Number field data - 8.8.7644119040000.1

Formats: - HTML - YAML - JSON - 2026-04-22T13:44:16.263893

• 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
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [5625, 0, -4500, 0, 900, 0, -60, 0, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 7644119040000, 'disc_rad': 30, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 6, 4], 'galois_label': '8T5', 'galt': 5, 'grd': 40.77706187633094, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.8.7644119040000.1', 'local_algs': ['2.1.8.24c1.57', '3.2.4.6a1.3', '5.2.2.2a1.1', '5.2.2.2a1.1'], 'monogenic': 0, 'narrow_class_group': [2, 2, 2], 'narrow_class_number': 8, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 5], 'rd': 40.7770618763, 'regulator': {'__RealLiteral__': 0, 'data': '4900.6997022', 'prec': 40}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-2.0.1', '-3.0.1', '-6.0.1', '1.0.-4.0.1'], 'torsion_order': 2, 'unit_signature_rank': 6, '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, [0]], [7, [[4, 2]]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[4, 2]]], [23, [[2, 4]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[4, 2]]], [47, [[1, 8]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'label': '8.8.7644119040000.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{375} a^{6} - \\frac{11}{75} a^{4} + \\frac{8}{5} a^{2} - 3 \\)', '\\( \\frac{1}{375} a^{6} - \\frac{2}{15} a^{4} + a^{2} + 1 \\)', '\\( \\frac{1}{375} a^{6} - \\frac{11}{75} a^{4} + \\frac{9}{5} a^{2} - 6 \\)', '\\( \\frac{4}{375} a^{6} + \\frac{1}{75} a^{5} - \\frac{41}{75} a^{4} - \\frac{3}{5} a^{3} + 5 a^{2} + 3 a - 10 \\)', '\\( \\frac{1}{375} a^{7} - \\frac{1}{75} a^{6} - \\frac{2}{15} a^{5} + \\frac{53}{75} a^{4} + a^{3} - \\frac{36}{5} a^{2} + a + 14 \\)', '\\( \\frac{1}{125} a^{6} - \\frac{31}{75} a^{4} + 4 a^{2} - a - 8 \\)', '\\( \\frac{2}{375} a^{7} + \\frac{4}{375} a^{6} - \\frac{22}{75} a^{5} - \\frac{43}{75} a^{4} + \\frac{17}{5} a^{3} + \\frac{31}{5} a^{2} - 10 a - 16 \\)'], 'zk': ['1', 'a', '1/5*a^2', '1/5*a^3', '1/75*a^4', '1/75*a^5', '1/375*a^6', '1/375*a^7']}