Number field data - 8.2.1626347584.2

Formats: - HTML - YAML - JSON - 2025-12-04T04:33:05.642166

• 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': [], 'class_number': 1, 'cm': False, 'coeffs': [-4, 0, -16, 0, 19, 0, -8, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 1626347584, 'disc_rad': 142, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1]]], [5, [[3, 2], [1, 2]]], [7, [[8, 1]]], [11, [[8, 1]]], [13, [[4, 2]]], [17, [[6, 1], [2, 1]]], [19, [[2, 3], [1, 2]]], [23, [[2, 3], [1, 2]]], [29, [[4, 2]]], [31, [[8, 1]]], [37, [[6, 1], [2, 1]]], [41, [[6, 1], [2, 1]]], [43, [[8, 1]]], [47, [[8, 1]]], [53, [[3, 2], [1, 2]]], [59, [[2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48, 32], 'galois_label': '8T23', 'galt': 23, 'grd': 34.292743267870684, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '8.2.1626347584.2', 'local_algs': ['2.1.2.2a1.2', '2.2.1.0a1.1', '2.2.2.4a1.1', '71.1.1.0a1.1', '71.1.1.0a1.1', '71.2.3.4a1.2'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 3, 'ramps': [2, 71], 'rd': 14.1710382773, 'regulator': {'__RealLiteral__': 0, 'data': '76.3102907518', 'prec': 44}, 'res': {'ae': ['1,-1,-1,-4,6,-4,-1,-1,1'], 'sib': ['1,-5,12,7,-58,131,-398,969,-2274,5093,-9480,14033,-15806,14033,-9480,5093,-2274,969,-398,131,-58,7,12,-5,1', '1,0,3,0,5,0,38,0,6,0,38,0,5,0,3,0,1']}, 'subfield_mults': [1], 'subfields': ['10.-1.-5.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{8} a^{7} - a^{5} + \\frac{1}{4} a^{4} + \\frac{17}{8} a^{3} - \\frac{3}{4} a^{2} - \\frac{3}{4} a - 1 \\)', '\\( \\frac{1}{8} a^{7} - a^{5} + \\frac{1}{4} a^{4} + \\frac{17}{8} a^{3} - \\frac{3}{4} a^{2} - \\frac{7}{4} a \\)', '\\( \\frac{3}{8} a^{7} - 3 a^{5} - \\frac{1}{4} a^{4} + \\frac{59}{8} a^{3} + \\frac{3}{4} a^{2} - \\frac{29}{4} a - 1 \\)', '\\( \\frac{1}{8} a^{7} + \\frac{1}{4} a^{6} - a^{5} - \\frac{9}{4} a^{4} + \\frac{21}{8} a^{3} + 6 a^{2} - \\frac{13}{4} a - \\frac{9}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^2', '1/4*a^5 - 1/4*a^4 + 1/4*a^3 + 1/4*a^2 - 1/2', '1/4*a^6 - 1/2*a^3 + 1/4*a^2 - 1/2*a - 1/2', '1/8*a^7 - 1/4*a^4 + 1/8*a^3 - 1/4*a^2 + 1/4*a']}