Number field data - 9.1.56158593639367311360.1

Formats: - HTML - YAML - JSON - 2025-01-04T23:58:31.529993

• 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': [-1296, 486, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 56158593639367311360, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[4, 1], [3, 1], [2, 1]]], [11, [[9, 1]]], [13, [[4, 1], [3, 1], [1, 2]]], [17, [[9, 1]]], [19, [[7, 1], [2, 1]]], [23, [[7, 1], [2, 1]]], [29, [[3, 2], [2, 1], [1, 1]]], [31, [[4, 1], [2, 2], [1, 1]]], [37, [[5, 1], [2, 1], [1, 2]]], [41, [[3, 2], [2, 1], [1, 1]]], [43, [[6, 1], [2, 1], [1, 1]]], [47, [[8, 1], [1, 1]]], [53, [[9, 1]]], [59, [[9, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [1553580, 893760, 181440], 'galois_label': '9T34', 'galt': 34, 'grd': 650.7312305323685, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.1.56158593639367311360.1', 'local_algs': ['2.1.0.1', '2.8.30.51', '3.9.21.42', '5.2.1.2', '5.7.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 5], 'rd': 156.451445609, 'regulator': {'__RealLiteral__': 0, 'data': '7578466.00751', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3067}{189} a^{8} + \\frac{145}{21} a^{7} - \\frac{6521}{63} a^{6} + \\frac{11419}{63} a^{5} + \\frac{1263}{7} a^{4} - \\frac{28582}{21} a^{3} + \\frac{13040}{7} a^{2} + \\frac{24721}{7} a - \\frac{68017}{7} \\)', '\\( \\frac{731572}{9} a^{8} + \\frac{331264}{9} a^{7} - \\frac{5596384}{9} a^{6} + \\frac{22935920}{9} a^{5} - 7786976 a^{4} + \\frac{60399080}{3} a^{3} - 45296225 a^{2} + 87155215 a - 91187647 \\)', '\\( \\frac{74467640890}{189} a^{8} - \\frac{63141053977}{63} a^{7} + \\frac{15532133031}{7} a^{6} - \\frac{263286840812}{63} a^{5} + \\frac{126046262893}{21} a^{4} - \\frac{21142962682}{7} a^{3} - \\frac{143387979517}{7} a^{2} + \\frac{754872510668}{7} a - \\frac{1196333843609}{7} \\)', '\\( \\frac{21505669344580}{189} a^{8} + \\frac{13791164409842}{63} a^{7} + \\frac{2948001184686}{7} a^{6} + \\frac{51043375723027}{63} a^{5} + \\frac{32733116965789}{21} a^{4} + \\frac{20991106478316}{7} a^{3} + \\frac{40383556269062}{7} a^{2} + \\frac{77691549805118}{7} a + \\frac{536568255249847}{7} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', '1/3*a^3', '1/3*a^4', '1/9*a^5', '1/9*a^6', '1/27*a^7', '1/378*a^8 - 2/189*a^7 - 2/63*a^6 + 1/63*a^5 + 1/21*a^4 + 1/7*a^3 + 3/7*a^2 + 2/7*a + 1/7']}