Number field data - 5.3.28638964487.1

Formats: - HTML - YAML - JSON - 2026-06-06T04:37:15.815166

• 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': [10], 'class_number': 10, 'cm': False, 'coeffs': [-5113, 2652, -37, -99, -1, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 28638964487, 'disc_rad': 11431, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60, 60, 96], 'galois_label': '5T5', 'galt': 5, 'grd': 384.0781640645782, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.3.28638964487.1', 'local_algs': ['7.1.1.0a1.1', '7.1.2.1a1.1', '7.1.2.1a1.2', '23.1.1.0a1.1', '23.1.1.0a1.1', '23.1.1.0a1.1', '23.1.2.1a1.1', '71.1.5.4a1.4'], 'maxp': 71, 'monogenic': 0, 'narrow_class_group': [2, 10], 'narrow_class_number': 20, 'num_ram': 3, 'r2': 1, 'ramps': [7, 23, 71], 'rd': 123.421682417, 'regulator': {'__RealLiteral__': 0, 'data': '277.803262761', 'prec': 44}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 2, '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, [[4, 1], [1, 1]]], [7, [0]], [11, [[3, 1], [2, 1]]], [13, [[2, 2], [1, 1]]], [17, [[3, 1], [2, 1]]], [19, [[4, 1], [1, 1]]], [23, [0]], [29, [[5, 1]]], [31, [[5, 1]]], [37, [[3, 1], [2, 1]]], [41, [[3, 1], [1, 2]]], [43, [[4, 1], [1, 1]]], [47, [[5, 1]]], [53, [[4, 1], [1, 1]]], [59, [[5, 1]]]], 'label': '5.3.28638964487.1', 'res': {'sib': ['-12887364531713,99079162962506,-72496236901851,-467246260142027,196033529884496,574074867551722,-191177457909283,-437965701872171,-78856914009034,88580019581535,29293916762987,9141905156366,9024611794019,4242084691159,570849426561,299399816118,33340342534,10152740011,-485764722,462263702,-77079062,-12025802,4599540,-1184116,42893,14460,-4879,466,25,-9,1', '-136336863109,-11356304043,21497298591,-18403042566,4533125757,5505520493,-1629022246,-263764174,167146169,-55639773,-632019,6288978,-891110,-126218,52948,-10796,-563,618,-37,-10,1', '-2380063,11199643,-23740383,30549983,-26916457,17293424,-8343897,2998695,-767812,135789,-19685,3375,-475,35,-6,1', '114753347339,280511148177,280555498478,104950893050,-20195581294,-26472805896,-3226052072,892952064,59924258,92706088,18703310,-4867015,-95215,38437,-36802,980,1672,-665,112,-10,1', '16606,-2185,2934,-69,-58,0,1', '191451392645253800633809,0,705439099460530877830725,0,627174266779752538936323,0,61593731047647472148216,0,-4932629099091917463037,0,1966702537388829007289,0,-144215546360303037684,0,12583342206647870000,0,-353801735046008197,0,-7880589784087087,0,2197069518544759,0,-152623185119396,0,6431868959672,0,-104418472240,0,-2870449612,0,240973742,0,-6576891,0,68666,0,1635,0,-54,0,1', '24768024749,9939007846,-1520587546,10499195858,-486461754,568680210,1436388969,-657065568,498417609,-171497812,73586430,-17324100,4636574,-535140,82958,4644,-594,304,-33,-8,1', '286327189152,-749556562848,814595599234,-534890862733,329490444861,-230059627606,131077825198,-54674046035,21817756994,-9676602230,3490653886,-893516742,241480385,-80772346,13172953,555336,280365,-105461,-33448,2466,1030,298,-50,-6,1', '353577422519447,0,422285013940706,0,1322950944548905,0,1402564781980278,0,139299602615775,0,-82940341272236,0,9615823074648,0,1557797407559,0,-132089318656,0,9787083355,0,-471059820,0,20030262,0,-600922,0,12852,0,-169,0,1', '5466052170414559,3149757240001632,13316804830464361,21318254205734123,31709444833180409,32248247690296459,26877052785143594,17840941029393934,10027547476512934,4749186227403706,1954598531699100,697824332157863,220979177219947,61916420219926,15664546053270,3541746206291,730594597347,133541176960,22614824811,3379953478,533208887,79896127,15721309,2423847,466527,46030,7738,355,127,-3,1', '6315816,-67103,165231,-194610,93315,4450,-955,-386,20,40,3,-6,1', '6436343,0,50255,0,48829,0,6144,0,175,0,1', '97,754,1966,1625,-579,-1054,-36,88,-60,-1,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a - 3 \\)', '\\( \\frac{29}{49} a^{4} + \\frac{9}{7} a^{3} - \\frac{2710}{49} a^{2} - \\frac{9530}{49} a + \\frac{49843}{49} \\)', '\\( \\frac{180}{49} a^{4} + \\frac{52}{7} a^{3} - \\frac{16672}{49} a^{2} - \\frac{57359}{49} a + \\frac{301848}{49} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/49*a^4 + 2/7*a^3 + 13/49*a^2 + 11/49*a + 24/49']}