Number field data - 7.1.115501303.1

Formats: - HTML - YAML - JSON - 2026-03-02T15:26:01.749401

• 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
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [5, 9, -7, 2, -2, 3, -2, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 115501303, 'disc_rad': 487, 'disc_sign': -1, 'frobs': [[2, [[7, 1]]], [3, [[2, 3], [1, 1]]], [5, [[2, 3], [1, 1]]], [7, [[2, 3], [1, 1]]], [11, [[2, 3], [1, 1]]], [13, [[2, 3], [1, 1]]], [17, [[2, 3], [1, 1]]], [19, [[7, 1]]], [23, [[2, 3], [1, 1]]], [29, [[7, 1]]], [31, [[7, 1]]], [37, [[2, 3], [1, 1]]], [41, [[7, 1]]], [43, [[2, 3], [1, 1]]], [47, [[2, 3], [1, 1]]], [53, [[7, 1]]], [59, [[2, 3], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [7], 'galois_label': '7T2', 'galt': 2, 'grd': 22.06807649071391, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.1.115501303.1', 'local_algs': ['m487.1.1.0', 'm487.2.1.1', 'm487.2.1.1', 'm487.2.1.1'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 3, 'ramps': [487], 'rd': 14.183980523, 'regulator': {'__RealLiteral__': 0, 'data': '27.8998177498', 'prec': 44}, 'res': {'gal': ['441,504,-230,-391,-327,226,725,-594,18,108,-49,7,6,-4,1'], 'sib': ['441,504,-230,-391,-327,226,725,-594,18,108,-49,7,6,-4,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{35} a^{6} - \\frac{1}{7} a^{5} + \\frac{19}{35} a^{4} - \\frac{23}{35} a^{3} + \\frac{9}{7} a^{2} - \\frac{41}{35} a + \\frac{5}{7} \\)', '\\( \\frac{19}{105} a^{6} - \\frac{11}{21} a^{5} + \\frac{62}{105} a^{4} - \\frac{33}{35} a^{3} + \\frac{1}{21} a^{2} - \\frac{248}{105} a + \\frac{41}{21} \\)', '\\( \\frac{4}{105} a^{6} + \\frac{1}{21} a^{5} + \\frac{2}{105} a^{4} + \\frac{17}{35} a^{3} - \\frac{2}{21} a^{2} - \\frac{8}{105} a + \\frac{2}{21} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/105*a^6 - 5/21*a^5 - 52/105*a^4 + 13/35*a^3 + 10/21*a^2 - 2/105*a - 10/21']}
• nf_fields_extra •

  Column	Type
  dirichlet_group	bigint[]
  frobs	jsonb
  label	text
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [[7, 1]]], [3, [[2, 3], [1, 1]]], [5, [[2, 3], [1, 1]]], [7, [[2, 3], [1, 1]]], [11, [[2, 3], [1, 1]]], [13, [[2, 3], [1, 1]]], [17, [[2, 3], [1, 1]]], [19, [[7, 1]]], [23, [[2, 3], [1, 1]]], [29, [[7, 1]]], [31, [[7, 1]]], [37, [[2, 3], [1, 1]]], [41, [[7, 1]]], [43, [[2, 3], [1, 1]]], [47, [[2, 3], [1, 1]]], [53, [[7, 1]]], [59, [[2, 3], [1, 1]]]], 'label': '7.1.115501303.1', 'res': {'gal': ['441,504,-230,-391,-327,226,725,-594,18,108,-49,7,6,-4,1'], 'sib': ['441,504,-230,-391,-327,226,725,-594,18,108,-49,7,6,-4,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{3}{35} a^{6} - \\frac{1}{7} a^{5} + \\frac{19}{35} a^{4} - \\frac{23}{35} a^{3} + \\frac{9}{7} a^{2} - \\frac{41}{35} a + \\frac{5}{7} \\)', '\\( \\frac{19}{105} a^{6} - \\frac{11}{21} a^{5} + \\frac{62}{105} a^{4} - \\frac{33}{35} a^{3} + \\frac{1}{21} a^{2} - \\frac{248}{105} a + \\frac{41}{21} \\)', '\\( \\frac{4}{105} a^{6} + \\frac{1}{21} a^{5} + \\frac{2}{105} a^{4} + \\frac{17}{35} a^{3} - \\frac{2}{21} a^{2} - \\frac{8}{105} a + \\frac{2}{21} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/105*a^6 - 5/21*a^5 - 52/105*a^4 + 13/35*a^3 + 10/21*a^2 - 2/105*a - 10/21']}