Number field data - 21.5.211442929780702787875897344000000.1

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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': [-8, 0, 0, -88, 0, 0, -162, 0, 0, 421, 0, 0, -302, 0, 0, 100, 0, 0, -16, 0, 0, 1], 'conductor': 0, 'degree': 21, 'dirichlet_group': [], 'disc_abs': 211442929780702787875897344000000, 'disc_rad': 3390, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[7, 3]]], [11, [[10, 1], [6, 1], [5, 1]]], [13, [[7, 3]]], [17, [[18, 1], [2, 1], [1, 1]]], [19, [[7, 3]]], [23, [[6, 1], [4, 3], [3, 1]]], [29, [[12, 1], [6, 1], [3, 1]]], [31, [[12, 1], [3, 1], [2, 3]]], [37, [[7, 3]]], [41, [[12, 1], [6, 1], [3, 1]]], [43, [[12, 1], [6, 1], [3, 1]]], [47, [[12, 1], [6, 1], [3, 1]]], [53, [[6, 3], [2, 1], [1, 1]]], [59, [[6, 1], [4, 3], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_label': '21T129', 'galt': 129, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '21.5.211442929780702787875897344000000.1', 'local_algs': ['2.4.6.9', '2.8.12.14', '2.9.6.1', '3.6.3.2', '3.15.15.9', '5.3.0.1', '5.6.0.1', '5.12.6.2', '113.1.0.1', '113.2.1.2', '113.2.0.1', '113.2.1.2', '113.4.2.1', '113.4.2.1', '113.6.0.1'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 4, 'r2': 8, 'ramps': [2, 3, 5, 113], 'rd': 34.61743717895762, 'regulator': {'__RealLiteral__': 0, 'data': '178510738.2852738', 'prec': 57}, 'subfield_mults': [1], 'subfields': ['1.4.-1.-7.7.0.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( -\\frac{4}{3} a^{18} + \\frac{43}{2} a^{15} - \\frac{409}{3} a^{12} + \\frac{1270}{3} a^{9} - 629 a^{6} + \\frac{637}{2} a^{3} + \\frac{202}{3} \\)', '\\( \\frac{25}{12} a^{18} - \\frac{67}{2} a^{15} + \\frac{634}{3} a^{12} - \\frac{3905}{6} a^{9} + \\frac{3819}{4} a^{6} - 472 a^{3} - \\frac{307}{3} \\)', '\\( -\\frac{19}{12} a^{18} + \\frac{51}{2} a^{15} - \\frac{484}{3} a^{12} + \\frac{2993}{6} a^{9} - \\frac{2941}{4} a^{6} + 365 a^{3} + \\frac{241}{3} \\)', '\\( -a^{18} + \\frac{33}{2} a^{15} - 107 a^{12} + 339 a^{9} - 512 a^{6} + \\frac{521}{2} a^{3} + 56 \\)', '\\( \\frac{7}{12} a^{18} - 9 a^{15} + \\frac{163}{3} a^{12} - \\frac{959}{6} a^{9} + \\frac{893}{4} a^{6} - \\frac{209}{2} a^{3} - \\frac{70}{3} \\)', '\\( -\\frac{757}{36} a^{20} + \\frac{217}{36} a^{18} + \\frac{1019}{3} a^{17} - \\frac{583}{6} a^{15} - \\frac{19396}{9} a^{14} + \\frac{5536}{9} a^{12} + \\frac{120317}{18} a^{11} - \\frac{34259}{18} a^{9} - \\frac{118727}{12} a^{8} + \\frac{33719}{12} a^{6} + \\frac{29735}{6} a^{5} - \\frac{4210}{3} a^{3} + \\frac{9637}{9} a^{2} - \\frac{2734}{9} \\)', '\\( -\\frac{20}{3} a^{20} - \\frac{7}{6} a^{19} - \\frac{7}{6} a^{18} + \\frac{647}{6} a^{17} + \\frac{113}{6} a^{16} + \\frac{113}{6} a^{15} - \\frac{2056}{3} a^{14} - \\frac{358}{3} a^{13} - \\frac{358}{3} a^{12} + \\frac{6391}{3} a^{11} + \\frac{1108}{3} a^{10} + \\frac{1108}{3} a^{9} - \\frac{9491}{3} a^{8} - \\frac{3271}{6} a^{7} - \\frac{3271}{6} a^{6} + \\frac{9575}{6} a^{5} + \\frac{1637}{6} a^{4} + \\frac{1637}{6} a^{3} + 339 a^{2} + 56 a + 56 \\)', '\\( \\frac{14}{9} a^{20} - \\frac{55}{12} a^{19} - \\frac{13}{18} a^{18} - \\frac{151}{6} a^{17} + \\frac{445}{6} a^{16} + 12 a^{15} + \\frac{1439}{9} a^{14} - \\frac{1415}{3} a^{13} - \\frac{704}{9} a^{12} - \\frac{4466}{9} a^{11} + \\frac{8803}{6} a^{10} + \\frac{2237}{9} a^{9} + 734 a^{8} - \\frac{26155}{12} a^{7} - \\frac{2257}{6} a^{6} - \\frac{733}{2} a^{5} + \\frac{3296}{3} a^{4} + \\frac{580}{3} a^{3} - \\frac{719}{9} a^{2} + 233 a + \\frac{359}{9} \\)', '\\( -\\frac{85}{36} a^{20} + \\frac{145}{36} a^{19} + \\frac{41}{12} a^{18} + \\frac{229}{6} a^{17} - \\frac{391}{6} a^{16} - 55 a^{15} - \\frac{2182}{9} a^{14} + \\frac{3727}{9} a^{13} + \\frac{1043}{3} a^{12} + \\frac{13565}{18} a^{11} - \\frac{23153}{18} a^{10} - \\frac{6445}{6} a^{9} - \\frac{13451}{12} a^{8} + \\frac{22883}{12} a^{7} + \\frac{6335}{4} a^{6} + \\frac{1714}{3} a^{5} - \\frac{2875}{3} a^{4} - \\frac{1583}{2} a^{3} + \\frac{1018}{9} a^{2} - \\frac{1825}{9} a - \\frac{500}{3} \\)', '\\( \\frac{47}{18} a^{20} - \\frac{19}{36} a^{18} - \\frac{253}{6} a^{17} + \\frac{26}{3} a^{15} + \\frac{2407}{9} a^{14} - \\frac{505}{9} a^{12} - \\frac{7462}{9} a^{11} + \\frac{3209}{18} a^{9} + \\frac{7357}{6} a^{8} - \\frac{3257}{12} a^{6} - \\frac{3671}{6} a^{5} + \\frac{845}{6} a^{3} - \\frac{1216}{9} a^{2} + \\frac{268}{9} \\)', '\\( -\\frac{103}{18} a^{20} + \\frac{103}{36} a^{19} + \\frac{103}{36} a^{18} + \\frac{278}{3} a^{17} - \\frac{139}{3} a^{16} - \\frac{139}{3} a^{15} - \\frac{5306}{9} a^{14} + \\frac{2653}{9} a^{13} + \\frac{2653}{9} a^{12} + \\frac{16505}{9} a^{11} - \\frac{16505}{18} a^{10} - \\frac{16505}{18} a^{9} - \\frac{5447}{2} a^{8} + \\frac{5447}{4} a^{7} + \\frac{5447}{4} a^{6} + 1371 a^{5} - \\frac{1371}{2} a^{4} - \\frac{1371}{2} a^{3} + \\frac{2633}{9} a^{2} - \\frac{1312}{9} a - \\frac{1312}{9} \\)', '\\( \\frac{13}{9} a^{20} + \\frac{7}{18} a^{19} - \\frac{5}{12} a^{18} - \\frac{70}{3} a^{17} - \\frac{13}{2} a^{16} + \\frac{19}{3} a^{15} + \\frac{1333}{9} a^{14} + \\frac{386}{9} a^{13} - \\frac{112}{3} a^{12} - \\frac{4138}{9} a^{11} - \\frac{1253}{9} a^{10} + \\frac{635}{6} a^{9} + 681 a^{8} + \\frac{1309}{6} a^{7} - \\frac{1673}{12} a^{6} - 339 a^{5} - \\frac{719}{6} a^{4} + \\frac{353}{6} a^{3} - \\frac{721}{9} a^{2} - \\frac{203}{9} a + 12 \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', '1/2*a^15 - 1/2*a^3', '1/2*a^16 - 1/2*a^4', '1/6*a^17 + 1/6*a^16 + 1/6*a^15 - 1/3*a^14 - 1/3*a^13 - 1/3*a^12 + 1/3*a^11 + 1/3*a^10 + 1/3*a^9 - 1/3*a^8 - 1/3*a^7 - 1/3*a^6 + 1/6*a^5 + 1/6*a^4 + 1/6*a^3 - 1/3*a^2 - 1/3*a - 1/3', '1/12*a^18 + 1/3*a^12 + 1/6*a^9 - 1/4*a^6 - 1/2*a^3 - 1/3', '1/36*a^19 - 1/36*a^18 - 1/6*a^16 + 1/6*a^15 + 1/9*a^13 - 1/9*a^12 - 5/18*a^10 + 5/18*a^9 - 1/12*a^7 + 1/12*a^6 - 1/3*a^4 + 1/3*a^3 + 2/9*a - 2/9', '1/36*a^20 - 1/36*a^18 + 1/6*a^16 - 1/6*a^15 - 2/9*a^14 - 1/3*a^13 - 4/9*a^12 + 1/18*a^11 + 1/3*a^10 - 7/18*a^9 - 5/12*a^8 - 1/3*a^7 - 1/4*a^6 - 1/6*a^5 + 1/6*a^4 - 1/9*a^2 - 1/3*a + 4/9']}
• 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, [0]], [5, [0]], [7, [[7, 3]]], [11, [[10, 1], [6, 1], [5, 1]]], [13, [[7, 3]]], [17, [[18, 1], [2, 1], [1, 1]]], [19, [[7, 3]]], [23, [[6, 1], [4, 3], [3, 1]]], [29, [[12, 1], [6, 1], [3, 1]]], [31, [[12, 1], [3, 1], [2, 3]]], [37, [[7, 3]]], [41, [[12, 1], [6, 1], [3, 1]]], [43, [[12, 1], [6, 1], [3, 1]]], [47, [[12, 1], [6, 1], [3, 1]]], [53, [[6, 3], [2, 1], [1, 1]]], [59, [[6, 1], [4, 3], [3, 1]]]], 'label': '21.5.211442929780702787875897344000000.1', 'torsion_gen': '\\( -1 \\)', 'units': ['\\( -\\frac{4}{3} a^{18} + \\frac{43}{2} a^{15} - \\frac{409}{3} a^{12} + \\frac{1270}{3} a^{9} - 629 a^{6} + \\frac{637}{2} a^{3} + \\frac{202}{3} \\)', '\\( \\frac{25}{12} a^{18} - \\frac{67}{2} a^{15} + \\frac{634}{3} a^{12} - \\frac{3905}{6} a^{9} + \\frac{3819}{4} a^{6} - 472 a^{3} - \\frac{307}{3} \\)', '\\( -\\frac{19}{12} a^{18} + \\frac{51}{2} a^{15} - \\frac{484}{3} a^{12} + \\frac{2993}{6} a^{9} - \\frac{2941}{4} a^{6} + 365 a^{3} + \\frac{241}{3} \\)', '\\( -a^{18} + \\frac{33}{2} a^{15} - 107 a^{12} + 339 a^{9} - 512 a^{6} + \\frac{521}{2} a^{3} + 56 \\)', '\\( \\frac{7}{12} a^{18} - 9 a^{15} + \\frac{163}{3} a^{12} - \\frac{959}{6} a^{9} + \\frac{893}{4} a^{6} - \\frac{209}{2} a^{3} - \\frac{70}{3} \\)', '\\( -\\frac{757}{36} a^{20} + \\frac{217}{36} a^{18} + \\frac{1019}{3} a^{17} - \\frac{583}{6} a^{15} - \\frac{19396}{9} a^{14} + \\frac{5536}{9} a^{12} + \\frac{120317}{18} a^{11} - \\frac{34259}{18} a^{9} - \\frac{118727}{12} a^{8} + \\frac{33719}{12} a^{6} + \\frac{29735}{6} a^{5} - \\frac{4210}{3} a^{3} + \\frac{9637}{9} a^{2} - \\frac{2734}{9} \\)', '\\( -\\frac{20}{3} a^{20} - \\frac{7}{6} a^{19} - \\frac{7}{6} a^{18} + \\frac{647}{6} a^{17} + \\frac{113}{6} a^{16} + \\frac{113}{6} a^{15} - \\frac{2056}{3} a^{14} - \\frac{358}{3} a^{13} - \\frac{358}{3} a^{12} + \\frac{6391}{3} a^{11} + \\frac{1108}{3} a^{10} + \\frac{1108}{3} a^{9} - \\frac{9491}{3} a^{8} - \\frac{3271}{6} a^{7} - \\frac{3271}{6} a^{6} + \\frac{9575}{6} a^{5} + \\frac{1637}{6} a^{4} + \\frac{1637}{6} a^{3} + 339 a^{2} + 56 a + 56 \\)', '\\( \\frac{14}{9} a^{20} - \\frac{55}{12} a^{19} - \\frac{13}{18} a^{18} - \\frac{151}{6} a^{17} + \\frac{445}{6} a^{16} + 12 a^{15} + \\frac{1439}{9} a^{14} - \\frac{1415}{3} a^{13} - \\frac{704}{9} a^{12} - \\frac{4466}{9} a^{11} + \\frac{8803}{6} a^{10} + \\frac{2237}{9} a^{9} + 734 a^{8} - \\frac{26155}{12} a^{7} - \\frac{2257}{6} a^{6} - \\frac{733}{2} a^{5} + \\frac{3296}{3} a^{4} + \\frac{580}{3} a^{3} - \\frac{719}{9} a^{2} + 233 a + \\frac{359}{9} \\)', '\\( -\\frac{85}{36} a^{20} + \\frac{145}{36} a^{19} + \\frac{41}{12} a^{18} + \\frac{229}{6} a^{17} - \\frac{391}{6} a^{16} - 55 a^{15} - \\frac{2182}{9} a^{14} + \\frac{3727}{9} a^{13} + \\frac{1043}{3} a^{12} + \\frac{13565}{18} a^{11} - \\frac{23153}{18} a^{10} - \\frac{6445}{6} a^{9} - \\frac{13451}{12} a^{8} + \\frac{22883}{12} a^{7} + \\frac{6335}{4} a^{6} + \\frac{1714}{3} a^{5} - \\frac{2875}{3} a^{4} - \\frac{1583}{2} a^{3} + \\frac{1018}{9} a^{2} - \\frac{1825}{9} a - \\frac{500}{3} \\)', '\\( \\frac{47}{18} a^{20} - \\frac{19}{36} a^{18} - \\frac{253}{6} a^{17} + \\frac{26}{3} a^{15} + \\frac{2407}{9} a^{14} - \\frac{505}{9} a^{12} - \\frac{7462}{9} a^{11} + \\frac{3209}{18} a^{9} + \\frac{7357}{6} a^{8} - \\frac{3257}{12} a^{6} - \\frac{3671}{6} a^{5} + \\frac{845}{6} a^{3} - \\frac{1216}{9} a^{2} + \\frac{268}{9} \\)', '\\( -\\frac{103}{18} a^{20} + \\frac{103}{36} a^{19} + \\frac{103}{36} a^{18} + \\frac{278}{3} a^{17} - \\frac{139}{3} a^{16} - \\frac{139}{3} a^{15} - \\frac{5306}{9} a^{14} + \\frac{2653}{9} a^{13} + \\frac{2653}{9} a^{12} + \\frac{16505}{9} a^{11} - \\frac{16505}{18} a^{10} - \\frac{16505}{18} a^{9} - \\frac{5447}{2} a^{8} + \\frac{5447}{4} a^{7} + \\frac{5447}{4} a^{6} + 1371 a^{5} - \\frac{1371}{2} a^{4} - \\frac{1371}{2} a^{3} + \\frac{2633}{9} a^{2} - \\frac{1312}{9} a - \\frac{1312}{9} \\)', '\\( \\frac{13}{9} a^{20} + \\frac{7}{18} a^{19} - \\frac{5}{12} a^{18} - \\frac{70}{3} a^{17} - \\frac{13}{2} a^{16} + \\frac{19}{3} a^{15} + \\frac{1333}{9} a^{14} + \\frac{386}{9} a^{13} - \\frac{112}{3} a^{12} - \\frac{4138}{9} a^{11} - \\frac{1253}{9} a^{10} + \\frac{635}{6} a^{9} + 681 a^{8} + \\frac{1309}{6} a^{7} - \\frac{1673}{12} a^{6} - 339 a^{5} - \\frac{719}{6} a^{4} + \\frac{353}{6} a^{3} - \\frac{721}{9} a^{2} - \\frac{203}{9} a + 12 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', '1/2*a^15 - 1/2*a^3', '1/2*a^16 - 1/2*a^4', '1/6*a^17 + 1/6*a^16 + 1/6*a^15 - 1/3*a^14 - 1/3*a^13 - 1/3*a^12 + 1/3*a^11 + 1/3*a^10 + 1/3*a^9 - 1/3*a^8 - 1/3*a^7 - 1/3*a^6 + 1/6*a^5 + 1/6*a^4 + 1/6*a^3 - 1/3*a^2 - 1/3*a - 1/3', '1/12*a^18 + 1/3*a^12 + 1/6*a^9 - 1/4*a^6 - 1/2*a^3 - 1/3', '1/36*a^19 - 1/36*a^18 - 1/6*a^16 + 1/6*a^15 + 1/9*a^13 - 1/9*a^12 - 5/18*a^10 + 5/18*a^9 - 1/12*a^7 + 1/12*a^6 - 1/3*a^4 + 1/3*a^3 + 2/9*a - 2/9', '1/36*a^20 - 1/36*a^18 + 1/6*a^16 - 1/6*a^15 - 2/9*a^14 - 1/3*a^13 - 4/9*a^12 + 1/18*a^11 + 1/3*a^10 - 7/18*a^9 - 5/12*a^8 - 1/3*a^7 - 1/4*a^6 - 1/6*a^5 + 1/6*a^4 - 1/9*a^2 - 1/3*a + 4/9']}