Number field data - 9.9.31381059609.1

Formats: - HTML - YAML - JSON - 2026-07-16T04:54:14.560966

• 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, 9, 0, -30, 0, 27, 0, -9, 0, 1], 'conductor': 27, 'degree': 9, 'disc_abs': 31381059609, 'disc_rad': 3, 'disc_sign': 1, 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [22], 'galois_label': '9T1', 'galt': 1, 'grd': 14.665483999969616, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.9.31381059609.1', 'local_algs': ['3.1.9.22a3.6'], 'maxp': 3, 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 0, 'ramps': [3], 'rd': 14.665484, 'regulator': {'__RealLiteral__': 0, 'data': '159.898566189', 'prec': 44}, 'subfield_mults': [1], 'subfields': ['-1.-3.0.1'], 'torsion_order': 2, 'unit_signature_rank': 9, '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': [1, 4, 7, 10, 13, 16, 19, 22, 25], 'frobs': [[2, [[9, 1]]], [3, [0]], [5, [[9, 1]]], [7, [[9, 1]]], [11, [[9, 1]]], [13, [[9, 1]]], [17, [[3, 3]]], [19, [[3, 3]]], [23, [[9, 1]]], [29, [[9, 1]]], [31, [[9, 1]]], [37, [[3, 3]]], [41, [[9, 1]]], [43, [[9, 1]]], [47, [[9, 1]]], [53, [[1, 9]]], [59, [[9, 1]]]], 'label': '9.9.31381059609.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a^{6} - 6 a^{4} + 9 a^{2} - 2 \\)', '\\( a^{6} - 6 a^{4} - a^{3} + 9 a^{2} + 3 a - 2 \\)', '\\( a^{4} - 4 a^{2} + 2 \\)', '\\( a^{5} - 5 a^{3} + 5 a \\)', '\\( a^{8} - 8 a^{6} + 20 a^{4} - 16 a^{2} + 2 \\)', '\\( a \\)', '\\( a^{7} - 7 a^{5} + 14 a^{3} - a^{2} - 7 a + 2 \\)', '\\( a^{2} - 2 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8']}