Number field data - 9.1.895152515625.1

Formats: - HTML - YAML - JSON - 2024-12-12T18:11:30.312162

• 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': [-45, 45, -60, 24, -41, 11, -11, 4, -1, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 895152515625, 'disc_rad': 435, 'disc_sign': 1, 'frobs': [[2, [[9, 1]]], [3, [0]], [5, [0]], [7, [[9, 1]]], [11, [[9, 1]]], [13, [[9, 1]]], [17, [[9, 1]]], [19, [[2, 4], [1, 1]]], [23, [[2, 4], [1, 1]]], [29, [0]], [31, [[2, 4], [1, 1]]], [37, [[2, 4], [1, 1]]], [41, [[3, 3]]], [43, [[2, 4], [1, 1]]], [47, [[9, 1]]], [53, [[2, 4], [1, 1]]], [59, [[2, 4], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9, 12, 9], 'galois_label': '9T3', 'galt': 3, 'grd': 27.27342180226682, 'inessentialp': [3], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.1.895152515625.1', 'local_algs': ['3.1.0.1', '3.2.1.1', '3.2.1.1', '3.2.1.1', '3.2.1.1', '5.3.2.1', '5.6.4.1', '29.1.0.1', '29.2.1.2', '29.2.1.2', '29.2.1.2', '29.2.1.2'], 'monogenic': -1, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 29], 'rd': 21.2808298628, 'regulator': {'__RealLiteral__': 0, 'data': '1085.49841916', 'prec': 44}, 'res': {'sib': ['783,0,-506,0,817,0,-1574,0,1993,0,-1094,0,358,0,-56,0,7,0,1']}, 'subfield_mults': [1], 'subfields': ['1.2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{27} a^{8} + \\frac{1}{27} a^{7} - \\frac{2}{27} a^{5} - \\frac{14}{27} a^{4} - \\frac{4}{9} a^{3} - \\frac{5}{3} a^{2} - \\frac{1}{3} \\)', '\\( \\frac{1}{9} a^{8} - \\frac{2}{9} a^{7} + \\frac{4}{9} a^{6} - \\frac{11}{9} a^{5} + \\frac{13}{9} a^{4} - \\frac{26}{9} a^{3} + \\frac{4}{3} a^{2} - \\frac{1}{3} a - 1 \\)', '\\( \\frac{4}{27} a^{8} - \\frac{14}{27} a^{7} + \\frac{1}{3} a^{6} - \\frac{50}{27} a^{5} + \\frac{124}{27} a^{4} - \\frac{25}{9} a^{3} + \\frac{67}{9} a^{2} - 7 a + \\frac{19}{3} \\)', '\\( \\frac{5}{27} a^{8} - \\frac{10}{27} a^{7} + \\frac{8}{9} a^{6} - \\frac{70}{27} a^{5} + \\frac{77}{27} a^{4} - \\frac{16}{3} a^{3} + \\frac{46}{9} a^{2} - \\frac{17}{3} a + 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 - 1/3*a^3 + 1/3*a^2', '1/9*a^5 + 4/9*a^2 - 1/3', '1/9*a^6 + 4/9*a^3 - 1/3*a', '1/9*a^7 + 1/9*a^4 + 1/3*a^3 + 1/3*a^2', '1/27*a^8 + 1/27*a^7 + 1/27*a^5 + 4/27*a^4 - 1/9*a^3 + 4/9*a^2 + 1/3']}