Number field data - 7.7.42748699986001.1

Formats: - HTML - YAML - JSON - 2025-04-24T21:10:11.685116

• 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': [96, -200, -216, 430, 47, -47, -2, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 42748699986001, 'disc_rad': 2557, 'disc_sign': 1, 'frobs': [[2, [[3, 2], [1, 1]]], [3, [[3, 2], [1, 1]]], [5, [[3, 2], [1, 1]]], [7, [[3, 2], [1, 1]]], [11, [[3, 2], [1, 1]]], [13, [[3, 2], [1, 1]]], [17, [[3, 2], [1, 1]]], [19, [[3, 2], [1, 1]]], [23, [[3, 2], [1, 1]]], [29, [[3, 2], [1, 1]]], [31, [[3, 2], [1, 1]]], [37, [[3, 2], [1, 1]]], [41, [[3, 2], [1, 1]]], [43, [[3, 2], [1, 1]]], [47, [[3, 2], [1, 1]]], [53, [[7, 1]]], [59, [[3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [14], 'galois_label': '7T3', 'galt': 3, 'grd': 186.99090578896957, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.7.42748699986001.1', 'local_algs': ['m2557.1.1.0', 'm2557.3.1.2', 'm2557.3.1.2'], 'monogenic': 0, 'num_ram': 1, 'r2': 0, 'ramps': [2557], 'rd': 88.567564389, 'regulator': {'__RealLiteral__': 0, 'data': '139632.45493', 'prec': 40}, 'res': {'gal': ['117390125,-417714600,-90994860,1147450766,-320193790,-1139673182,534357842,521098075,-319030836,-115322580,94315852,10379052,-14968608,235844,1276607,-106868,-55496,6750,1066,-154,-6,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{21}{808} a^{6} - \\frac{3}{101} a^{5} - \\frac{2965}{2424} a^{4} + \\frac{535}{2424} a^{3} + \\frac{2137}{202} a^{2} + \\frac{809}{606} a - \\frac{395}{101} \\)', '\\( \\frac{9}{404} a^{6} - \\frac{103}{1212} a^{5} - \\frac{337}{404} a^{4} + \\frac{703}{303} a^{3} + \\frac{4079}{1212} a^{2} - \\frac{2351}{606} a + \\frac{51}{101} \\)', '\\( \\frac{1247}{1212} a^{6} - \\frac{929}{606} a^{5} - \\frac{59509}{1212} a^{4} + \\frac{28061}{1212} a^{3} + \\frac{274403}{606} a^{2} + \\frac{1287}{101} a - \\frac{19685}{101} \\)', '\\( \\frac{133}{1212} a^{6} - \\frac{59}{202} a^{5} - \\frac{6035}{1212} a^{4} + \\frac{9995}{1212} a^{3} + \\frac{25217}{606} a^{2} - \\frac{14497}{303} a + \\frac{1149}{101} \\)', '\\( \\frac{191}{1212} a^{6} - \\frac{175}{1212} a^{5} - \\frac{8723}{1212} a^{4} + \\frac{18}{101} a^{3} + \\frac{64063}{1212} a^{2} - \\frac{8207}{606} a - \\frac{2355}{101} \\)', '\\( \\frac{389}{303} a^{6} - \\frac{407}{202} a^{5} - \\frac{18460}{303} a^{4} + \\frac{19421}{606} a^{3} + \\frac{341101}{606} a^{2} - \\frac{3257}{303} a - \\frac{26205}{101} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/6*a^4 + 1/3*a^3 - 1/2*a^2 + 1/6*a', '1/12*a^5 + 5/12*a^3 + 1/12*a^2 + 1/3*a', '1/2424*a^6 - 5/404*a^5 - 5/808*a^4 - 383/808*a^3 + 545/1212*a^2 - 4/303*a + 29/101']}