Number field data - 5.3.4671875.1

Formats: - HTML - YAML - JSON - 2026-03-24T12:38:44.816005

• 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[]
  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': [-10, -25, -30, -15, 0, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 4671875, 'disc_rad': 1495, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [156, 60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 140.1188614638235, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.3.4671875.1', 'local_algs': ['5.1.5.6a1.1', '13.1.2.1a1.1', '13.3.1.0a1.1', '23.1.2.1a1.1', '23.3.1.0a1.1'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 1, 'ramps': [5, 13, 23], 'rd': 21.5723889925, 'regulator': {'__RealLiteral__': 0, 'data': '50.1747617933', 'prec': 44}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 3, '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, 1], [1, 1]]], [3, [[5, 1]]], [5, [0]], [7, [[5, 1]]], [11, [[2, 2], [1, 1]]], [13, [0]], [17, [[3, 1], [2, 1]]], [19, [[5, 1]]], [23, [0]], [29, [[2, 2], [1, 1]]], [31, [[3, 1], [2, 1]]], [37, [[2, 2], [1, 1]]], [41, [[3, 1], [2, 1]]], [43, [[4, 1], [1, 1]]], [47, [[2, 1], [1, 3]]], [53, [[4, 1], [1, 1]]], [59, [[4, 1], [1, 1]]]], 'label': '5.3.4671875.1', 'res': {'sib': ['-2153,-11675,16185,-15320,5935,-6466,3285,675,-1405,1035,-172,140,-30,15,0,1', '-44111,234240,64105,-715155,-2098125,-1681219,-746715,-161280,104380,94260,-7413,-7720,-9260,-4255,975,632,75,-10,-40,-5,1', '100,-50,-175,275,-230,93,-15,-5,10,-5,1', '108267264,-260082816,394300352,-301294752,634033216,-248005240,354857500,-145249120,116769715,-32122905,27146827,176627,3429906,1036209,148268,134260,10045,4350,335,590,-171,84,22,-7,1', '235,3125,-75525,170325,-116695,106860,187230,-243700,250980,-131840,-3906,26420,-14795,2555,1245,-351,-80,25,15,-5,1', '315,-1660,4880,-4360,-2580,4516,381,-1406,95,160,-21,-6,1', '3397,-1641,545,-105,45,-2,1', '3756282422786000,-45340979022890000,277984384118309000,-437190366414964750,192081737700743875,251495108015121275,-446422398023406625,285173114093766925,1170160266729925,-178789996311470800,196751994054371840,-131069599845753225,62489289690996175,-22711943354323775,7306488641253670,-3151360225820495,2026211644926060,-1274890873068695,647491790566910,-260781781537085,85747867830861,-24767060588110,7212698972480,-2352625712175,797918227515,-244672966777,63748021405,-14724027550,3563678905,-1044603610,324535764,-85478740,16364475,-1807135,-26290,46162,-6390,-115,150,-20,1', '407885,8668100,71496630,149065855,687289655,-85520894,144433285,-142221205,35768515,-16346155,7458071,-1976615,516975,-124965,39165,-6034,745,-305,30,0,1', '4742000,30845000,17629000,-159706000,-55003125,337502100,-129748500,-51082425,4048625,-76780975,105997475,366500,-55009720,37241390,-6155615,-12233628,11577910,-4652165,309915,1057795,-814783,332950,-71840,-12130,17505,-8766,2910,-705,125,-15,1', '502767100,2497734250,7948351875,23102048975,48981412900,69824243235,71861983400,55623622240,41802291835,33441038590,20248887678,10443691335,5748257080,2016878030,990980880,239227517,73138210,12580615,-1891165,-1385570,-699419,-265510,-7320,-20065,3040,-742,365,-20,20,0,1', '520731852800,-410010624000,1038325862400,-1627066035200,2031497481600,-2780418357920,2883168014400,-2266100999600,1813000034600,-1435719593660,947454819025,-545966618760,309573333240,-167361236855,80189442135,-34930884978,14535612975,-5680246415,1990488975,-616886205,171469117,-42720855,9323185,-1746465,275665,-36646,4285,-525,80,-10,1', '871732,-134320,246855,-70130,34825,-3578,1340,-60,70,0,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a^{4} - a^{3} - 14 a^{2} - 16 a - 9 \\)', '\\( \\frac{1}{2} a^{4} - 8 a^{2} - \\frac{29}{2} a - 6 \\)', '\\( a^{4} - \\frac{3}{2} a^{3} - \\frac{31}{2} a^{2} - \\frac{5}{2} a + 14 \\)'], 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a', '1/2*a^4 - 1/2*a']}