Number field data - 8.2.181398528.1

Formats: - HTML - YAML - JSON - 2026-07-21T13:51:27.921771

• 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': [-3, 0, 4, 0, -6, 0, 0, 0, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 181398528, 'disc_rad': 6, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [64, 88], 'galois_label': '8T23', 'galt': 23, 'grd': 18.88407114158967, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.181398528.1', 'local_algs': ['2.1.8.10b1.1', '3.1.2.1a1.2', '3.2.3.10a1.5'], 'maxp': 3, 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 3, 'ramps': [2, 3], 'rd': 10.7728154462, 'regulator': {'__RealLiteral__': 0, 'data': '16.6622023168', 'prec': 44}, 'subfield_mults': [1], 'subfields': ['3.-6.0.-2.1'], 'torsion_order': 2, 'unit_signature_rank': 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[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1]]], [7, [[4, 2]]], [11, [[8, 1]]], [13, [[6, 1], [2, 1]]], [17, [[8, 1]]], [19, [[3, 2], [1, 2]]], [23, [[8, 1]]], [29, [[2, 3], [1, 2]]], [31, [[3, 2], [1, 2]]], [37, [[4, 2]]], [41, [[2, 3], [1, 2]]], [43, [[6, 1], [2, 1]]], [47, [[2, 3], [1, 2]]], [53, [[8, 1]]], [59, [[8, 1]]]], 'label': '8.2.181398528.1', 'res': {'ae': ['1,0,-2,-2,0,-2,-2,0,1'], 'sib': ['1,-6,18,-38,78,-138,170,-114,-33,312,-684,960,-1036,960,-684,312,-33,-114,170,-138,78,-38,18,-6,1', '1,0,2,-4,4,-2,0,8,-9,8,0,-2,4,-4,2,0,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{4} a^{7} + \\frac{1}{4} a^{4} - \\frac{7}{4} a^{3} + \\frac{1}{2} a^{2} + a - \\frac{5}{4} \\)', '\\( \\frac{1}{4} a^{7} + \\frac{1}{4} a^{5} - \\frac{5}{4} a^{3} - \\frac{1}{2} a^{2} - \\frac{1}{4} a - \\frac{1}{2} \\)', '\\( \\frac{1}{4} a^{5} + \\frac{1}{4} a^{4} + \\frac{1}{2} a^{3} - \\frac{1}{4} a + \\frac{1}{4} \\)', '\\( \\frac{1}{4} a^{7} - \\frac{1}{4} a^{4} - \\frac{7}{4} a^{3} + \\frac{1}{2} a^{2} + a + \\frac{1}{4} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/4*a^5 - 1/4*a^4 - 1/2*a^3 - 1/4*a - 1/4', '1/4*a^6 - 1/4*a^4 - 1/2*a^3 - 1/4*a^2 - 1/2*a + 1/4', '1/4*a^7 - 1/4*a^4 + 1/4*a^3 - 1/2*a^2 + 1/4']}