Number field data - 8.0.23973872753.1

Formats: - HTML - YAML - JSON - 2026-03-13T02:59:23.814135

• 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

  
  {'class_group': [5], 'class_number': 5, 'cm': False, 'coeffs': [51, -25, 50, -23, 29, -9, 8, -1, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 23973872753, 'disc_rad': 799, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 8], 'galois_label': '8T6', 'galt': 6, 'grd': 28.26658805020514, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.0.23973872753.1', 'local_algs': ['17.1.1.0a1.1', '17.1.1.0a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '17.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1', '47.1.2.1a1.1'], 'maximal_cm_subfield': [12, -1, 1], 'minimal_sibling': [19, -27, 6, 23, -15, 1, 2, -1, 1], 'monogenic': 0, 'narrow_class_group': [5], 'narrow_class_number': 5, 'num_ram': 2, 'r2': 4, 'ramps': [17, 47], 'rd': 19.836601759, 'regulator': {'__RealLiteral__': 0, 'data': '39.0059184349', 'prec': 44}, 'subfield_mults': [1, 1], 'subfields': ['12.-1.1', '1.1.10.-1.1'], 'torsion_order': 2, '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[]
  unit_signature_rank	smallint
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [[4, 2]]], [3, [[2, 3], [1, 2]]], [5, [[8, 1]]], [7, [[2, 3], [1, 2]]], [11, [[8, 1]]], [13, [[2, 4]]], [17, [0]], [19, [[2, 4]]], [23, [[8, 1]]], [29, [[8, 1]]], [31, [[8, 1]]], [37, [[2, 3], [1, 2]]], [41, [[8, 1]]], [43, [[2, 4]]], [47, [0]], [53, [[2, 4]]], [59, [[4, 2]]]], 'label': '8.0.23973872753.1', 'res': {'gal': ['2448,8568,10208,3912,4393,-2374,2820,-2361,1614,-460,317,-118,6,15,4,-4,1'], 'sib': ['19,-27,6,23,-15,1,2,-1,1', '2448,8568,10208,3912,4393,-2374,2820,-2361,1614,-460,317,-118,6,15,4,-4,1']}, 'torsion_gen': '\\( -1 \\)', 'unit_signature_rank': 0, 'units': ['\\( \\frac{2}{63} a^{7} + \\frac{1}{7} a^{6} + \\frac{13}{63} a^{5} + \\frac{43}{63} a^{4} - \\frac{10}{63} a^{3} + \\frac{88}{63} a^{2} - \\frac{25}{63} a + \\frac{53}{21} \\)', '\\( \\frac{5}{63} a^{7} - \\frac{1}{7} a^{6} + \\frac{43}{63} a^{5} - \\frac{71}{63} a^{4} + \\frac{143}{63} a^{3} - \\frac{137}{63} a^{2} + \\frac{137}{63} a - \\frac{4}{21} \\)', '\\( \\frac{5}{63} a^{7} - \\frac{1}{7} a^{6} + \\frac{43}{63} a^{5} - \\frac{50}{63} a^{4} + \\frac{143}{63} a^{3} - \\frac{53}{63} a^{2} + \\frac{95}{63} a + \\frac{38}{21} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 + 1/3*a^2 + 1/3*a', '1/3*a^5 + 1/3*a^3 + 1/3*a^2', '1/3*a^6 + 1/3*a^3 - 1/3*a^2 - 1/3*a', '1/63*a^7 - 2/21*a^6 - 4/63*a^5 - 10/63*a^4 - 26/63*a^3 - 19/63*a^2 - 2/63*a - 5/21']}