Number field data - 5.1.14637128256.1

Formats: - HTML - YAML - JSON - 2026-06-06T03:15:59.666210

• 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': [15], 'class_number': 15, 'cm': False, 'coeffs': [-498, 238, 34, -28, -1, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 14637128256, 'disc_rad': 426, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [90, 30, 48], 'galois_label': '5T4', 'galt': 4, 'grd': 148.29014841167913, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.14637128256.1', 'local_algs': ['2.1.1.0a1.1', '2.1.4.6a2.1', '3.1.1.0a1.1', '3.2.2.2a1.2', '71.1.5.4a1.4'], 'maxp': 71, 'monogenic': 0, 'narrow_class_group': [15], 'narrow_class_number': 15, 'num_ram': 3, 'r2': 2, 'ramps': [2, 3, 71], 'rd': 107.917325978, 'regulator': {'__RealLiteral__': 0, 'data': '275.003234611', 'prec': 44}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 1, '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, [0]], [3, [0]], [5, [[5, 1]]], [7, [[5, 1]]], [11, [[5, 1]]], [13, [[3, 1], [1, 2]]], [17, [[2, 2], [1, 1]]], [19, [[5, 1]]], [23, [[3, 1], [1, 2]]], [29, [[5, 1]]], [31, [[3, 1], [1, 2]]], [37, [[5, 1]]], [41, [[5, 1]]], [43, [[5, 1]]], [47, [[3, 1], [1, 2]]], [53, [[5, 1]]], [59, [[5, 1]]]], 'label': '5.1.14637128256.1', 'res': {'sib': ['-57,-24,11,-8,-4,0,1', '2601,0,33156,0,12586,0,1630,0,9,0,-14,0,1', '3644,-568,-3308,-2840,-1953,-568,15,0,-12,0,1', '62916624,0,-77962464,0,28567432,0,34490720,0,7118281,0,220106,0,-77927,0,-2194,0,946,0,-52,0,1', '78336,123584,-16384,-40591,3184,-31690,17728,-6287,-1392,1314,432,74,-16,-16,0,1', '-35956123641,0,10236583251,0,36776839212,0,-471641805,0,-15940263843,0,-3062079285,0,2156751982,0,1032041051,0,128078145,0,28588625,0,6094304,0,235313,0,11195,0,1233,0,38,0,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{17} a^{4} + \\frac{7}{17} a^{3} - \\frac{6}{17} a^{2} - \\frac{116}{17} a - \\frac{197}{17} \\)', '\\( \\frac{104174}{17} a^{4} + \\frac{268059}{17} a^{3} - \\frac{2192784}{17} a^{2} - \\frac{5207905}{17} a + \\frac{9874861}{17} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/17*a^4 + 7/17*a^3 - 6/17*a^2 + 3/17*a + 7/17']}