Number field data - 8.0.1340095640625.1

Formats: - HTML - YAML - JSON - 2024-05-05T19:27:49.980570

• 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
  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, 2], 'class_number': 8, 'cm': True, 'coeffs': [4561, -3069, 1528, -450, 201, -60, 22, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 1340095640625, 'disc_rad': 105, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [0]], [7, [0]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[2, 4]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[1, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 6, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 32.801369337662685, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.1340095640625.1', 'local_algs': ['3.8.6.1', '5.4.3.1', '5.4.3.1', '7.8.6.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 7], 'rd': 32.8013693377, 'regulator': {'__RealLiteral__': 0, 'data': '53.1582098182', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-5.-1.1', '-1.-1.1', '-26.-1.1', '16.0.-13.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{184}{161129} a^{7} - \\frac{147}{161129} a^{6} + \\frac{2730}{161129} a^{5} - \\frac{3339}{161129} a^{4} + \\frac{10948}{161129} a^{3} - \\frac{38220}{161129} a^{2} + \\frac{124180}{161129} a - \\frac{93605}{161129} \\)', '\\( \\frac{920}{412381} a^{7} - \\frac{735}{412381} a^{6} + \\frac{16381}{412381} a^{5} - \\frac{30350}{412381} a^{4} + \\frac{95705}{412381} a^{3} - \\frac{259375}{412381} a^{2} + \\frac{689175}{412381} a + \\frac{130064}{412381} \\)', '\\( \\frac{2576}{24330479} a^{7} - \\frac{2058}{24330479} a^{6} - \\frac{284038}{24330479} a^{5} + \\frac{1564544}{24330479} a^{4} - \\frac{4680598}{24330479} a^{3} + \\frac{7521370}{24330479} a^{2} - \\frac{6317930}{24330479} a + \\frac{1106465}{24330479} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/118*a^6 + 15/59*a^5 - 27/118*a^4 - 25/118*a^3 + 53/118*a^2 + 8/59*a - 29/118', '1/48660958*a^7 - 19/412381*a^6 - 23434429/48660958*a^5 - 13218637/48660958*a^4 + 356455/48660958*a^3 + 5287973/24330479*a^2 + 18757361/48660958*a - 10323798/24330479']}