Number field data - 10.2.236340051968.1

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• 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': [-47, 0, -67, 0, -30, 0, 2, 0, 5, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 236340051968, 'disc_rad': 26038, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[10, 1]]], [5, [[4, 1], [3, 2]]], [7, [[10, 1]]], [11, [[4, 2], [1, 2]]], [13, [[10, 1]]], [17, [[4, 2], [1, 2]]], [19, [[6, 1], [2, 1], [1, 2]]], [23, [[6, 1], [2, 1], [1, 2]]], [29, [[10, 1]]], [31, [[8, 1], [2, 1]]], [37, [[4, 2], [1, 2]]], [41, [[10, 1]]], [43, [[4, 2], [1, 2]]], [47, [0]], [53, [[8, 1], [2, 1]]], [59, [[10, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [8976, 1920, 1920], 'galois_label': '10T39', 'galt': 39, 'grd': 576.6953217629489, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.2.236340051968.1', 'local_algs': ['2.1.10.16a1.16', '47.1.2.1a1.2', '47.2.1.0a1.1', '47.2.1.0a1.1', '47.2.1.0a1.1', '47.2.1.0a1.1', 'm277.1.1.0', 'm277.1.1.0', 'm277.1.2.0', 'm277.1.2.0', 'm277.2.1.1', 'm277.2.1.1'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 47, 277], 'rd': 13.7199880363, 'regulator': {'__RealLiteral__': 0, 'data': '77.1530176137', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-1.2.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{8} + \\frac{3}{2} a^{6} - 2 a^{4} - \\frac{23}{2} a^{2} - \\frac{23}{2} \\)', '\\( \\frac{1}{4} a^{8} + a^{6} - a^{4} - 7 a^{2} - \\frac{25}{4} \\)', '\\( a^{8} - \\frac{1}{4} a^{7} + \\frac{11}{4} a^{6} - \\frac{1}{4} a^{5} - \\frac{17}{4} a^{4} + \\frac{5}{4} a^{3} - \\frac{83}{4} a^{2} + \\frac{9}{4} a - \\frac{83}{4} \\)', '\\( \\frac{1}{4} a^{9} - \\frac{1}{2} a^{8} + \\frac{3}{4} a^{7} - \\frac{7}{4} a^{6} - \\frac{3}{4} a^{5} + \\frac{7}{4} a^{4} - \\frac{23}{4} a^{3} + \\frac{51}{4} a^{2} - \\frac{15}{2} a + \\frac{55}{4} \\)', '\\( \\frac{1}{2} a^{9} + \\frac{5}{4} a^{8} + \\frac{5}{4} a^{7} + \\frac{13}{4} a^{6} - \\frac{7}{4} a^{5} - \\frac{23}{4} a^{4} - \\frac{37}{4} a^{3} - \\frac{101}{4} a^{2} - \\frac{39}{4} a - \\frac{51}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/2*a^5 - 1/2*a', '1/2*a^6 - 1/2*a^2', '1/4*a^7 - 1/4*a^6 - 1/4*a^5 - 1/4*a^4 - 1/4*a^3 + 1/4*a^2 + 1/4*a + 1/4', '1/4*a^8 - 1/4', '1/4*a^9 - 1/4*a']}
• 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, [0]], [3, [[10, 1]]], [5, [[4, 1], [3, 2]]], [7, [[10, 1]]], [11, [[4, 2], [1, 2]]], [13, [[10, 1]]], [17, [[4, 2], [1, 2]]], [19, [[6, 1], [2, 1], [1, 2]]], [23, [[6, 1], [2, 1], [1, 2]]], [29, [[10, 1]]], [31, [[8, 1], [2, 1]]], [37, [[4, 2], [1, 2]]], [41, [[10, 1]]], [43, [[4, 2], [1, 2]]], [47, [0]], [53, [[8, 1], [2, 1]]], [59, [[10, 1]]]], 'label': '10.2.236340051968.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{2} a^{8} + \\frac{3}{2} a^{6} - 2 a^{4} - \\frac{23}{2} a^{2} - \\frac{23}{2} \\)', '\\( \\frac{1}{4} a^{8} + a^{6} - a^{4} - 7 a^{2} - \\frac{25}{4} \\)', '\\( a^{8} - \\frac{1}{4} a^{7} + \\frac{11}{4} a^{6} - \\frac{1}{4} a^{5} - \\frac{17}{4} a^{4} + \\frac{5}{4} a^{3} - \\frac{83}{4} a^{2} + \\frac{9}{4} a - \\frac{83}{4} \\)', '\\( \\frac{1}{4} a^{9} - \\frac{1}{2} a^{8} + \\frac{3}{4} a^{7} - \\frac{7}{4} a^{6} - \\frac{3}{4} a^{5} + \\frac{7}{4} a^{4} - \\frac{23}{4} a^{3} + \\frac{51}{4} a^{2} - \\frac{15}{2} a + \\frac{55}{4} \\)', '\\( \\frac{1}{2} a^{9} + \\frac{5}{4} a^{8} + \\frac{5}{4} a^{7} + \\frac{13}{4} a^{6} - \\frac{7}{4} a^{5} - \\frac{23}{4} a^{4} - \\frac{37}{4} a^{3} - \\frac{101}{4} a^{2} - \\frac{39}{4} a - \\frac{51}{2} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/2*a^5 - 1/2*a', '1/2*a^6 - 1/2*a^2', '1/4*a^7 - 1/4*a^6 - 1/4*a^5 - 1/4*a^4 - 1/4*a^3 + 1/4*a^2 + 1/4*a + 1/4', '1/4*a^8 - 1/4', '1/4*a^9 - 1/4*a']}