Elliptic curve data - 249690.cj5

Formats: - HTML - YAML - JSON - 2025-12-06T03:51:56.384224

• 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': '249690cj', 'Clabel': '249690cj5', 'Cnumber': 5, 'abc_quality': 1.0143884721484036, 'absD': 18551296611518877695051385524100, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3995040, 'ainvs': [1, 0, 0, -10026429070, -438485381299000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 29, 41], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 249690, 'degree': 763363328, 'elladic_images': ['16.96.0.25'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.7269195070408155899036286821', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 61, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-111471172596350616707438857829030881, 18551296611518877695051385524100], 'lmfdb_iso': '249690.cj', 'lmfdb_label': '249690.cj5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -10026429070, -438485381299000], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '8.48.0-8.q.1.2', '16.96.0-16.j.1.2', '328.96.0.?', '656.192.1.?', '840.96.0.?', '1680.192.1.?', '4640.192.2.?', '17220.48.0.?', '19488.192.2.?', '34440.192.1.?', '68880.384.5.?', '97440.384.5.?', '190240.384.5.?', '799008.384.5.?', '3995040.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '18.982458473207593116161023456', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 83230], [5, 6, 49938], [7, 8, 35670], [29, 30, 8610], [41, 42, 6090]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '4.7269195070408155899036286821', 'prec': 100}, 'szpiro_ratio': 6.513678545460616, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 1, 1, 1, 1, 1, 1, 1, -4, 1, -2, 1, 1, 1, 2, 1, 4, 1], 'aplist': [1, 1, 1, 1, -4, -2, 2, 4, 8, 1, 0, 6, 1, -4, 0, 6, -4, -2, -12, -8, 10, -16, -12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 249690, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8, 16, 16], [2, 1, 2, 2, 4, 4, 8, 8], [4, 2, 1, 4, 8, 8, 16, 16], [4, 2, 4, 1, 2, 2, 4, 4], [8, 4, 8, 2, 1, 4, 8, 8], [8, 4, 8, 2, 4, 1, 2, 2], [16, 8, 16, 4, 8, 2, 1, 4], [16, 8, 16, 4, 8, 2, 4, 1]], 'lmfdb_iso': '249690.cj', 'trace_hash': 2097685752872184617}
• 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': '0.000078388054045866521634537812866', 'prec': 117}, 'conductor': 249690, 'gens': [[390031675, 7701320879825, 6]], 'heights': [{'__RealLiteral__': 0, 'data': '18.982458473207593116161023456', 'prec': 100}], 'lmfdb_label': '249690.cj5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.0074755334480238556695477011209', 'prec': 110}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '18.163712414999963320828938200090379627', 'prec': 130}, 'tamagawa_product': 512, 'torsion_generators': [[294140, 148381940, 1]], 'xcoord_integral_points': [294140]}
• lmfdb_label 249690.cj5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10749823
    {'degree': 2, 'field': [-210, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [8]}
  • id: 10749822
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 4]}
  • id: 10749824
    {'degree': 2, 'field': [210, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [8]}
  • id: 10749828
    {'degree': 4, 'field': [-35301000, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [16]}
  • id: 10749827
    {'degree': 4, 'field': [1681, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 8]}
  • id: 10749826
    {'degree': 4, 'field': [11025, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 8]}
  • id: 10749829
    {'degree': 4, 'field': [21000, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [16]}
  • id: 10749825
    {'degree': 4, 'field': [1157776, 0, 2153, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [4, 4]}
  • id: 10749830
    {'degree': 8, 'field': [65536, 0, 0, 0, 4817, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [4, 8]}
  • id: 10749833
    {'degree': 8, 'field': [176610, -706440, 706440, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '249690.cj5', 'torsion': [12]}
  • id: 10749831
    {'degree': 8, 'field': [27552001, 0, 63004, 0, -10494, 0, 4, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 16]}
  • id: 10749832
    {'degree': 8, 'field': [77885055213001, 0, -105902996, 0, 17650506, 0, 4, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 16]}
  • id: 10749840
    {'degree': 16, 'field': [31191092100, 0, 249528736800, 0, 499057473600, 0, 1766101, 0, 4591862, 0, -1412879, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 12]}
  • id: 10749836
    {'degree': 16, 'field': [1103814991876, 0, 25845334000, 0, 155492504, 0, 180400, 0, 2101256, 0, -41000, 0, 4, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 16]}
  • id: 10749837
    {'degree': 16, 'field': [2800239157605796, 1369520528594400, 334897552080000, 48475806792000, 2883928570324, -356489683200, -99666000000, -10603387200, -254316939, 74890200, 8820000, 478800, -11366, -4200, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [4, 16]}
  • id: 10749834
    {'degree': 16, 'field': [5498391374910100, 158254837608000, -3866349807600, -5108925343200, 1103560900600, 1104835200, -41211223200, 155668800, 149047881, 4890480, 62244, -68880, 3046, 0, 84, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [4, 8]}
  • id: 10749835
    {'degree': 16, 'field': [106878361544643844, 0, 141866083087344, 0, 48384539032, 0, 3182256, 0, 653845128, 0, -723240, 0, 4, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [2, 16]}
  • id: 10749842
    {'degree': 16, 'field': [3272366941172261100, -181315224206890200, 183916933735329900, -5225550509668020, 2668236818099790, -66926605426380, 22931651209741, -536951441048, 138168708120, -2634208150, 540508613, -7485372, 1273133, -11830, 1710, -8, 1], 'lmfdb_label': '249690.cj5', 'torsion': [24]}
  • id: 10749841
    {'degree': 16, 'field': [4354253993095883100, 107471137719972600, -105270103130188500, -4378465378249620, 2130362534906130, 70254522998100, -22770282387299, -552250166168, 134214009540, 2552165210, -496934227, -7332492, 1196693, 11690, -1650, -8, 1], 'lmfdb_label': '249690.cj5', 'torsion': [24]}
  • id: 10749839
    {'degree': 16, 'field': [3714971422092072636816000000, 0, 0, 0, -827167518492134400000, 0, 0, 0, 208398478197000, 0, 0, 0, -21638400, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [32]}
  • id: 10749838
    {'degree': 16, 'field': [965590899219065848248576000000, 0, 0, 0, 165455041178885453452800000, 0, 0, 0, -165444640956357000, 0, 0, 0, -1150984800, 0, 0, 0, 1], 'lmfdb_label': '249690.cj5', 'torsion': [32]}
• 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: 6191846
    {'conductor': 249690, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '249690.cj5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6191847
    {'conductor': 249690, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '249690.cj5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6191848
    {'conductor': 249690, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '249690.cj5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6191849
    {'conductor': 249690, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '249690.cj5', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6191850
    {'conductor': 249690, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '249690.cj5', 'prime': 29, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 6191851
    {'conductor': 249690, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '249690.cj5', 'prime': 41, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 3249217
    {'adelic_gens': [[2996285, 1997528, 124673, 1747555], [1, 0, 32, 1], [1, 32, 0, 1], [413281, 16, 0, 1], [2853625, 16, 3993654, 3994153], [1331705, 16, 3993654, 3994153], [1753949, 8, 2142654, 3994757], [3995009, 32, 3995008, 33], [1, 16, 0, 2496901], [25, 32, 3199414, 4329], [1, 32, 4, 129], [25, 16, 3993304, 3993929]], 'adelic_image': '3995040.768.13.?', 'conductor': 249690, 'lmfdb_label': '249690.cj5', 'prime': 0}
  • id: 901429
    {'conductor': 249690, 'elladic_image': '16.96.0.25', 'lmfdb_label': '249690.cj5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 249690.cj does not appear in ec_padic