Elliptic curve data - 21312.bn2

Formats: - HTML - YAML - JSON - 2025-10-08T22:25:41.454319

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '21312bq', 'Clabel': '21312bq2', 'Cnumber': 2, 'abc_quality': 0.9727427413985318, 'absD': 2363266368, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 7992, 'ainvs': [0, 0, 0, -840, -9074], 'analytic_rank': 1, 'bad_primes': [2, 3, 37], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 21312, 'degree': 8640, 'elladic_images': ['9.36.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.56865514980367600971540106626', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 39, 'isogeny_degrees': [1, 3], 'jinv': [1404928000, 50653], 'lmfdb_iso': '21312.bn', 'lmfdb_label': '21312.bn2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -23, -50], 'min_quad_twist_disc': 24, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '9.36.0.b.1', '24.24.0-3.a.1.2', '72.72.0.?', '74.2.0.?', '222.24.1.?', '333.108.4.?', '666.216.13.?', '888.48.1.?', '999.324.16.?', '1998.648.43.?', '2664.432.13.?', '7992.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.9712008689374540716860327427', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 333], [3, 2, 64], [37, 38, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32722458481035149069083761293', 'prec': 107}, 'szpiro_ratio': 3.1919059978466993, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -3, 0, 4, 0, 0, 0, -6, 0, 2, 0], 'aplist': [0, 0, 0, 1, -3, 4, -6, 2, 6, -6, 4, -1, 9, 8, 3, -3, -12, -8, -4, -15, 11, 10, -9, -6, 8], 'class_deg': 9, 'class_size': 3, 'conductor': 21312, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '21312.bn', 'trace_hash': 2151671631145938472}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.32068039706623277798367989989', 'prec': 103}, 'conductor': 21312, 'gens': [[-429, 2119, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '5.9712008689374540716860327427', 'prec': 100}], 'lmfdb_label': '21312.bn2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.88877415887230520663111795915', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3070490297474637050408223724193702253', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '21312.bn2'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 1084686
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [3]}
  • id: 1084687
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [3]}
  • id: 1084688
    {'degree': 3, 'field': [1, -3, -1, 1], 'lmfdb_label': '21312.bn2', 'torsion': [2]}
  • id: 1084689
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [3, 3]}
  • id: 1084691
    {'degree': 6, 'field': [-54, 0, 72, 0, -18, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [6]}
  • id: 1084690
    {'degree': 6, 'field': [1, -5, 0, 9, -2, -3, 1], 'lmfdb_label': '21312.bn2', 'torsion': [2, 2]}
  • id: 1084692
    {'degree': 6, 'field': [2, 0, 8, 0, 6, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [6]}
  • id: 1084694
    {'degree': 12, 'field': [4, 0, -16, 0, 52, 0, -44, 0, 28, 0, -6, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [3, 6]}
  • id: 1084696
    {'degree': 12, 'field': [4, 0, 72, 0, 220, 0, 252, 0, 120, 0, 22, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [2, 6]}
  • id: 1084695
    {'degree': 12, 'field': [9313, 22922, -6995, -27030, 2156, 11714, -847, -2350, 256, 210, -31, -6, 1], 'lmfdb_label': '21312.bn2', 'torsion': [2, 6]}
  • id: 1084693
    {'degree': 12, 'field': [26973, 0, 54432, 0, -5589, 0, -4320, 0, -369, 0, 0, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [4]}
  • id: 1084697
    {'degree': 18, 'field': [-13824, 0, 191232, 0, -185472, 0, 39424, 0, -16992, 0, -2208, 0, -392, 0, -72, 0, -6, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [9]}
  • id: 1084698
    {'degree': 18, 'field': [8064657, -296784, 11143656, -372600, 5098140, -136944, 998838, 4464, 219708, 7174, 49932, 72, -1311, -36, 144, -6, 18, 0, 1], 'lmfdb_label': '21312.bn2', 'torsion': [9]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 485285
    {'conductor': 21312, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '21312.bn2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 485286
    {'conductor': 21312, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21312.bn2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 485287
    {'conductor': 21312, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '21312.bn2', 'prime': 37, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1806533
    {'adelic_gens': [[7973, 7938, 7416, 7091], [3995, 0, 0, 7991], [19, 54, 576, 2899], [6047, 7938, 6048, 7937], [1, 27, 27, 730], [7939, 54, 7938, 55], [1, 54, 0, 1], [6695, 7938, 6519, 7181], [6193, 7148, 7008, 6953], [5993, 0, 0, 7991], [43, 30, 3702, 4999], [1, 0, 54, 1]], 'adelic_image': '7992.1296.43.?', 'conductor': 21312, 'lmfdb_label': '21312.bn2', 'prime': 0}
  • id: 98837
    {'conductor': 21312, 'elladic_image': '9.36.0.2', 'lmfdb_label': '21312.bn2', 'modell_image': '3Cs', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 998897
    {'lmfdb_iso': '21312.bn', 'p': 7, 'prec': 20, 'unit': 9515096234414122, 'val': -1}
  • id: 998896
    {'lmfdb_iso': '21312.bn', 'p': 11, 'prec': 20, 'unit': 5015376058685126133, 'val': 1}
  • id: 998901
    {'lmfdb_iso': '21312.bn', 'p': 13, 'prec': 20, 'unit': 1108447054581998044885, 'val': 1}
  • id: 998903
    {'lmfdb_iso': '21312.bn', 'p': 17, 'prec': 20, 'unit': 13290610270860591476821, 'val': 1}
  • id: 998904
    {'lmfdb_iso': '21312.bn', 'p': 19, 'prec': 20, 'unit': 19734215243905073096070, 'val': 2}
  • id: 998908
    {'lmfdb_iso': '21312.bn', 'p': 23, 'prec': 20, 'unit': 12830379045280602657014302, 'val': 1}
  • id: 998900
    {'lmfdb_iso': '21312.bn', 'p': 29, 'prec': 20, 'unit': 4622927197763556807987231283, 'val': 1}
  • id: 998914
    {'lmfdb_iso': '21312.bn', 'p': 31, 'prec': 20, 'unit': 20996684746970678076228697042, 'val': 1}
  • id: 998898
    {'lmfdb_iso': '21312.bn', 'p': 41, 'prec': 20, 'unit': 4190880480103167211817577366520, 'val': 1}
  • id: 998899
    {'lmfdb_iso': '21312.bn', 'p': 43, 'prec': 20, 'unit': 3139803976673551043086818098945, 'val': 1}
  • id: 998911
    {'lmfdb_iso': '21312.bn', 'p': 47, 'prec': 20, 'unit': 16436642002750537813430161976041, 'val': 1}
  • id: 998905
    {'lmfdb_iso': '21312.bn', 'p': 53, 'prec': 20, 'unit': 96261832978495211361661405655669, 'val': 1}
  • id: 998906
    {'lmfdb_iso': '21312.bn', 'p': 59, 'prec': 20, 'unit': 1003325674703473894833063619754619, 'val': 1}
  • id: 998912
    {'lmfdb_iso': '21312.bn', 'p': 61, 'prec': 20, 'unit': 4183226611350635857138762824444730, 'val': 1}
  • id: 998895
    {'lmfdb_iso': '21312.bn', 'p': 67, 'prec': 20, 'unit': 26096105901405448208161394584943989, 'val': 1}
  • id: 998910
    {'lmfdb_iso': '21312.bn', 'p': 71, 'prec': 20, 'unit': 3349884401297761882885957857889112, 'val': 1}
  • id: 998907
    {'lmfdb_iso': '21312.bn', 'p': 73, 'prec': 20, 'unit': 5417386196022630735734014001967174, 'val': 1}
  • id: 998902
    {'lmfdb_iso': '21312.bn', 'p': 79, 'prec': 20, 'unit': 548255728012916434080734281203506219, 'val': 1}
  • id: 998913
    {'lmfdb_iso': '21312.bn', 'p': 83, 'prec': 20, 'unit': 16566079400357863257691493316933182, 'val': 1}
  • id: 998909
    {'lmfdb_iso': '21312.bn', 'p': 89, 'prec': 20, 'unit': 3644281093575419150775661540307463523, 'val': 1}
  • id: 998894
    {'lmfdb_iso': '21312.bn', 'p': 97, 'prec': 20, 'unit': 18347567369695626345324168370203181220, 'val': 1}