Number field data - 14.0.9669040949311.1

Formats: - HTML - YAML - JSON - 2026-05-20T13:12:55.152650

• 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, -1, 3, -6, 5, -9, 11, -7, 11, -9, 5, -6, 3, -1, 1], 'conductor': 0, 'degree': 14, 'disc_abs': 9669040949311, 'disc_rad': 27637913, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [322560, 322560, 322560], 'galois_label': '14T57', 'galt': 57, 'grd': 5257.1772844369625, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '14.0.9669040949311.1', 'local_algs': ['19.2.1.0a1.1', '19.2.1.0a1.1', '19.3.1.0a1.1', '19.3.1.0a1.1', '19.2.2.2a1.2', '79.1.1.0a1.1', '79.1.1.0a1.1', '79.1.2.1a1.1', '79.5.1.0a1.1', '79.5.1.0a1.1', 'm18413.1.2.0', 'm18413.1.2.0', 'm18413.1.2.0', 'm18413.1.2.0', 'm18413.1.2.0', 'm18413.2.2.2'], 'maxp': 18413, 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 7, 'ramps': [19, 79, 18413], 'rd': 8.46305933364, 'regulator': {'__RealLiteral__': 0, 'data': '2.65828702774', 'prec': 44}, 'subfield_mults': [1], 'subfields': ['1.-1.1.0.-1.1.-1.1'], '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, [[7, 2]]], [3, [[14, 1]]], [5, [[8, 1], [6, 1]]], [7, [[6, 2], [2, 1]]], [11, [[12, 1], [2, 1]]], [13, [[4, 3], [2, 1]]], [17, [[14, 1]]], [19, [0]], [23, [[4, 3], [2, 1]]], [29, [[4, 2], [2, 3]]], [31, [[7, 2]]], [37, [[14, 1]]], [41, [[4, 2], [2, 1], [1, 4]]], [43, [[14, 1]]], [47, [[14, 1]]], [53, [[8, 1], [2, 2], [1, 2]]], [59, [[4, 1], [3, 2], [2, 2]]]], 'label': '14.0.9669040949311.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( 2 a^{13} - 3 a^{12} + 6 a^{11} - 12 a^{10} + 12 a^{9} - 14 a^{8} + 19 a^{7} - 16 a^{6} + 14 a^{5} - 14 a^{4} + 11 a^{3} - 5 a^{2} + 3 a - 2 \\)', '\\( a \\)', '\\( a^{13} - 2 a^{12} + 4 a^{11} - 9 a^{10} + 10 a^{9} - 13 a^{8} + 17 a^{7} - 13 a^{6} + 14 a^{5} - 14 a^{4} + 8 a^{3} - 7 a^{2} + 4 a - 1 \\)', '\\( 2 a^{13} - 2 a^{12} + 5 a^{11} - 10 a^{10} + 7 a^{9} - 11 a^{8} + 15 a^{7} - 8 a^{6} + 11 a^{5} - 11 a^{4} + 5 a^{3} - 4 a^{2} + 3 a - 1 \\)', '\\( a^{13} + a^{11} - 2 a^{10} - 3 a^{9} + 6 a^{6} + 2 a^{4} - 4 a^{3} - 2 a + 1 \\)', '\\( a^{13} - a^{10} - 5 a^{9} + 5 a^{8} - 2 a^{7} + 10 a^{6} - 7 a^{5} + 3 a^{4} - 9 a^{3} + 5 a^{2} - a + 3 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13']}