Number field data - 8.0.47453100346125.2

Formats: - HTML - YAML - JSON - 2025-12-04T13:51:58.940325

• 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': [3, 6], 'class_number': 18, 'cm': False, 'coeffs': [729, -891, 1251, -780, 352, -88, 7, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 47453100346125, 'disc_rad': 885, 'disc_sign': 1, 'frobs': [[2, [[4, 1], [2, 2]]], [3, [0]], [5, [0]], [7, [[4, 1], [2, 2]]], [11, [[2, 4]]], [13, [[8, 1]]], [17, [[4, 1], [1, 4]]], [19, [[4, 2]]], [23, [[4, 1], [2, 2]]], [29, [[4, 1], [2, 1], [1, 2]]], [31, [[4, 2]]], [37, [[8, 1]]], [41, [[4, 1], [2, 1], [1, 2]]], [43, [[8, 1]]], [47, [[4, 1], [2, 2]]], [53, [[4, 1], [2, 2]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [64, 64, 96], 'galois_label': '8T35', 'galt': 35, 'grd': 82.44885679537175, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '8.0.47453100346125.2', 'local_algs': ['3.1.2.1a1.2', '3.1.2.1a1.2', '3.4.1.0a1.1', '5.1.1.0a1.1', '5.1.1.0a1.1', '5.1.2.1a1.1', '5.2.2.2a1.2', '59.2.4.6a1.2'], 'maximal_cm_subfield': [15, -1, 1], 'minimal_sibling': [15, -27, 23, 11, 8, -1, -3, -2, 1], 'monogenic': -1, 'narrow_class_group': [3, 6], 'narrow_class_number': 18, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 59], 'rd': 51.2310284171, 'regulator': {'__RealLiteral__': 0, 'data': '893.944303353', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['15.-1.1', '180.-48.-7.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{734}{94203} a^{7} - \\frac{2003}{94203} a^{6} + \\frac{10357}{188406} a^{5} - \\frac{143197}{188406} a^{4} + \\frac{718831}{188406} a^{3} - \\frac{593657}{62802} a^{2} + \\frac{304201}{20934} a - \\frac{26415}{2326} \\)', '\\( \\frac{18701}{376812} a^{7} - \\frac{13229}{376812} a^{6} + \\frac{15368}{94203} a^{5} - \\frac{819541}{188406} a^{4} + \\frac{1467497}{94203} a^{3} - \\frac{637939}{31401} a^{2} + \\frac{789809}{41868} a - \\frac{48931}{4652} \\)', '\\( \\frac{757}{376812} a^{7} + \\frac{2141}{376812} a^{6} - \\frac{3187}{188406} a^{5} - \\frac{11596}{94203} a^{4} + \\frac{20896}{94203} a^{3} - \\frac{55519}{62802} a^{2} + \\frac{19795}{41868} a - \\frac{3293}{4652} \\)'], '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^4 + 1/6*a^3 - 1/6*a^2 + 1/6*a - 1/2', '1/36*a^6 + 1/18*a^5 + 1/9*a^4 - 1/9*a^3 - 1/18*a^2 - 1/3*a - 1/4', '1/376812*a^7 - 365/188406*a^6 - 410/94203*a^5 - 15142/94203*a^4 + 2309/188406*a^3 + 7234/31401*a^2 + 16471/41868*a - 341/1163']}