Number field data - 8.2.3294172000000.4

Formats: - HTML - YAML - JSON - 2024-12-21T11:48:58.254192

• 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[]
  minimal_sibling	numeric[]
  monogenic	smallint
  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': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, -10, -28, -28, 0, 14, 0, -4, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 3294172000000, 'disc_rad': 70, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[5, 1], [2, 1], [1, 1]]], [5, [0]], [7, [0]], [11, [[3, 2], [1, 2]]], [13, [[5, 1], [2, 1], [1, 1]]], [17, [[5, 1], [2, 1], [1, 1]]], [19, [[6, 1], [1, 2]]], [23, [[7, 1], [1, 1]]], [29, [[4, 1], [2, 1], [1, 2]]], [31, [[8, 1]]], [37, [[3, 1], [2, 2], [1, 1]]], [41, [[5, 1], [2, 1], [1, 1]]], [43, [[6, 1], [2, 1]]], [47, [[8, 1]]], [53, [[6, 1], [2, 1]]], [59, [[4, 1], [3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [44640, 52416, 45120], 'galois_label': '8T50', 'galt': 50, 'grd': 154.0455526727784, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 4, 'label': '8.2.3294172000000.4', 'local_algs': ['2.8.8.13', '5.1.0.1', '5.2.0.1', '5.5.6.1', '7.1.0.1', '7.7.7.4'], 'monogenic': 0, 'num_ram': 3, 'r2': 3, 'ramps': [2, 5, 7], 'rd': 36.7044130824, 'regulator': {'__RealLiteral__': 0, 'data': '6460.34536915', 'prec': 44}, 'res': {'sib': ['-40569439270,53157490050,-1189649298810,-173622527120,1195162997280,1911790066438,-1132393608640,-533828888625,445984684810,-240911254990,-705001542070,-49389556195,267844380720,157399531520,63790689840,-2210091345,-24934975100,-10813898480,-3585922620,-1730319395,-304425464,-136812930,-45445820,5996795,767410,413602,98350,-7315,3020,-4130,-1372,-35,0,0,0,1', '1306709492,2890947840,-8467172440,-145243980,25362177400,-49486303944,49824913740,-25578516700,-506070630,10104181790,-5987760814,426113310,1105318270,-376570320,-122440380,109320450,-15401230,-13647060,9515380,-3355520,604394,174260,-162405,48220,-8820,490,700,-280,60,-10,1', '42350,62370,41588,-13860,-32340,-19250,588,4620,2345,-110,-140,0,56,0,0,0,1', '9150625,27951000,37056250,18634000,-22815625,-42581000,-24033800,5984000,19783925,14014000,-119350,-7330400,-4610725,609840,1895800,689920,-242501,-311080,-42042,55440,25165,-3080,-6160,0,735,0,-42,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( 33 a^{7} - 150 a^{6} + 72 a^{5} + 477 a^{4} - 335 a^{3} - 808 a^{2} - 322 a - 73 \\)', '\\( 21 a^{7} - 87 a^{6} + 4 a^{5} + 355 a^{4} - 156 a^{3} - 619 a^{2} - 259 a - 67 \\)', '\\( \\frac{53}{5} a^{7} - \\frac{263}{5} a^{6} + \\frac{241}{5} a^{5} + 115 a^{4} - 133 a^{3} - \\frac{884}{5} a^{2} - \\frac{356}{5} a - \\frac{73}{5} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/5*a^7 - 1/5*a^6 + 2/5*a^5 + 2/5*a^2 - 2/5*a - 1/5']}