Number field data - 8.0.136048896.1

Formats: - HTML - YAML - JSON - 2026-08-15T07:56:19.512027

• 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[]
  maxp	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': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 4, -2, 5, -2, 4, -4, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 136048896, 'disc_rad': 6, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [28, 44], 'galois_label': '8T14', 'galt': 14, 'grd': 16.82379477331321, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.0.136048896.1', 'local_algs': ['2.2.4.8a1.1', '3.1.2.1a1.1', '3.1.6.11a1.5'], 'maximal_cm_subfield': [1, -1, 1], 'maxp': 3, 'minimal_sibling': [3, -6, 0, -2, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 10.3923048454, 'regulator': {'__RealLiteral__': 0, 'data': '28.1796625828', 'prec': 40}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '3.-6.0.-2.1'], 'torsion_order': 6, '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, [0]], [3, [0]], [5, [[4, 2]]], [7, [[2, 4]]], [11, [[4, 2]]], [13, [[3, 2], [1, 2]]], [17, [[4, 2]]], [19, [[3, 2], [1, 2]]], [23, [[4, 2]]], [29, [[2, 4]]], [31, [[3, 2], [1, 2]]], [37, [[2, 4]]], [41, [[2, 4]]], [43, [[3, 2], [1, 2]]], [47, [[2, 4]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'label': '8.0.136048896.1', 'res': {'gal': ['1,-12,78,-340,1113,-2892,6196,-11232,17604,-24278,30012,-33780,35087,-33780,30012,-24278,17604,-11232,6196,-2892,1113,-340,78,-12,1'], 'sib': ['-1,0,3,-6,-3,0,1', '-3,0,-36,-22,-45,-18,-30,0,-9,0,0,0,1', '3,-6,0,-2,1', '30,18,0,-12,0,0,1', '49,0,-33,0,-30,0,7,0,6,0,3,0,1']}, 'torsion_gen': '\\( -\\frac{8}{3} a^{7} + \\frac{28}{3} a^{6} - 6 a^{5} + \\frac{7}{3} a^{4} - \\frac{38}{3} a^{3} - \\frac{32}{3} a + \\frac{19}{3} \\)', 'units': ['\\( \\frac{4}{3} a^{7} - \\frac{14}{3} a^{6} + 3 a^{5} - \\frac{2}{3} a^{4} + \\frac{16}{3} a^{3} + \\frac{13}{3} a - \\frac{8}{3} \\)', '\\( 7 a^{7} - 25 a^{6} + 17 a^{5} - 6 a^{4} + 32 a^{3} + 28 a - 15 \\)', '\\( \\frac{20}{3} a^{7} - \\frac{70}{3} a^{6} + 15 a^{5} - \\frac{16}{3} a^{4} + \\frac{89}{3} a^{3} + 2 a^{2} + \\frac{80}{3} a - \\frac{40}{3} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/3*a^7 + 1/3*a^6 + 1/3*a^4 + 1/3*a^3 + 1/3*a + 1/3']}