Number field data - 5.1.1609.1

Formats: - HTML - YAML - JSON - 2026-06-12T12:28:41.224337

• 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': [1, 1, -1, -1, 0, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 1609, 'disc_rad': 1609, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60], 'galois_label': '5T5', 'galt': 5, 'grd': 40.11234224026316, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.1609.1', 'local_algs': ['m1609.1.1.0', 'm1609.1.2.0', 'm1609.2.1.1'], 'maxp': 1609, 'monogenic': 1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 2, 'ramps': [1609], 'rd': 4.37835739203, 'regulator': {'__RealLiteral__': 0, 'data': '0.268355550838', 'prec': 47}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 1, '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, [[5, 1]]], [3, [[5, 1]]], [5, [[5, 1]]], [7, [[3, 1], [2, 1]]], [11, [[3, 1], [1, 2]]], [13, [[3, 1], [1, 2]]], [17, [[4, 1], [1, 1]]], [19, [[3, 1], [2, 1]]], [23, [[4, 1], [1, 1]]], [29, [[4, 1], [1, 1]]], [31, [[2, 2], [1, 1]]], [37, [[4, 1], [1, 1]]], [41, [[5, 1]]], [43, [[4, 1], [1, 1]]], [47, [[4, 1], [1, 1]]], [53, [[4, 1], [1, 1]]], [59, [[3, 1], [1, 2]]]], 'label': '5.1.1609.1', 'res': {'sib': ['-4099849,334708,-283188,-14731,-1518,-1592,205,-15,29,-2,1', '1,-1,-1,0,3,-1,-2,3,-1,-1,1', '32,-176,160,12,-14,-3,1', '-265184,495856,454400,-1532036,2037394,-4104841,4759639,-2420694,678406,-186374,403506,-668828,1103653,-491255,-121906,226457,-66826,-13127,15997,-1723,-8821,5683,235,-1721,589,144,-162,34,9,-6,1', '-43,-148,-174,-114,-311,-209,313,60,-156,48,6,-21,16,-1,-3,1', '1,-1,0,6,-10,9,8,2,34,-22,58,-67,41,0,-27,93,-82,122,-95,45,39,-89,102,-73,52,-36,29,-20,11,-4,1', '1,-5,12,-21,36,-63,103,-143,166,-170,169,-170,166,-143,103,-63,36,-21,12,-5,1', '1,0,475,0,7364,0,18414,0,-9942,0,2521,0,-8184,0,4045,0,-266,0,-81,0,60,0,-8,0,1', '36,0,-1417,0,220,0,-108,0,-23,0,6,0,1', '4163357,-8367616,4648377,1877040,-4779663,3191768,-67217,-1027219,540266,-19351,-117381,41228,1868,-5591,2916,154,-228,63,-3,-6,1', '56096,-890432,6225800,-25749136,71909304,-146767415,229068863,-279250301,266921963,-196815559,104916335,-30235191,-8835043,17409170,-11319184,3619192,470080,-1322045,854945,-327235,75837,-9729,4477,-5529,3849,-1879,709,-206,48,-9,1', '90193009,364846249,389212100,-236639903,-563796486,434468816,1850500924,2206348851,1915785294,1807947326,1245033635,280305453,-337401460,-546336977,-402423505,-189297480,-44432550,64398856,103999371,95982849,61772027,31822207,13208689,3920824,405402,-812139,-511717,-260304,-36601,-4500,12888,3334,3183,584,217,-130,-41,-28,4,0,1', '9497,12969,-2496,-3528,6453,-12709,9806,-13180,7631,-6751,4732,-1384,2044,-286,431,-78,68,-13,9,0,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a^{4} - a^{2} - a + 1 \\)', '\\( a^{4} - a^{3} - a^{2} + 1 \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4']}