Number field data - 10.4.3204506051.1

Formats: - HTML - YAML - JSON - 2026-04-29T09:44:21.373963

• 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
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 1, 0, 2, -2, -4, 3, 2, -2, -1, 1], 'conductor': 0, 'degree': 10, 'disc_abs': 3204506051, 'disc_rad': 3204506051, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [1814400], 'galois_label': '10T45', 'galt': 45, 'grd': 56608.35672407388, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.4.3204506051.1', 'local_algs': ['m3204506051.1.2.0', 'm3204506051.1.2.0', 'm3204506051.2.1.1', 'm3204506051.1.4.0'], 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 3, 'ramps': [3204506051], 'rd': 8.92434003898, 'regulator': {'__RealLiteral__': 0, 'data': '4.907691153330467', 'prec': 57}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 4, '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, [[10, 1]]], [3, [[6, 1], [4, 1]]], [5, [[7, 1], [3, 1]]], [7, [[3, 2], [2, 2]]], [11, [[8, 1], [2, 1]]], [13, [[10, 1]]], [17, [[8, 1], [2, 1]]], [19, [[10, 1]]], [23, [[10, 1]]], [29, [[7, 1], [2, 1], [1, 1]]], [31, [[8, 1], [2, 1]]], [37, [[7, 1], [2, 1], [1, 1]]], [41, [[7, 1], [2, 1], [1, 1]]], [43, [[8, 1], [1, 2]]], [47, [[4, 1], [3, 1], [2, 1], [1, 1]]], [53, [[5, 1], [3, 1], [1, 2]]], [59, [[6, 1], [4, 1]]]], 'label': '10.4.3204506051.1', 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a \\)', '\\( 3 a^{8} - a^{7} - 4 a^{6} + 2 a^{5} + 7 a^{4} - 5 a^{3} - 4 a^{2} - 2 a - 3 \\)', '\\( a^{9} - 2 a^{7} + a^{6} + 3 a^{5} - 2 a^{4} - 3 a^{3} + a^{2} - a - 1 \\)', '\\( 2 a^{8} - a^{7} - 3 a^{6} + 2 a^{5} + 5 a^{4} - 4 a^{3} - 3 a^{2} - 2 \\)', '\\( a^{9} - a^{7} + 2 a^{5} - a^{4} - a^{3} - 2 a^{2} - 2 a - 1 \\)', '\\( a^{9} - 3 a^{8} + 4 a^{6} - 7 a^{4} + 4 a^{3} + a^{2} + 3 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9']}