Number field data - 8.2.5598720000.2

Formats: - HTML - YAML - JSON - 2025-11-10T01:19:45.101112

• 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': [], 'class_number': 1, 'cm': False, 'coeffs': [-5, 16, -32, -2, 4, 4, -2, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 5598720000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[6, 1], [2, 1]]], [11, [[8, 1]]], [13, [[6, 1], [2, 1]]], [17, [[8, 1]]], [19, [[3, 2], [1, 2]]], [23, [[8, 1]]], [29, [[8, 1]]], [31, [[3, 2], [1, 2]]], [37, [[4, 2]]], [41, [[2, 3], [1, 2]]], [43, [[3, 2], [1, 2]]], [47, [[8, 1]]], [53, [[2, 3], [1, 2]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [76, 42, 32], 'galois_label': '8T23', 'galt': 23, 'grd': 22.913526127091433, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '8.2.5598720000.2', 'local_algs': ['2.1.8.12b1.1', '3.1.8.7a1.2', '5.1.1.0a1.1', '5.1.1.0a1.1', '5.2.3.4a1.2'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 5], 'rd': 16.5390703135, 'regulator': {'__RealLiteral__': 0, 'data': '135.442819173', 'prec': 44}, 'res': {'ae': ['-3,0,12,0,-6,0,0,0,1'], 'sib': ['-27,0,-108,0,-270,0,-432,0,-405,0,-468,0,-396,0,-144,0,63,0,60,0,54,0,12,0,1', '9,0,36,0,126,0,72,0,39,0,24,0,6,0,0,0,1']}, 'subfield_mults': [1], 'subfields': ['4.-8.0.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{11}{309} a^{7} - \\frac{49}{309} a^{6} + \\frac{14}{309} a^{5} + \\frac{122}{309} a^{4} - \\frac{4}{103} a^{3} - \\frac{236}{309} a^{2} - \\frac{475}{309} a + \\frac{958}{309} \\)', '\\( \\frac{5}{103} a^{7} - \\frac{20}{309} a^{6} - \\frac{3}{103} a^{5} - \\frac{49}{309} a^{4} - \\frac{7}{309} a^{3} - \\frac{23}{103} a^{2} - \\frac{11}{309} a + \\frac{89}{103} \\)', '\\( \\frac{167}{309} a^{7} - \\frac{257}{309} a^{6} - \\frac{157}{103} a^{5} + \\frac{457}{309} a^{4} + \\frac{1007}{309} a^{3} - \\frac{2}{103} a^{2} - \\frac{1817}{103} a + \\frac{57}{103} \\)', '\\( \\frac{15}{103} a^{7} - \\frac{20}{103} a^{6} - \\frac{130}{309} a^{5} + \\frac{59}{309} a^{4} + \\frac{185}{309} a^{3} + \\frac{205}{309} a^{2} - \\frac{1166}{309} a - \\frac{23}{309} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 - 1/3*a^3 - 1/3*a + 1/3', '1/3*a^5 - 1/3*a^3 - 1/3*a^2 + 1/3', '1/3*a^6 + 1/3*a^3 + 1/3', '1/309*a^7 + 11/103*a^6 + 20/309*a^5 - 17/309*a^4 + 130/309*a^3 + 16/309*a^2 + 13/309*a + 59/309']}