Number field data - 8.2.143327232000000.8

Formats: - HTML - YAML - JSON - 2025-12-04T02:12:26.823650

• 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
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [-300, 0, -360, 0, 390, 0, 20, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 143327232000000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[6, 1], [2, 1]]], [11, [[8, 1]]], [13, [[4, 2]]], [17, [[2, 3], [1, 2]]], [19, [[3, 2], [1, 2]]], [23, [[8, 1]]], [29, [[2, 3], [1, 2]]], [31, [[3, 2], [1, 2]]], [37, [[6, 1], [2, 1]]], [41, [[8, 1]]], [43, [[6, 1], [2, 1]]], [47, [[8, 1]]], [53, [[8, 1]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [132, 56, 40], 'galois_label': '8T23', 'galt': 23, 'grd': 92.67208955435932, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 8, 'label': '8.2.143327232000000.8', 'local_algs': ['2.2.4.22a1.72', '3.1.1.0a1.1', '3.1.1.0a1.1', '3.1.6.7a1.1', '5.1.2.1a1.1', '5.1.6.5a1.2'], 'minimal_sibling': [-300, 0, -2080, 0, 60, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2, 4], 'narrow_class_number': 8, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 5], 'rd': 58.8221763993, 'regulator': {'__RealLiteral__': 0, 'data': '8359.7330129', 'prec': 40}, 'res': {'ae': ['-300,0,-2080,0,60,0,0,0,1'], 'sib': ['-48000000,0,38400000,0,-39840000,0,21248000,0,-7014000,0,2160000,0,-490800,0,105600,0,-12900,0,960,0,-60,0,0,0,1', '160000,0,-32000,0,306400,0,-226400,0,22900,0,7360,0,820,0,40,0,1']}, 'subfield_mults': [1], 'subfields': ['-15.6.3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{47}{27770} a^{6} + \\frac{115}{2777} a^{4} + \\frac{2465}{2777} a^{2} + \\frac{1109}{2777} \\)', '\\( \\frac{13}{5554} a^{6} + \\frac{259}{5554} a^{4} + \\frac{1991}{2777} a^{2} - \\frac{3134}{2777} \\)', '\\( \\frac{1449}{13885} a^{7} + \\frac{2188}{13885} a^{6} + \\frac{6500}{2777} a^{5} + \\frac{8462}{2777} a^{4} + \\frac{118076}{2777} a^{3} + \\frac{138398}{2777} a^{2} + \\frac{63890}{2777} a + \\frac{73417}{2777} \\)', '\\( \\frac{8572}{13885} a^{7} - \\frac{67599}{2777} a^{6} - \\frac{58083}{2777} a^{5} + \\frac{3910}{2777} a^{4} - \\frac{5801812}{2777} a^{3} - \\frac{6769826}{2777} a^{2} - \\frac{3076060}{2777} a - \\frac{3619603}{2777} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/2*a^5', '1/27770*a^6 + 773/5554*a^4 - 952/2777*a^2 - 390/2777', '1/27770*a^7 + 773/5554*a^5 - 952/2777*a^3 - 390/2777*a']}