Number field data - 8.0.49787136.1

Formats: - HTML - YAML - JSON - 2025-11-01T16:28:45.738764

• 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': True, 'coeffs': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'conductor': 84, 'degree': 8, 'dirichlet_group': [1, 71, 41, 43, 13, 83, 55, 29], 'disc_abs': 49787136, 'disc_rad': 42, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 4]]], [7, [0]], [11, [[2, 4]]], [13, [[2, 4]]], [17, [[2, 4]]], [19, [[2, 4]]], [23, [[2, 4]]], [29, [[2, 4]]], [31, [[2, 4]]], [37, [[1, 8]]], [41, [[2, 4]]], [43, [[2, 4]]], [47, [[2, 4]]], [53, [[2, 4]]], [59, [[2, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 4, 4], 'galois_label': '8T3', 'galt': 3, 'grd': 9.16515138991168, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.49787136.1', 'local_algs': ['2.2.2.4a1.1', '2.2.2.4a1.1', '3.2.2.2a1.2', '3.2.2.2a1.2', '7.2.2.2a1.2', '7.2.2.2a1.2'], 'maximal_cm_subfield': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 7], 'rd': 9.16515138991, 'regulator': {'__RealLiteral__': 0, 'data': '22.8515026384', 'prec': 44}, 'relative_class_number': 1, 'res': {}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '-5.-1.1', '21.0.1', '-7.0.1', '2.-1.1', '-3.0.1', '1.-1.1', '25.0.11.0.1', '4.0.-3.0.1', '1.0.-1.0.1', '1.0.-5.0.1', '4.-2.-1.-1.1', '49.0.7.0.1', '22.2.-1.-2.1'], 'torsion_gen': '\\( -\\frac{1}{40} a^{7} + \\frac{1}{8} a^{5} - \\frac{1}{8} a^{3} - \\frac{3}{10} a \\)', 'torsion_order': 12, 'units': ['\\( \\frac{1}{40} a^{7} - \\frac{1}{8} a^{5} + \\frac{1}{8} a^{3} + \\frac{3}{10} a - 1 \\)', '\\( \\frac{1}{40} a^{7} - \\frac{1}{8} a^{5} + \\frac{1}{8} a^{3} - \\frac{7}{10} a \\)', '\\( \\frac{1}{10} a^{7} - \\frac{9}{20} a^{6} + \\frac{1}{2} a^{5} - \\frac{3}{4} a^{4} + \\frac{1}{2} a^{3} - \\frac{5}{4} a^{2} + \\frac{6}{5} a - \\frac{12}{5} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^3 - 1/2*a', '1/20*a^6 - 1/4*a^4 + 1/4*a^2 - 2/5', '1/40*a^7 - 1/8*a^5 + 1/8*a^3 + 3/10*a']}