Elliptic curve data - 286650.ek2

Formats: - HTML - YAML - JSON - 2025-10-18T12:45:34.868371

• 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': '286650ek', 'Clabel': '286650ek3', 'Cnumber': 3, 'abc_quality': 1.0346538273212997, 'absD': 2133877548792781209600000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 10920, 'ainvs': [1, -1, 0, -588487167, -5927128598259], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 286650, 'degree': 149299200, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9857926383797303355552815139', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 114, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-16818951115904497561, 1592332281446400], 'lmfdb_iso': '286650.ek', 'lmfdb_label': '286650.ek2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -53378, -5124652], 'min_quad_twist_disc': 105, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '40.6.0.c.1', '78.24.0.?', '105.8.0.?', '120.24.0.?', '168.24.0.?', '210.24.0.?', '840.48.0.?', '1560.48.1.?', '2184.48.0.?', '2730.48.0.?', '10920.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 143325], [3, 6, 1225], [5, 18, 5733], [7, 26, 5850], [13, 14, 22050]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6588124633009686500046028571', 'prec': 100}, 'szpiro_ratio': 5.7571397364359616, '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, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, -2, 0], 'aplist': [-1, 0, 0, 0, 0, 1, 0, -2, -6, 0, -8, -2, 6, 4, 0, -6, 0, -14, 4, 0, -4, -16, 12, -6, -4], 'class_deg': 6, 'class_size': 4, 'conductor': 286650, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '286650.ek', 'trace_hash': 2106191104672697253}
• 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': '0.00034513142316544049751573045339', 'prec': 113}, 'conductor': 286650, 'gens': [], 'heights': [], 'lmfdb_label': '286650.ek2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.015244181273133753684035594863', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.36586035055521008841685427672136853754', 'prec': 133}, 'tamagawa_product': 96, 'torsion_generators': [[28254, -14127, 1]], 'xcoord_integral_points': [28254]}
• lmfdb_label 286650.ek2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12180500
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '286650.ek2', 'torsion': [6]}
  • id: 12180499
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '286650.ek2', 'torsion': [2, 2]}
  • id: 12180501
    {'degree': 4, 'field': [-89, -62, -7, -2, 1], 'lmfdb_label': '286650.ek2', 'torsion': [4]}
  • id: 12180502
    {'degree': 4, 'field': [1, 0, 37, 0, 1], 'lmfdb_label': '286650.ek2', 'torsion': [2, 6]}
  • id: 12180503
    {'degree': 6, 'field': [-320, 0, 0, -85, 0, 0, 1], 'lmfdb_label': '286650.ek2', 'torsion': [6]}
  • id: 12180506
    {'degree': 8, 'field': [1, 0, 544, 0, 62, 0, 16, 0, 1], 'lmfdb_label': '286650.ek2', 'torsion': [12]}
  • id: 12180505
    {'degree': 8, 'field': [50911, 68600, 27972, 3920, 233, -140, 22, 0, 1], 'lmfdb_label': '286650.ek2', 'torsion': [2, 4]}
  • id: 12180504
    {'degree': 8, 'field': [95286, -73362, 16635, -5406, 4273, -446, 45, -2, 1], 'lmfdb_label': '286650.ek2', 'torsion': [2, 4]}
  • id: 12180507
    {'degree': 12, 'field': [1024, -4992, 10032, -9360, 5940, -2892, 1051, -156, -30, 0, 12, -6, 1], 'lmfdb_label': '286650.ek2', 'torsion': [3, 6]}
  • id: 12180508
    {'degree': 12, 'field': [2555904, 4672512, 3612288, 1091280, -40680, -94833, -3854, 1929, -345, -35, 63, -6, 1], 'lmfdb_label': '286650.ek2', 'torsion': [2, 6]}
  • id: 12180511
    {'degree': 16, 'field': [529344, 1184256, 1906080, -5146368, 6950752, -4006272, 1835016, -732992, 275960, -98048, 32954, -8336, 2055, -336, 62, -4, 1], 'lmfdb_label': '286650.ek2', 'torsion': [2, 12]}
  • id: 12180510
    {'degree': 16, 'field': [18147600, 0, -1535760, 0, -3229716, 0, 308916, 0, 142549, 0, -15898, 0, 1611, 0, -34, 0, 1], 'lmfdb_label': '286650.ek2', 'torsion': [2, 12]}
  • id: 12180509
    {'degree': 16, 'field': [5544858321, -19647530640, 4566679908, 1793323704, -1545891518, 175700024, 58208416, -19370448, -1487925, 1069912, -48192, -28528, 4242, 744, -92, -8, 1], 'lmfdb_label': '286650.ek2', 'torsion': [8]}
  • id: 12180512
    {'degree': 18, 'field': [125785327221, -32134693815, 5534597565, 10308545082, 1157604264, -4567507974, 3665346696, -1408919886, 402082371, -71433251, 9562149, -456894, 21954, 792, 1296, -420, 99, -9, 1], 'lmfdb_label': '286650.ek2', 'torsion': [18]}
• 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: 7099863
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 30, 'j_denominator_valuation': 30, 'kodaira_symbol': 34, 'lmfdb_label': '286650.ek2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7099864
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '286650.ek2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7099865
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '286650.ek2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 7099866
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '286650.ek2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7099867
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '286650.ek2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 3470791
    {'adelic_gens': [[9610, 6237, 5747, 3128], [11, 2, 10870, 10911], [2183, 3108, 3738, 7727], [5461, 7812, 9366, 3193], [1, 0, 12, 1], [10909, 12, 10908, 13], [1450, 4683, 8253, 7792], [3119, 0, 0, 10919], [1, 6, 6, 37], [6315, 9688, 4718, 1877], [1, 12, 0, 1]], 'adelic_image': '10920.96.1.?', 'conductor': 286650, 'lmfdb_label': '286650.ek2', 'prime': 0}
  • id: 1016712
    {'conductor': 286650, 'elladic_image': '2.3.0.1', 'lmfdb_label': '286650.ek2', 'modell_image': '2B', 'prime': 2}
  • id: 1016713
    {'conductor': 286650, 'elladic_image': '3.4.0.1', 'lmfdb_label': '286650.ek2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 286650.ek does not appear in ec_padic