Number field data - 4.4.278784.1

Formats: - HTML - YAML - JSON - 2026-04-18T01:57:04.549785

• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [25, 0, -34, 0, 1], 'conductor': 264, 'degree': 4, 'disc_abs': 278784, 'disc_rad': 66, 'disc_sign': 1, 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 22.978250586152114, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.278784.1', 'local_algs': ['2.1.4.8b1.6', '3.2.2.2a1.2', '11.2.2.2a1.2'], 'monogenic': -1, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 0, 'ramps': [2, 3, 11], 'rd': 22.9782505862, 'regulator': {'__RealLiteral__': 0, 'data': '33.3994415189', 'prec': 44}, 'subfield_mults': [1, 1, 1], 'subfields': ['-66.0.1', '-6.0.1', '-11.0.1'], 'torsion_order': 2, 'unit_signature_rank': 3, '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, 155, 197, 175], 'frobs': [[2, [0]], [3, [0]], [5, [[1, 4]]], [7, [[2, 2]]], [11, [0]], [13, [[2, 2]]], [17, [[2, 2]]], [19, [[1, 4]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[1, 4]]], [47, [[2, 2]]], [53, [[1, 4]]], [59, [[2, 2]]]], 'label': '4.4.278784.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{4} a^{3} - \\frac{1}{4} a^{2} - \\frac{33}{4} a + \\frac{29}{4} \\)', '\\( \\frac{1}{20} a^{3} - \\frac{1}{4} a^{2} - \\frac{9}{20} a + \\frac{5}{4} \\)', '\\( \\frac{7}{10} a^{3} - \\frac{1}{2} a^{2} - \\frac{233}{10} a + \\frac{33}{2} \\)'], 'unitsGmodule': [[13, 1]], 'unitsType': 'Type III', 'zk': ['1', 'a', '1/2*a^2 - 1/2', '1/20*a^3 - 1/4*a^2 - 9/20*a + 1/4']}