Number field data - 10.4.3540851199.1

Formats: - HTML - YAML - JSON - 2026-04-29T09:44:51.412506

• 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, 3, 0, -5, 1, 4, 1, -3, -1, 1], 'conductor': 0, 'degree': 10, 'disc_abs': 3540851199, 'disc_rad': 393427911, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [1814400, 1814400, 1814400], 'galois_label': '10T45', 'galt': 45, 'grd': 19835.017292656943, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.4.3540851199.1', 'local_algs': ['3.4.1.0a1.1', '3.3.2.3a1.1', 'm3779.2.1.1', 'm3779.1.8.0', 'm34703.2.1.1', 'm34703.1.3.0', 'm34703.1.5.0'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 3, 'ramps': [3, 3779, 34703], 'rd': 9.01385915212, 'regulator': {'__RealLiteral__': 0, 'data': '5.219912631781355', '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, [[5, 2]]], [3, [0]], [5, [[5, 2]]], [7, [[6, 1], [2, 2]]], [11, [[5, 2]]], [13, [[10, 1]]], [17, [[5, 1], [3, 1], [2, 1]]], [19, [[7, 1], [3, 1]]], [23, [[10, 1]]], [29, [[7, 1], [3, 1]]], [31, [[5, 1], [2, 2], [1, 1]]], [37, [[5, 1], [4, 1], [1, 1]]], [41, [[10, 1]]], [43, [[10, 1]]], [47, [[8, 1], [2, 1]]], [53, [[9, 1], [1, 1]]], [59, [[5, 1], [3, 1], [1, 2]]]], 'label': '10.4.3540851199.1', 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a^{9} - a^{8} - 3 a^{7} + a^{6} + 4 a^{5} + a^{4} - 5 a^{3} + 3 a - 1 \\)', '\\( \\frac{12}{7} a^{9} - \\frac{18}{7} a^{8} - \\frac{27}{7} a^{7} + \\frac{22}{7} a^{6} + \\frac{37}{7} a^{5} + \\frac{4}{7} a^{4} - \\frac{55}{7} a^{3} + \\frac{24}{7} a^{2} + \\frac{17}{7} a - \\frac{17}{7} \\)', '\\( \\frac{15}{7} a^{9} - \\frac{19}{7} a^{8} - \\frac{32}{7} a^{7} + \\frac{17}{7} a^{6} + \\frac{34}{7} a^{5} + \\frac{5}{7} a^{4} - \\frac{53}{7} a^{3} + \\frac{30}{7} a^{2} + \\frac{16}{7} a - \\frac{16}{7} \\)', '\\( \\frac{15}{7} a^{9} - \\frac{19}{7} a^{8} - \\frac{32}{7} a^{7} + \\frac{17}{7} a^{6} + \\frac{34}{7} a^{5} + \\frac{5}{7} a^{4} - \\frac{53}{7} a^{3} + \\frac{30}{7} a^{2} + \\frac{9}{7} a - \\frac{16}{7} \\)', '\\( \\frac{18}{7} a^{9} - \\frac{27}{7} a^{8} - \\frac{37}{7} a^{7} + \\frac{33}{7} a^{6} + \\frac{45}{7} a^{5} - \\frac{1}{7} a^{4} - \\frac{79}{7} a^{3} + \\frac{43}{7} a^{2} + \\frac{22}{7} a - \\frac{29}{7} \\)', '\\( \\frac{9}{7} a^{9} - \\frac{10}{7} a^{8} - \\frac{22}{7} a^{7} + \\frac{6}{7} a^{6} + \\frac{26}{7} a^{5} + \\frac{10}{7} a^{4} - \\frac{36}{7} a^{3} + \\frac{11}{7} a^{2} + \\frac{18}{7} a - \\frac{4}{7} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/7*a^9 + 2/7*a^8 + 3/7*a^7 + 3/7*a^6 - 1/7*a^5 - 2/7*a^4 + 3/7*a^3 + 2/7*a^2 + 2/7*a - 2/7']}