Number field data - 7.7.58280536320561.1

Formats: - HTML - YAML - JSON - 2025-04-29T13:51:25.239424

• 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': [-432, 1800, -1476, 204, 143, -36, -3, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 58280536320561, 'disc_rad': 921, 'disc_sign': 1, 'frobs': [[2, [[3, 2], [1, 1]]], [3, [0]], [5, [[7, 1]]], [7, [[7, 1]]], [11, [[3, 2], [1, 1]]], [13, [[7, 1]]], [17, [[7, 1]]], [19, [[7, 1]]], [23, [[3, 2], [1, 1]]], [29, [[7, 1]]], [31, [[3, 2], [1, 1]]], [37, [[3, 2], [1, 1]]], [41, [[3, 2], [1, 1]]], [43, [[3, 2], [1, 1]]], [47, [[7, 1]]], [53, [[3, 2], [1, 1]]], [59, [[3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [28, 14], 'galois_label': '7T3', 'galt': 3, 'grd': 196.903720979923, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.7.58280536320561.1', 'local_algs': ['3.1.0.1', '3.3.4.2', '3.3.4.2', 'm307.1.1.0', 'm307.3.1.2', 'm307.3.1.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 0, 'ramps': [3, 307], 'rd': 92.5770553478, 'regulator': {'__RealLiteral__': 0, 'data': '211240.508114', 'prec': 44}, 'res': {'gal': ['-81509214357,66923283294,124809311214,-106894803033,-63387903753,58771678437,15757359786,-16215924114,-2263249053,2598539442,207353142,-258137205,-13052876,16261443,589602,-643525,-18570,15279,356,-195,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{6} a^{6} - \\frac{11}{2} a^{4} + \\frac{41}{6} a^{3} + \\frac{83}{2} a^{2} - 95 a + 49 \\)', '\\( \\frac{1}{72} a^{6} + \\frac{1}{8} a^{5} - a^{4} - \\frac{145}{72} a^{3} + \\frac{56}{3} a^{2} - \\frac{51}{2} a + 5 \\)', '\\( \\frac{23}{72} a^{6} - \\frac{31}{24} a^{5} - \\frac{13}{2} a^{4} + \\frac{2713}{72} a^{3} - \\frac{95}{2} a^{2} + \\frac{17}{2} a + 1 \\)', '\\( \\frac{7}{24} a^{6} + \\frac{5}{24} a^{5} - \\frac{39}{4} a^{4} + \\frac{137}{24} a^{3} + \\frac{965}{12} a^{2} - \\frac{265}{2} a + 34 \\)', '\\( \\frac{1}{3} a^{6} - \\frac{5}{12} a^{5} - \\frac{47}{4} a^{4} + \\frac{71}{3} a^{3} + \\frac{1073}{12} a^{2} - 232 a + 64 \\)', '\\( \\frac{7}{6} a^{6} + \\frac{1}{3} a^{5} - \\frac{81}{2} a^{4} + \\frac{203}{6} a^{3} + \\frac{2005}{6} a^{2} - 615 a + 209 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^3 - 1/2*a', '1/12*a^5 - 1/4*a^4 - 1/12*a^2', '1/72*a^6 - 1/24*a^5 + 35/72*a^3 - 1/6*a^2']}