Number field data - 10.0.76017106944.1

Formats: - HTML - YAML - JSON - 2026-03-02T01:38:23.258943

• 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
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 76017106944, 'disc_rad': 2154, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1], [2, 1]]], [7, [[4, 1], [3, 2]]], [11, [[4, 1], [3, 2]]], [13, [[6, 1], [4, 1]]], [17, [[8, 1], [2, 1]]], [19, [[4, 1], [3, 2]]], [23, [[8, 1], [1, 2]]], [29, [[4, 2], [1, 2]]], [31, [[4, 2], [2, 1]]], [37, [[5, 2]]], [41, [[4, 2], [1, 2]]], [43, [[8, 1], [1, 2]]], [47, [[4, 1], [1, 6]]], [53, [[5, 2]]], [59, [[6, 1], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [8976, 1920, 1920], 'galois_label': '10T39', 'galt': 39, 'grd': 165.86909171812445, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.76017106944.1', 'local_algs': ['2.1.10.16a1.16', '3.1.2.1a1.1', '3.1.2.1a1.1', '3.6.1.0a1.1', 'm359.1.1.0', 'm359.1.1.0', 'm359.2.1.1', 'm359.2.1.1', 'm359.1.4.0'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 359], 'rd': 12.2487320355, 'regulator': {'__RealLiteral__': 0, 'data': '48.1156635945', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.3.-2.4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{5} - a \\)', '\\( \\frac{1}{2} a^{5} - a^{3} \\)', '\\( \\frac{1}{4} a^{9} - \\frac{1}{2} a^{7} - \\frac{1}{2} a^{6} + \\frac{1}{2} a^{5} + \\frac{1}{2} a^{4} \\)', '\\( \\frac{1}{2} a^{9} + \\frac{1}{2} a^{8} - \\frac{1}{2} a^{7} - a^{6} - a^{5} + a^{3} + a^{2} - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5', '1/2*a^6', '1/2*a^7', '1/2*a^8', '1/4*a^9 - 1/2*a^4']}
• 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, [0]], [3, [0]], [5, [[8, 1], [2, 1]]], [7, [[4, 1], [3, 2]]], [11, [[4, 1], [3, 2]]], [13, [[6, 1], [4, 1]]], [17, [[8, 1], [2, 1]]], [19, [[4, 1], [3, 2]]], [23, [[8, 1], [1, 2]]], [29, [[4, 2], [1, 2]]], [31, [[4, 2], [2, 1]]], [37, [[5, 2]]], [41, [[4, 2], [1, 2]]], [43, [[8, 1], [1, 2]]], [47, [[4, 1], [1, 6]]], [53, [[5, 2]]], [59, [[6, 1], [2, 2]]]], 'label': '10.0.76017106944.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{2} a^{5} - a \\)', '\\( \\frac{1}{2} a^{5} - a^{3} \\)', '\\( \\frac{1}{4} a^{9} - \\frac{1}{2} a^{7} - \\frac{1}{2} a^{6} + \\frac{1}{2} a^{5} + \\frac{1}{2} a^{4} \\)', '\\( \\frac{1}{2} a^{9} + \\frac{1}{2} a^{8} - \\frac{1}{2} a^{7} - a^{6} - a^{5} + a^{3} + a^{2} - 1 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5', '1/2*a^6', '1/2*a^7', '1/2*a^8', '1/4*a^9 - 1/2*a^4']}