Number field data - 8.0.1686221298140625.1

Formats: - HTML - YAML - JSON - 2026-04-18T01:53:31.298873

• 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, 6, 6], 'class_number': 72, 'cm': True, 'coeffs': [565795, -110850, 39520, -4635, 1836, -192, 64, -3, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 1686221298140625, 'disc_rad': 345, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 6, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 80.05055021202112, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.1686221298140625.1', 'local_algs': ['3.2.4.6a1.3', '5.1.4.3a1.4', '5.1.4.3a1.4', '23.2.4.6a1.3'], 'maximal_cm_subfield': [565795, -110850, 39520, -4635, 1836, -192, 64, -3, 1], 'monogenic': 0, 'narrow_class_group': [2, 6, 6], 'narrow_class_number': 72, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 23], 'rd': 80.050550212, 'regulator': {'__RealLiteral__': 0, 'data': '235.623843305', 'prec': 44}, 'relative_class_number': 72, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-17.-1.1', '-1.-1.1', '-86.-1.1', '256.0.-37.0.1'], 'torsion_order': 2, 'unit_signature_rank': 0, '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, [[4, 2]]], [3, [0]], [5, [0]], [7, [[4, 2]]], [11, [[2, 4]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[4, 2]]], [23, [0]], [29, [[4, 2]]], [31, [[1, 8]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'label': '8.0.1686221298140625.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{601}{69920996} a^{7} + \\frac{2709}{69920996} a^{6} + \\frac{23787}{69920996} a^{5} + \\frac{130509}{69920996} a^{4} + \\frac{162427}{69920996} a^{3} + \\frac{365709}{34960498} a^{2} + \\frac{5822035}{69920996} a - \\frac{13451789}{34960498} \\)', '\\( \\frac{9015}{125464564} a^{7} + \\frac{40635}{125464564} a^{6} + \\frac{725457}{125464564} a^{5} + \\frac{114375}{125464564} a^{4} + \\frac{13495965}{125464564} a^{3} - \\frac{7417185}{62732282} a^{2} + \\frac{140785065}{125464564} a - \\frac{742343551}{62732282} \\)', '\\( \\frac{3985231}{35694668458} a^{7} + \\frac{17963379}{35694668458} a^{6} - \\frac{331715375}{35694668458} a^{5} + \\frac{3312640039}{35694668458} a^{4} - \\frac{13606355723}{35694668458} a^{3} + \\frac{19555660399}{17847334229} a^{2} - \\frac{32363896855}{35694668458} a + \\frac{51429790346}{17847334229} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^3 - 1/2*a - 1/2', '1/4552*a^6 + 229/4552*a^5 + 1045/4552*a^4 - 775/4552*a^3 - 2059/4552*a^2 + 729/2276*a - 1943/4552', '1/285557347664*a^7 + 2961779/71389336916*a^6 - 1113940305/35694668458*a^5 - 33644557125/71389336916*a^4 - 3078513299/71389336916*a^3 + 103105931573/285557347664*a^2 + 30215055775/285557347664*a - 72836877657/285557347664']}