'data': '324.950191435', 'prec': 44}, 'res': {'sib': ['-27,0,-7,0,1', '9,-3,7,-1,1']}, 'subfield_mults': [1, 1, 1, 1, 2, 2], 'subfields': ['118.-1.1', '-39.-1.1', '1.-1.1', '1521.39.40.-1.1', '-27.0.-7.0.1', '9.-3.7.-1.1'], 'torsion_gen': '\\( -\\frac{7}{2052} a^{6} - \\frac{1}{27} a^{4} - \\frac{7}{27} a^{2} + \\frac{49}{76} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{10}{4617} a^{7} - \\frac{7}{1026} a^{6} - \\frac{2}{243} a^{5} - \\frac{2}{27} a^{4} + \\frac{13}{243} a^{3} - \\frac{14}{27} a^{2} - \\frac{374}{171} a - \\frac{103}{38} \\)', '\\( \\frac{83}{9234} a^{7} - \\frac{7}{1026} a^{6} + \\frac{16}{243} a^{5} - \\frac{2}{27} a^{4} + \\frac{139}{243} a^{3} - \\frac{14}{27} a^{2} - \\frac{505}{342} a + \\frac{125}{38} \\)', '\\( \\frac{1}{57} a^{7} - \\frac{31}{2052} a^{6} + \\frac{11}{27} a^{4} - \\frac{31}{27} a^{2} + \\frac{20}{57} a + \\frac{217}{76} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2', '1/2*a^4 - 1/2*a', '1/6*a^5 + 1/6*a^3 - 1/2*a^2 - 1/3*a - 1/2', '1/2052*a^6 + 4/27*a^4 + 1/27*a^2 - 7/76', '1/36936*a^7 - 1/4104*a^6 + 2/243*a^5 - 2/27*a^4 - 13/243*a^3 - 1/54*a^2 - 539/1368*a + 7/152']}