Elliptic curve data - 64896.bd1

Formats: - HTML - YAML - JSON - 2025-10-29T00:39:25.923899

• 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': '64896n', 'Clabel': '64896n1', 'Cnumber': 1, 'abc_quality': 1.1592979456015535, 'absD': 77183109548483328, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 24, 'ainvs': [0, 1, 0, -473763, -124957611], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 64896, 'degree': 602112, 'elladic_images': ['8.6.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0760903396998131866005856559', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 29, 'isogeny_degrees': [1, 2], 'jinv': [9517173136000, 62462907], 'lmfdb_iso': '64896.bd', 'lmfdb_label': '64896.bd1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2803, 57739], 'min_quad_twist_disc': -52, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.d.1', '12.6.0.a.1', '24.12.0.w.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 507], [3, 4, 21632], [7, 2, 21632], [13, 98, 384]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.33151754059574794562902052081', 'prec': 103}, 'szpiro_ratio': 4.586327629986421, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, -2, 0, 1, 0, 4, 0, 0, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 1, 0, -2, 4, 0, -2, -4, -4, 0, 6, 2, 6, 0, 12, 8, 12, 6, 0, -12, -6, 14, -4, 18, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 64896, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '64896.bd', 'trace_hash': 1294175617897532056}
• 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': '0.015730076802106353486075765692', 'prec': 107}, 'conductor': 64896, 'gens': [], 'heights': [], 'lmfdb_label': '64896.bd1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.18204591134979394216091189599', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5486427588971151902527665438190740580', 'prec': 130}, 'tamagawa_product': 56, 'torsion_generators': [[-373, 0, 1]], 'xcoord_integral_points': [-373]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0, 0], '7': [2, 0], '13': 'a'}, 'iwp0': 11, 'lmfdb_label': '64896.bd1'}
• ec_torsion_growth •

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

  
  
  • id: 3099182
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '64896.bd1', 'torsion': [2, 2]}
  • id: 3099183
    {'degree': 4, 'field': [507, 0, -26, 0, 1], 'lmfdb_label': '64896.bd1', 'torsion': [4]}
  • id: 3099186
    {'degree': 8, 'field': [-397488, 0, 39104, 0, -2184, 0, 0, 0, 1], 'lmfdb_label': '64896.bd1', 'torsion': [6]}
  • id: 3099184
    {'degree': 8, 'field': [121, 0, -70, 0, -96, 0, -22, 0, 1], 'lmfdb_label': '64896.bd1', 'torsion': [2, 4]}
  • id: 3099185
    {'degree': 8, 'field': [5329, 3796, 3292, 1060, 108, -4, -20, -4, 1], 'lmfdb_label': '64896.bd1', 'torsion': [2, 4]}
  • id: 3099187
    {'degree': 16, 'field': [1138489, 0, 423160, 0, -23772, 0, -45976, 0, 250, 0, 3224, 0, 588, 0, 40, 0, 1], 'lmfdb_label': '64896.bd1', 'torsion': [8]}
  • id: 3099188
    {'degree': 16, 'field': [506250000, 0, -128520000, 0, 24703200, 0, 2027808, 0, -290808, 0, -14928, 0, -216, 0, -24, 0, 1], 'lmfdb_label': '64896.bd1', 'torsion': [2, 6]}
• 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: 1567537
    {'conductor': 64896, 'conductor_valuation': 7, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '64896.bd1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1567538
    {'conductor': 64896, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '64896.bd1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1567539
    {'conductor': 64896, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '64896.bd1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2093841
    {'adelic_gens': [[1, 2, 2, 5], [13, 4, 2, 9], [21, 4, 20, 5], [3, 4, 8, 11], [4, 1, 17, 18], [1, 4, 0, 1], [10, 1, 7, 0], [1, 0, 4, 1]], 'adelic_image': '24.12.0.?', 'conductor': 64896, 'lmfdb_label': '64896.bd1', 'prime': 0}
  • id: 272178
    {'conductor': 64896, 'elladic_image': '8.6.0.4', 'lmfdb_label': '64896.bd1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 64896.bd does not appear in ec_padic