Number field data - 20.2.1816889967552059474944.1

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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[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	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': [-1, 0, 2, 0, 0, 0, 6, 0, -17, 0, 3, 0, 11, 0, 0, 0, -6, 0, 0, 0, 1], 'conductor': 0, 'degree': 20, 'dirichlet_group': [], 'disc_abs': 1816889967552059474944, 'disc_rad': 72994, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 2], [4, 1]]], [5, [[6, 2], [4, 2]]], [7, [[8, 1], [6, 2]]], [11, [[6, 2], [4, 1], [2, 2]]], [13, [[8, 2], [2, 2]]], [17, [[5, 4]]], [19, [[10, 1], [5, 2]]], [23, [[8, 1], [4, 2], [2, 2]]], [29, [[16, 1], [4, 1]]], [31, [[4, 5]]], [37, [[16, 1], [4, 1]]], [41, [[6, 2], [4, 2]]], [43, [[12, 1], [4, 2]]], [47, [[6, 2], [4, 1], [2, 2]]], [53, [[8, 2], [2, 2]]], [59, [[4, 1], [2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [3809280, 983040], 'galois_label': '20T992', 'galt': 992, 'grd': 731.7693250181059, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '20.2.1816889967552059474944.1', 'local_algs': ['2.10.0.1', '2.10.10.12', 'm36497.1.1.0', 'm36497.1.1.0', 'm36497.1.2.0', 'm36497.1.2.0', 'm36497.1.2.0', 'm36497.2.1.1', 'm36497.2.1.1', 'm36497.1.4.0', 'm36497.2.2.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 9, 'ramps': [2, 36497], 'rd': 11.5602288431, 'regulator': {'__RealLiteral__': 0, 'data': '201.865023128', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.5.-3.-2.1', '1.-1.0.1.-1.1.-1.1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{412}{1129} a^{18} + \\frac{563}{1129} a^{16} - \\frac{2100}{1129} a^{14} - \\frac{3056}{1129} a^{12} + \\frac{2603}{1129} a^{10} + \\frac{5996}{1129} a^{8} - \\frac{2603}{1129} a^{6} - \\frac{4546}{1129} a^{4} - \\frac{463}{1129} a^{2} + \\frac{490}{1129} \\)', '\\( a \\)', '\\( \\frac{287}{1129} a^{18} - \\frac{49}{1129} a^{16} - \\frac{1989}{1129} a^{14} - \\frac{101}{1129} a^{12} + \\frac{4496}{1129} a^{10} + \\frac{2434}{1129} a^{8} - \\frac{6754}{1129} a^{6} - \\frac{980}{1129} a^{4} + \\frac{1434}{1129} a^{2} + \\frac{1706}{1129} \\)', '\\( \\frac{2646}{1129} a^{19} + \\frac{560}{1129} a^{18} + \\frac{2869}{2258} a^{17} + \\frac{1103}{2258} a^{16} - \\frac{14868}{1129} a^{15} - \\frac{5917}{2258} a^{14} - \\frac{7953}{1129} a^{13} - \\frac{5929}{2258} a^{12} + \\frac{23442}{1129} a^{11} + \\frac{4119}{1129} a^{10} + \\frac{19962}{1129} a^{9} + \\frac{11729}{2258} a^{8} - \\frac{63819}{2258} a^{7} - \\frac{5248}{1129} a^{6} + \\frac{465}{1129} a^{5} - \\frac{3907}{2258} a^{4} - \\frac{5969}{2258} a^{3} - \\frac{875}{2258} a^{2} + \\frac{3695}{1129} a + \\frac{107}{1129} \\)', '\\( \\frac{3557}{2258} a^{19} + \\frac{950}{1129} a^{18} + \\frac{1871}{2258} a^{17} + \\frac{1851}{2258} a^{16} - \\frac{10101}{1129} a^{15} - \\frac{4908}{1129} a^{14} - \\frac{10567}{2258} a^{13} - \\frac{9917}{2258} a^{12} + \\frac{16280}{1129} a^{11} + \\frac{6161}{1129} a^{10} + \\frac{13667}{1129} a^{9} + \\frac{19595}{2258} a^{8} - \\frac{21925}{1129} a^{7} - \\frac{7290}{1129} a^{6} + \\frac{163}{2258} a^{5} - \\frac{2941}{1129} a^{4} - \\frac{3167}{2258} a^{3} - \\frac{3319}{2258} a^{2} + \\frac{3359}{2258} a + \\frac{1613}{2258} \\)', '\\( \\frac{1079}{1129} a^{19} - \\frac{4691}{2258} a^{18} + \\frac{1091}{2258} a^{17} - \\frac{2889}{2258} a^{16} - \\frac{6278}{1129} a^{15} + \\frac{13287}{1129} a^{14} - \\frac{3334}{1129} a^{13} + \\frac{8278}{1129} a^{12} + \\frac{21159}{2258} a^{11} - \\frac{21142}{1129} a^{10} + \\frac{19053}{2258} a^{9} - \\frac{40889}{2258} a^{8} - \\frac{27933}{2258} a^{7} + \\frac{54703}{2258} a^{6} - \\frac{4147}{2258} a^{5} + \\frac{6573}{2258} a^{4} - \\frac{596}{1129} a^{3} + \\frac{3559}{2258} a^{2} + \\frac{5263}{2258} a - \\frac{3439}{1129} \\)', '\\( \\frac{3557}{2258} a^{19} + \\frac{3213}{1129} a^{18} + \\frac{1871}{2258} a^{17} + \\frac{3887}{2258} a^{16} - \\frac{10101}{1129} a^{15} - \\frac{18054}{1129} a^{14} - \\frac{10567}{2258} a^{13} - \\frac{21895}{2258} a^{12} + \\frac{16280}{1129} a^{11} + \\frac{28304}{1129} a^{10} + \\frac{13667}{1129} a^{9} + \\frac{53479}{2258} a^{8} - \\frac{21925}{1129} a^{7} - \\frac{37336}{1129} a^{6} + \\frac{163}{2258} a^{5} - \\frac{2903}{1129} a^{4} - \\frac{3167}{2258} a^{3} - \\frac{6361}{2258} a^{2} + \\frac{3359}{2258} a + \\frac{8651}{2258} \\)', '\\( \\frac{1079}{1129} a^{19} + \\frac{3577}{2258} a^{18} + \\frac{1091}{2258} a^{17} + \\frac{1427}{2258} a^{16} - \\frac{6278}{1129} a^{15} - \\frac{10426}{1129} a^{14} - \\frac{3334}{1129} a^{13} - \\frac{4278}{1129} a^{12} + \\frac{21159}{2258} a^{11} + \\frac{17664}{1129} a^{10} + \\frac{19053}{2258} a^{9} + \\frac{26233}{2258} a^{8} - \\frac{27933}{2258} a^{7} - \\frac{47747}{2258} a^{6} - \\frac{4147}{2258} a^{5} + \\frac{315}{2258} a^{4} - \\frac{596}{1129} a^{3} - \\frac{4735}{2258} a^{2} + \\frac{5263}{2258} a + \\frac{3637}{1129} \\)', '\\( \\frac{1079}{1129} a^{19} + \\frac{4691}{2258} a^{18} + \\frac{1091}{2258} a^{17} + \\frac{2889}{2258} a^{16} - \\frac{6278}{1129} a^{15} - \\frac{13287}{1129} a^{14} - \\frac{3334}{1129} a^{13} - \\frac{8278}{1129} a^{12} + \\frac{21159}{2258} a^{11} + \\frac{21142}{1129} a^{10} + \\frac{19053}{2258} a^{9} + \\frac{40889}{2258} a^{8} - \\frac{27933}{2258} a^{7} - \\frac{54703}{2258} a^{6} - \\frac{4147}{2258} a^{5} - \\frac{6573}{2258} a^{4} - \\frac{596}{1129} a^{3} - \\frac{3559}{2258} a^{2} + \\frac{5263}{2258} a + \\frac{3439}{1129} \\)', '\\( \\frac{3557}{2258} a^{19} - \\frac{3213}{1129} a^{18} + \\frac{1871}{2258} a^{17} - \\frac{3887}{2258} a^{16} - \\frac{10101}{1129} a^{15} + \\frac{18054}{1129} a^{14} - \\frac{10567}{2258} a^{13} + \\frac{21895}{2258} a^{12} + \\frac{16280}{1129} a^{11} - \\frac{28304}{1129} a^{10} + \\frac{13667}{1129} a^{9} - \\frac{53479}{2258} a^{8} - \\frac{21925}{1129} a^{7} + \\frac{37336}{1129} a^{6} + \\frac{163}{2258} a^{5} + \\frac{2903}{1129} a^{4} - \\frac{3167}{2258} a^{3} + \\frac{6361}{2258} a^{2} + \\frac{3359}{2258} a - \\frac{8651}{2258} \\)'], 'used_grh': False, '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^14 - 1/2*a^12 - 1/2*a^10 - 1/2*a^6 - 1/2*a^5 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^16 - 1/2*a^14 - 1/2*a^13 - 1/2*a^12 - 1/2*a^11 - 1/2*a^10 - 1/2*a^7 - 1/2*a^5 - 1/2*a^3 - 1/2', '1/2*a^17 - 1/2*a^13 - 1/2*a^11 - 1/2*a^10 - 1/2*a^8 - 1/2*a^5 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/2258*a^18 - 124/1129*a^16 - 597/2258*a^14 + 157/2258*a^12 - 1/2*a^11 + 295/1129*a^10 - 1/2*a^9 - 338/1129*a^8 + 539/2258*a^6 - 1/2*a^5 - 222/1129*a^4 - 1/2*a^3 - 265/1129*a^2 - 1/2*a + 239/1129', '1/2258*a^19 - 124/1129*a^17 + 266/1129*a^15 - 1/2*a^14 + 157/2258*a^13 + 295/1129*a^11 - 338/1129*a^9 + 539/2258*a^7 + 685/2258*a^5 - 1/2*a^4 - 265/1129*a^3 - 651/2258*a - 1/2']}