Number field data - 20.0.1597098119556903839111328125.2

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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[]
  maxp	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
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1331, 0, 0, 0, 0, -858, 0, 0, 0, 0, 179, 0, 0, 0, 0, -12, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 20, 'disc_abs': 1597098119556903839111328125, 'disc_rad': 55, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [715, 400], 'galois_label': '20T125', 'galt': 125, 'grd': 68.02072465087673, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '20.0.1597098119556903839111328125.2', 'local_algs': ['5.1.20.27a1.4', '11.1.5.4a1.1', '11.1.5.4a1.3', '11.5.1.0a1.1', '11.5.1.0a1.1'], 'maximal_cm_subfield': [1, -1, 1, -1, 1], 'maxp': 11, 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 10, 'ramps': [5, 11], 'rd': 22.9174651666, 'regulator': {'__RealLiteral__': 0, 'data': '1387068.91153', 'prec': 40}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1'], 'torsion_order': 10, 'unit_signature_rank': 0, 'used_grh': False}
• 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, [[4, 5]]], [3, [[4, 5]]], [5, [0]], [7, [[4, 5]]], [11, [0]], [13, [[4, 5]]], [17, [[4, 5]]], [19, [[10, 2]]], [23, [[4, 5]]], [29, [[10, 2]]], [31, [[5, 4]]], [37, [[4, 5]]], [41, [[5, 4]]], [43, [[4, 5]]], [47, [[4, 5]]], [53, [[4, 5]]], [59, [[10, 2]]]], 'label': '20.0.1597098119556903839111328125.2', 'res': {}, 'torsion_gen': '\\( \\frac{3}{550} a^{15} - \\frac{1}{25} a^{10} + \\frac{188}{275} a^{5} - \\frac{51}{50} \\)', 'units': ['\\( \\frac{1}{550} a^{15} - \\frac{9}{550} a^{10} + \\frac{227}{550} a^{5} - \\frac{41}{25} \\)', '\\( \\frac{19}{6050} a^{19} + \\frac{13}{6050} a^{18} + \\frac{2}{275} a^{16} - \\frac{1}{550} a^{15} - \\frac{92}{3025} a^{14} - \\frac{101}{6050} a^{13} - \\frac{1}{275} a^{12} - \\frac{37}{550} a^{11} + \\frac{1}{50} a^{10} + \\frac{1508}{3025} a^{9} + \\frac{351}{1210} a^{8} + \\frac{6}{275} a^{7} + \\frac{639}{550} a^{6} - \\frac{239}{550} a^{5} - \\frac{171}{110} a^{4} - \\frac{56}{275} a^{3} - \\frac{19}{25} a^{2} - \\frac{147}{50} a + \\frac{7}{5} \\)', '\\( \\frac{19}{6050} a^{19} + \\frac{4}{3025} a^{18} + \\frac{3}{550} a^{17} + \\frac{1}{275} a^{16} + \\frac{1}{275} a^{15} - \\frac{92}{3025} a^{14} - \\frac{48}{3025} a^{13} - \\frac{29}{550} a^{12} - \\frac{19}{550} a^{11} - \\frac{13}{275} a^{10} + \\frac{1508}{3025} a^{9} + \\frac{119}{605} a^{8} + \\frac{43}{50} a^{7} + \\frac{59}{110} a^{6} + \\frac{196}{275} a^{5} - \\frac{171}{110} a^{4} - \\frac{301}{275} a^{3} - \\frac{62}{25} a^{2} - \\frac{113}{50} a - \\frac{68}{25} \\)', '\\( \\frac{7}{3025} a^{19} - \\frac{3}{3025} a^{18} - \\frac{1}{550} a^{17} - \\frac{1}{550} a^{16} + \\frac{3}{550} a^{15} - \\frac{27}{1210} a^{14} + \\frac{17}{6050} a^{13} + \\frac{4}{275} a^{12} + \\frac{8}{275} a^{11} - \\frac{8}{275} a^{10} + \\frac{2187}{6050} a^{9} - \\frac{173}{1210} a^{8} - \\frac{83}{275} a^{7} - \\frac{107}{275} a^{6} + \\frac{9}{11} a^{5} - \\frac{509}{550} a^{4} + \\frac{39}{550} a^{3} + \\frac{23}{50} a^{2} + \\frac{3}{2} a - \\frac{67}{50} \\)', '\\( \\frac{19}{6050} a^{19} - \\frac{23}{6050} a^{18} + \\frac{1}{275} a^{17} - \\frac{3}{550} a^{16} - \\frac{92}{3025} a^{14} + \\frac{243}{6050} a^{13} - \\frac{3}{110} a^{12} + \\frac{21}{550} a^{11} - \\frac{3}{550} a^{10} + \\frac{1508}{3025} a^{9} - \\frac{3677}{6050} a^{8} + \\frac{271}{550} a^{7} - \\frac{17}{22} a^{6} + \\frac{73}{550} a^{5} - \\frac{171}{110} a^{4} + \\frac{109}{55} a^{3} - \\frac{37}{50} a^{2} + \\frac{36}{25} a + \\frac{3}{50} \\)', '\\( \\frac{2}{3025} a^{19} - \\frac{19}{6050} a^{18} - \\frac{1}{275} a^{17} - \\frac{1}{275} a^{16} - \\frac{1}{550} a^{15} - \\frac{3}{1210} a^{14} + \\frac{92}{3025} a^{13} + \\frac{17}{550} a^{12} + \\frac{1}{22} a^{11} + \\frac{2}{55} a^{10} + \\frac{397}{6050} a^{9} - \\frac{1508}{3025} a^{8} - \\frac{283}{550} a^{7} - \\frac{331}{550} a^{6} - \\frac{119}{275} a^{5} + \\frac{51}{550} a^{4} + \\frac{171}{110} a^{3} + \\frac{3}{2} a^{2} + \\frac{127}{50} a + \\frac{101}{50} \\)', '\\( \\frac{1}{1210} a^{19} + \\frac{9}{6050} a^{18} - \\frac{1}{550} a^{17} - \\frac{1}{275} a^{16} + \\frac{2}{275} a^{15} - \\frac{49}{6050} a^{14} - \\frac{54}{3025} a^{13} + \\frac{4}{275} a^{12} + \\frac{1}{22} a^{11} - \\frac{4}{55} a^{10} + \\frac{829}{6050} a^{9} + \\frac{149}{605} a^{8} - \\frac{83}{275} a^{7} - \\frac{331}{550} a^{6} + \\frac{301}{275} a^{5} - \\frac{173}{275} a^{4} - \\frac{581}{550} a^{3} + \\frac{23}{50} a^{2} + \\frac{127}{50} a - \\frac{57}{25} \\)', '\\( \\frac{23}{6050} a^{19} - \\frac{3}{1210} a^{18} - \\frac{1}{550} a^{17} + \\frac{2}{275} a^{16} - \\frac{4}{275} a^{15} - \\frac{199}{6050} a^{14} + \\frac{169}{6050} a^{13} + \\frac{3}{275} a^{12} - \\frac{3}{55} a^{11} + \\frac{7}{55} a^{10} + \\frac{3413}{6050} a^{9} - \\frac{2619}{6050} a^{8} - \\frac{7}{25} a^{7} + \\frac{271}{275} a^{6} - \\frac{57}{25} a^{5} - \\frac{402}{275} a^{4} + \\frac{453}{275} a^{3} - \\frac{3}{10} a^{2} - \\frac{37}{25} a + \\frac{134}{25} \\)', '\\( \\frac{9}{3025} a^{18} - \\frac{3}{550} a^{17} + \\frac{1}{275} a^{16} + \\frac{1}{275} a^{15} - \\frac{86}{3025} a^{13} + \\frac{27}{550} a^{12} - \\frac{9}{275} a^{11} - \\frac{13}{550} a^{10} + \\frac{1358}{3025} a^{8} - \\frac{461}{550} a^{7} + \\frac{172}{275} a^{6} + \\frac{259}{550} a^{5} - \\frac{438}{275} a^{3} + \\frac{68}{25} a^{2} - \\frac{42}{25} a - \\frac{49}{50} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/5*a^7 - 1/5*a^6 - 1/5*a^5 + 2/5*a^2 - 2/5*a - 2/5', '1/5*a^8 - 2/5*a^6 - 1/5*a^5 + 2/5*a^3 + 1/5*a - 2/5', '1/5*a^9 + 2/5*a^6 - 2/5*a^5 + 2/5*a^4 - 1/5*a + 1/5', '1/110*a^10 + 49/110*a^5 - 1/10', '1/110*a^11 + 49/110*a^6 - 1/10*a', '1/110*a^12 + 1/22*a^7 + 2/5*a^6 + 2/5*a^5 + 1/10*a^2 - 1/5*a - 1/5', '1/110*a^13 + 1/22*a^8 - 1/5*a^6 + 2/5*a^5 + 1/10*a^3 - 2/5*a - 1/5', '1/550*a^14 - 1/275*a^13 - 1/550*a^12 + 1/275*a^11 + 1/550*a^10 + 49/550*a^9 + 6/275*a^8 - 49/550*a^7 - 61/275*a^6 - 61/550*a^5 - 21/50*a^4 + 6/25*a^3 + 21/50*a^2 + 9/25*a + 9/50', '1/550*a^15 + 1/550*a^10 + 167/550*a^5 + 4/25', '1/550*a^16 + 1/550*a^11 + 167/550*a^6 + 4/25*a', '1/550*a^17 + 1/550*a^12 - 53/550*a^7 + 2/5*a^6 + 2/5*a^5 + 9/25*a^2 - 1/5*a - 1/5', '1/6050*a^18 + 21/6050*a^13 - 503/6050*a^8 - 6/275*a^3', '1/6050*a^19 - 1/6050*a^14 - 1/550*a^13 + 1/275*a^12 + 1/550*a^11 - 1/275*a^10 - 371/6050*a^9 - 49/550*a^8 - 6/275*a^7 - 171/550*a^6 - 104/275*a^5 + 12/55*a^4 + 21/50*a^3 - 6/25*a^2 - 11/50*a + 11/25']}