Elliptic curve isogeny class data - 8400.bn

Formats: - HTML - YAML - JSON - 2025-10-15T14:10:24.177638

• 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, 1, 0, 0, 0, -1, 0, 1, 0, -4, 0, 2, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 1, 0, -1, -4, 2, 6, -4, 0, -2, 0, -6, 2, -4, 0, -6, -12, -2, 4, 0, 6, 16, -12, -14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 8400, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '8400.bn', 'trace_hash': 2290046165040161316}
• ec_padic •

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

  
  
  • id: 347759
    {'lmfdb_iso': '8400.bn', 'p': 11, 'prec': 20, 'unit': 13421543864773824078, 'val': 1}
  • id: 347757
    {'lmfdb_iso': '8400.bn', 'p': 13, 'prec': 20, 'unit': 1387175109816607645526, 'val': 1}
  • id: 347760
    {'lmfdb_iso': '8400.bn', 'p': 17, 'prec': 20, 'unit': 156276361596263273476494, 'val': 1}
  • id: 347761
    {'lmfdb_iso': '8400.bn', 'p': 19, 'prec': 20, 'unit': 453194290931677514995206, 'val': 1}
  • id: 347756
    {'lmfdb_iso': '8400.bn', 'p': 29, 'prec': 20, 'unit': 4224076780519105273188426533, 'val': 1}
  • id: 347753
    {'lmfdb_iso': '8400.bn', 'p': 37, 'prec': 20, 'unit': 365922974193928652840853496859, 'val': 1}
  • id: 347754
    {'lmfdb_iso': '8400.bn', 'p': 41, 'prec': 20, 'unit': 684380956990344787890699580503, 'val': 1}
  • id: 347755
    {'lmfdb_iso': '8400.bn', 'p': 43, 'prec': 20, 'unit': 478331369985979089629340571404, 'val': 1}
  • id: 347762
    {'lmfdb_iso': '8400.bn', 'p': 53, 'prec': 20, 'unit': 524451711947125821635195455100578, 'val': 1}
  • id: 347765
    {'lmfdb_iso': '8400.bn', 'p': 59, 'prec': 20, 'unit': 758227817090617189510991334507755, 'val': 1}
  • id: 347766
    {'lmfdb_iso': '8400.bn', 'p': 61, 'prec': 20, 'unit': 6961780023334741759134087019001250, 'val': 1}
  • id: 347752
    {'lmfdb_iso': '8400.bn', 'p': 67, 'prec': 20, 'unit': 11382735023678161814779446129024160, 'val': 1}
  • id: 347763
    {'lmfdb_iso': '8400.bn', 'p': 73, 'prec': 20, 'unit': 226237777197397201795613351008189554, 'val': 1}
  • id: 347758
    {'lmfdb_iso': '8400.bn', 'p': 79, 'prec': 20, 'unit': 457095401889500635299170798239475748, 'val': 1}
  • id: 347751
    {'lmfdb_iso': '8400.bn', 'p': 83, 'prec': 20, 'unit': 1627170111078640652544643726674543355, 'val': 1}
  • id: 347764
    {'lmfdb_iso': '8400.bn', 'p': 89, 'prec': 20, 'unit': 4843584548542391345853774866019949644, 'val': 1}
  • id: 347750
    {'lmfdb_iso': '8400.bn', 'p': 97, 'prec': 20, 'unit': 26966345202635350897287849898749348369, 'val': 1}
• 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[]

  
  
  • id: 54118
    {'Ciso': '8400cd', 'Clabel': '8400cd5', 'Cnumber': 5, 'abc_quality': 1.0508747826837916, 'absD': 9408000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, 1, 0, -313608, 67492788], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8400, 'degree': 32768, 'elladic_images': ['16.24.0.13'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5720715201679352674758776427', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [53297461115137, 147], 'lmfdb_iso': '8400.bn', 'lmfdb_label': '8400.bn1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -784, -8515], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '12.12.0.h.1', '16.24.0.e.2', '20.12.0-4.c.1.2', '24.24.0.bl.1', '40.24.0-8.n.1.1', '48.48.0.y.1', '56.24.0.bu.1', '60.24.0-12.h.1.2', '80.48.0.?', '112.48.0.?', '120.48.0.?', '168.48.0.?', '240.96.0.?', '280.48.0.?', '336.96.1.?', '560.96.0.?', '840.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8895804796035982625482423830', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 4, 2800], [5, 14, 336], [7, 8, 1200]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854629', 'prec': 107}, 'szpiro_ratio': 5.487093278980915, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 54117
    {'Ciso': '8400cd', 'Clabel': '8400cd4', 'Cnumber': 4, 'abc_quality': 1.0814902740568197, 'absD': 1382976000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 840, 'ainvs': [0, 1, 0, -19608, 1048788], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8400, 'degree': 16384, 'elladic_images': ['8.24.0.18'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2254979298879626127672615820', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4], 'jinv': [13027640977, 21609], 'lmfdb_iso': '8400.bn', 'lmfdb_label': '8400.bn2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -49, -136], 'min_quad_twist_disc': -20, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.1', '12.24.0.c.1', '20.24.0-4.b.1.3', '24.48.0.j.2', '40.48.0-8.e.1.9', '56.48.0.u.1', '60.48.0-12.c.1.1', '120.96.0.?', '168.96.1.?', '280.96.0.?', '840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4447902398017991312741211915', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 2800], [5, 14, 336], [7, 8, 1200]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020607', 'prec': 107}, 'szpiro_ratio': 4.566710075698052, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 54116
    {'Ciso': '8400cd', 'Clabel': '8400cd3', 'Cnumber': 3, 'abc_quality': 1.0015974661127929, 'absD': 2939328000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, 1, 0, -15608, -751212], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8400, 'degree': 16384, 'elladic_images': ['8.24.0.88'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2254979298879626127672615820', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6570725617, 45927], 'lmfdb_iso': '8400.bn', 'lmfdb_label': '8400.bn3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -39, 90], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '20.12.0-4.c.1.1', '28.12.0.h.1', '40.48.0-8.bb.1.8', '48.48.0.bf.1', '56.48.0.bl.2', '140.24.0.?', '240.96.0.?', '280.96.0.?', '336.96.1.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4447902398017991312741211915', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 175], [3, 4, 2800], [5, 14, 336], [7, 8, 1200]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020607', 'prec': 107}, 'szpiro_ratio': 4.490963058797872, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 54119
    {'Ciso': '8400cd', 'Clabel': '8400cd6', 'Cnumber': 6, 'abc_quality': 1.042661241253942, 'absD': 1106841792000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, 1, 0, -13608, 1708788], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8400, 'degree': 32768, 'elladic_images': ['8.24.0.90'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5720715201679352674758776427', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-4354703137, 17294403], 'lmfdb_iso': '8400.bn', 'lmfdb_label': '8400.bn4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -34, -217], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '8.24.0.bb.2', '12.12.0.g.1', '20.12.0-4.c.1.2', '24.48.0.bj.1', '40.48.0-8.bb.2.4', '60.24.0-12.g.1.2', '112.48.0.?', '120.96.0.?', '336.96.1.?', '560.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8895804796035982625482423830', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 4, 2800], [5, 14, 336], [7, 8, 1200]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854629', 'prec': 107}, 'szpiro_ratio': 4.673649651944412, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 54115
    {'Ciso': '8400cd', 'Clabel': '8400cd2', 'Cnumber': 2, 'abc_quality': 1.1486166056524132, 'absD': 254016000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 840, 'ainvs': [0, 1, 0, -1608, 4788], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8400, 'degree': 8192, 'elladic_images': ['8.24.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.87892433960798995805864552128', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4], 'jinv': [7189057, 3969], 'lmfdb_iso': '8400.bn', 'lmfdb_label': '8400.bn5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -4, -1], 'min_quad_twist_disc': -20, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.2', '20.24.0-4.b.1.1', '24.48.0.w.2', '28.24.0.c.1', '40.48.0-8.e.2.4', '56.48.0.i.1', '120.96.0.?', '140.48.0.?', '168.96.1.?', '280.96.0.?', '840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.72239511990089956563706059576', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 2800], [5, 14, 336], [7, 8, 1200]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61894179716900553865896626679', 'prec': 107}, 'szpiro_ratio': 3.7364445372392874, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 54114
    {'Ciso': '8400cd', 'Clabel': '8400cd1', 'Cnumber': 1, 'abc_quality': 0.9786808587681587, 'absD': 4032000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, 1, 0, 392, 788], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 8400, 'degree': 4096, 'elladic_images': ['16.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.53235074932801730335002946056', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [103823, 63], 'lmfdb_iso': '8400.bn', 'lmfdb_label': '8400.bn6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1, 0], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '14.6.0.b.1', '16.24.0.e.1', '20.12.0-4.c.1.1', '24.24.0.bz.1', '28.12.0.g.1', '40.24.0-8.n.1.5', '48.48.0.bd.1', '56.24.0.bf.1', '80.48.0.?', '112.48.0.?', '120.48.0.?', '140.24.0.?', '168.48.0.?', '240.96.0.?', '280.48.0.?', '336.96.1.?', '560.96.0.?', '840.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4447902398017991312741211915', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 175], [3, 4, 2800], [5, 14, 336], [7, 8, 1200]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.96551538744897819336758232751', 'prec': 107}, 'szpiro_ratio': 3.2674722192514314, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}