Number field data - 8.2.95693045760.3

Formats: - HTML - YAML - JSON - 2025-12-04T13:51:58.843963

• 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
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-15, -20, 36, -44, 20, -12, 4, -4, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 95693045760, 'disc_rad': 390, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[6, 1], [1, 2]]], [11, [[8, 1]]], [13, [0]], [17, [[3, 2], [1, 2]]], [19, [[4, 1], [2, 1], [1, 2]]], [23, [[4, 2]]], [29, [[8, 1]]], [31, [[4, 2]]], [37, [[6, 1], [1, 2]]], [41, [[8, 1]]], [43, [[3, 2], [2, 1]]], [47, [[6, 1], [2, 1]]], [53, [[4, 2]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1056, 192, 192, 192], 'galois_label': '8T44', 'galt': 44, 'grd': 93.9398351563814, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '8.2.95693045760.3', 'local_algs': ['2.1.8.22d1.22', '3.1.1.0a1.1', '3.1.1.0a1.1', '3.3.2.3a1.1', '5.1.2.1a1.2', '5.3.1.0a1.1', '5.3.1.0a1.1', '13.1.2.1a1.1', '13.1.2.1a1.1', '13.4.1.0a1.1'], 'monogenic': 0, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 4, 'r2': 3, 'ramps': [2, 3, 5, 13], 'rd': 23.5835971228, 'regulator': {'__RealLiteral__': 0, 'data': '499.929118855', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-4.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{554}{14339} a^{7} - \\frac{2519}{14339} a^{6} + \\frac{2429}{14339} a^{5} - \\frac{5880}{14339} a^{4} + \\frac{17816}{14339} a^{3} - \\frac{23560}{14339} a^{2} + \\frac{32985}{14339} a - \\frac{4972}{14339} \\)', '\\( \\frac{3014}{14339} a^{7} - \\frac{10495}{14339} a^{6} + \\frac{4570}{14339} a^{5} - \\frac{28625}{14339} a^{4} + \\frac{49665}{14339} a^{3} - \\frac{78896}{14339} a^{2} + \\frac{70849}{14339} a + \\frac{40711}{14339} \\)', '\\( \\frac{5755}{14339} a^{7} - \\frac{21224}{14339} a^{6} + \\frac{19202}{14339} a^{5} - \\frac{74748}{14339} a^{4} + \\frac{101059}{14339} a^{3} - \\frac{252094}{14339} a^{2} + \\frac{196181}{14339} a - \\frac{144206}{14339} \\)', '\\( \\frac{211}{14339} a^{7} - \\frac{1710}{14339} a^{6} + \\frac{5144}{14339} a^{5} - \\frac{9849}{14339} a^{4} + \\frac{12635}{14339} a^{3} - \\frac{25124}{14339} a^{2} + \\frac{31949}{14339} a - \\frac{24101}{14339} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/14339*a^7 + 1419/14339*a^6 - 2558/14339*a^5 + 2060/14339*a^4 + 6244/14339*a^3 - 5012/14339*a^2 - 5557/14339*a - 6842/14339']}