Number field data - 5.1.8812500.1

Formats: - HTML - YAML - JSON - 2026-03-24T12:38:44.452496

• 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': [-50, 25, 0, 0, 0, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 8812500, 'disc_rad': 1410, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [80, 60, 156, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 152.74156135696145, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.8812500.1', 'local_algs': ['2.1.1.0a1.1', '2.1.1.0a1.1', '2.1.3.2a1.1', '3.1.2.1a1.1', '3.3.1.0a1.1', '5.1.5.6a1.1', '47.1.1.0a1.1', '47.1.2.1a1.1', '47.2.1.0a1.1'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 4, 'r2': 2, 'ramps': [2, 3, 5, 47], 'rd': 24.4917504671, 'regulator': {'__RealLiteral__': 0, 'data': '258.163469853', 'prec': 44}, '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, [0]], [3, [0]], [5, [0]], [7, [[5, 1]]], [11, [[3, 1], [1, 2]]], [13, [[3, 1], [2, 1]]], [17, [[4, 1], [1, 1]]], [19, [[4, 1], [1, 1]]], [23, [[3, 1], [1, 2]]], [29, [[2, 2], [1, 1]]], [31, [[3, 1], [2, 1]]], [37, [[5, 1]]], [41, [[3, 1], [1, 2]]], [43, [[3, 1], [2, 1]]], [47, [0]], [53, [[3, 1], [2, 1]]], [59, [[4, 1], [1, 1]]]], 'label': '5.1.8812500.1', 'res': {'sib': ['-11481993216,0,2035814400,0,6377441280,0,-2144679680,0,-1425223680,0,602392064,0,-204057600,0,95173120,0,-24528640,0,4011680,0,-401344,0,34400,0,-5760,0,640,0,-40,0,1', '-117636864,279563520,-120982400,-92628160,21218480,24852080,11732960,-7156300,-891605,1036600,75637,-20280,-61200,440,305,-120,760,0,-55,0,1', '-1556,1208,-660,240,-40,-2,1', '-5316,14850,-12185,-2750,650,-100,-255,-50,-20,0,1', '-53554372,33851540,-157738300,168983265,-236665270,337243665,-457212415,455771980,-402540335,292681905,-167703884,101946985,-55911485,23357220,-7697445,126308,1671330,-1270750,914800,-704345,427724,-206955,86755,-34560,12545,-3687,920,-225,55,-10,1', '-598895703125,1013653125000,-1511731640625,1319788875000,-1009542578125,489933670000,-338995735625,92391730000,-70191115625,7528775000,-18306840789,-1288312600,-4740619825,-885612640,-1025618045,-272872480,-202139135,-65399880,-24991955,-9691320,-2207687,-1128720,-186875,-95280,-13955,-3480,-615,-40,5,0,1', '1296,-9720,35640,-79920,123570,-141498,130620,-106215,77770,-45120,13359,6335,-10570,6785,-2435,118,385,-195,60,-10,1', '1600,0,-400,0,-100,80,25,-10,0,0,1', '25,0,-2106,0,175,0,-140,0,55,0,-10,0,1', '2500,-2500,2500,-5575,0,-1694,-2000,-625,-2500,40,-500,55,0,10,0,1', '2822499935639296,3905328289088000,19595533877030400,-25638168703677440,-9893950271043840,12557209221575680,5468229228254720,-289079873274880,287144513347840,324357641701120,67682736369664,431263497705280,38600764524000,-63514823889600,17158482982080,-31042931501120,7060483220960,-2921834968320,1214652151120,-333741680960,79691848016,-50752717840,8811261200,491378820,2445827255,746403370,329616410,25499500,22995795,-5914580,761824,-625120,39950,-35770,9110,-2080,895,-60,40,0,1', '5842736,-19764640,19239200,-7501600,9121280,-5489360,3390640,880200,-424280,952780,124688,72420,55975,1530,3270,500,-115,-20,-20,0,1', '613489324,181176508,367301256,804335592,574731834,479446874,322560773,173301606,87236892,41633174,23432272,7825904,3912683,1684456,220052,99248,170106,-85218,47519,-14562,4076,-758,124,-12,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( 13 a^{4} + 29 a^{2} + 68 a + 161 \\)', '\\( 25 a^{4} + \\frac{824}{5} a^{3} - 799 a^{2} + 2022 a - 2019 \\)'], 'zk': ['1', 'a', 'a^2', '1/5*a^3', '1/10*a^4 - 1/10*a^3 - 1/2*a^2 - 1/2*a']}