Number field data - 34.2.11885748945456377039253666531245020090157279092950049.1

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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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 34, 'dirichlet_group': [], 'disc_abs': 11885748945456377039253666531245020090157279092950049, 'disc_rad': 11885748945456377039253666531245020090157279092950049, 'disc_sign': 1, 'frobs': [[2, [[30, 1], [4, 1]]], [3, [[17, 1], [12, 1], [3, 1], [2, 1]]], [5, [[20, 1], [10, 1], [3, 1], [1, 1]]], [7, [0]], [11, [[15, 1], [9, 2], [1, 1]]], [13, [[19, 1], [10, 1], [5, 1]]], [17, [[29, 1], [5, 1]]], [19, [[31, 1], [2, 1], [1, 1]]], [23, [[24, 1], [9, 1], [1, 1]]], [29, [[18, 1], [8, 1], [6, 1], [1, 2]]], [31, [[16, 1], [8, 1], [4, 1], [3, 2]]], [37, [[14, 1], [9, 1], [8, 1], [2, 1], [1, 1]]], [41, [[31, 1], [3, 1]]], [43, [[17, 1], [8, 1], [5, 1], [3, 1], [1, 1]]], [47, [[16, 1], [10, 1], [3, 1], [2, 2], [1, 1]]], [53, [[11, 1], [10, 1], [7, 1], [2, 3]]], [59, [[28, 1], [5, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [147616399519802070423809304821760000000, 147616399519802070423809304821760000000, 147616399519802070423809304821760000000, 147616399519802070423809304821760000000], 'galois_label': '34T115', 'galt': 115, 'grd': 1.0902178197707272e+26, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '34.2.11885748945456377039253666531245020090157279092950049.1', 'local_algs': ['7.2.1.1', '7.2.0.1', '7.15.0.1', '7.15.0.1', '191.2.0.1', '191.2.0.1', '191.2.1.2', '191.11.0.1', '191.17.0.1', 'm607.1.1.0', 'm607.1.1.0', 'm607.1.1.0', 'm607.1.2.0', 'm607.2.1.1', 'm607.1.5.0', 'm607.1.6.0', 'm607.1.16.0', 'm14645575916792712592989131451003587034531413111.2.1.1', 'm14645575916792712592989131451003587034531413111.1.11.0', 'm14645575916792712592989131451003587034531413111.1.21.0'], 'monogenic': 1, 'num_ram': 4, 'r2': 16, 'ramps': [7, 191, 607, 14645575916792712592989131451003587034531413111], 'rd': 34.0109237751, 'regulator': {'__RealLiteral__': 0, 'data': '2995765078540.3994', 'prec': 60}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{33} - 1 \\)', '\\( a^{33} - a^{32} - a^{15} - 1 \\)', '\\( a^{14} - a^{3} \\)', '\\( a^{21} - a^{20} \\)', '\\( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} + a^{27} - a^{26} + a^{25} - a^{24} - a^{22} - 1 \\)', '\\( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} + a^{27} \\)', '\\( a^{31} - a^{30} + a^{29} - a^{28} + a^{27} \\)', '\\( a^{33} - a^{32} + a^{31} - a^{30} + a^{27} - a^{26} - 1 \\)', '\\( a^{12} - a^{9} + a^{6} \\)', '\\( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} - a^{15} + a^{14} + a^{8} - a^{7} - 1 \\)', '\\( 2 a^{33} - 3 a^{32} + 3 a^{31} - 3 a^{30} + 3 a^{29} - 3 a^{28} + 3 a^{27} - 3 a^{26} + 3 a^{25} - 3 a^{24} + 3 a^{23} - 2 a^{22} + 2 a^{21} - a^{20} + a^{19} - a^{18} - a^{16} + a^{12} - a^{11} + a^{10} - a^{9} + a^{8} - a^{7} + a^{6} + a^{4} - a^{3} + a^{2} - a - 2 \\)', '\\( a^{32} - 2 a^{31} + a^{30} + a^{28} - a^{27} + a^{24} - a^{23} + a^{20} - a^{18} + a^{16} - a^{14} + a^{12} - a^{10} + a^{8} + a^{7} - a^{6} - a^{5} + a^{4} + a^{3} - a^{2} - a + 1 \\)', '\\( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} + a^{27} - a^{26} + a^{25} - a^{24} + a^{12} + a^{10} - a^{5} - 1 \\)', '\\( a^{33} - a^{32} + a^{31} - a^{30} + a^{29} - a^{28} - a^{26} + a^{25} + a^{18} - a^{13} - a^{7} + a^{5} + a^{4} - 1 \\)', '\\( 2 a^{33} - 2 a^{32} + 2 a^{31} - 2 a^{30} + a^{29} - a^{28} + 2 a^{27} - a^{26} + a^{25} - a^{24} + a^{23} + a^{19} + a^{14} - a^{9} + a^{6} - a^{4} - a^{3} - 2 \\)', '\\( a^{33} - a^{27} + a^{26} + a^{12} - a^{11} + a^{6} - a^{2} - 1 \\)', '\\( a^{33} - a^{32} - a^{30} - a^{27} + a^{26} + a^{23} + a^{20} - a^{18} + a^{17} - a^{16} - a^{14} - a^{12} - a^{9} + a^{8} + a^{7} + a^{5} + a^{4} + a^{2} - 2 \\)'], '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', 'a^15', 'a^16', 'a^17', 'a^18', 'a^19', 'a^20', 'a^21', 'a^22', 'a^23', 'a^24', 'a^25', 'a^26', 'a^27', 'a^28', 'a^29', 'a^30', 'a^31', 'a^32', 'a^33']}