Elliptic curve data - 336336.bg1

Formats: - HTML - YAML - JSON - 2025-11-01T07:15:36.490271

• 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': '336336bg', 'Clabel': '336336bg4', 'Cnumber': 4, 'abc_quality': 1.0400391704321605, 'absD': 933988314896594141184, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, -1, 0, -10401344, -12824203776], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 336336, 'degree': 15925248, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8539610597728569137247618402', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4], 'jinv': [258252149810350513, 1938176193096], 'lmfdb_iso': '336336.bg', 'lmfdb_label': '336336.bg1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -13267, -589879], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '56.24.0-8.m.1.2', '264.24.0.?', '924.12.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.5201753064575253202350954545', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1617], [3, 4, 112112], [7, 26, 6864], [11, 12, 30576], [13, 14, 25872]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1878588046852549517548533470', 'prec': 100}, 'szpiro_ratio': 4.721560023904025, '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, -2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, -2, 0, -4, 0], 'aplist': [0, -1, -2, 0, 1, 1, -2, -4, -4, -2, 0, -2, -10, 4, -4, 2, -4, -10, 4, -12, -2, 4, -12, -2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 336336, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '336336.bg', 'trace_hash': 97544363576108966}
• 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': '0.0033195630387644591801130293165', 'prec': 110}, 'conductor': 336336, 'gens': [[-1814, 8450, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.5201753064575253202350954545', 'prec': 100}], 'lmfdb_label': '336336.bg1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.084105361947966730641979753148', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3913641011510103061152478546712589373', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-1983, 0, 1]], 'xcoord_integral_points': [-1983, -1814, 6298]}
• lmfdb_label 336336.bg1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14083339
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [2, 2]}
  • id: 14083340
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [4]}
  • id: 14083341
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '336336.bg1', 'torsion': [4]}
  • id: 14083342
    {'degree': 4, 'field': [400, 0, -26, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [2, 4]}
  • id: 14083346
    {'degree': 8, 'field': [-115248, 0, -79919, 0, -1176, 0, 0, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [6]}
  • id: 14083345
    {'degree': 8, 'field': [928, -496, 626, -256, 109, 34, -16, -2, 1], 'lmfdb_label': '336336.bg1', 'torsion': [8]}
  • id: 14083344
    {'degree': 8, 'field': [12849, -360, -2848, 560, 214, -40, 0, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [8]}
  • id: 14083343
    {'degree': 8, 'field': [158404, 0, -110768, 0, -12, 0, -56, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [2, 4]}
  • id: 14083348
    {'degree': 16, 'field': [4692928, -923904, 724736, -868256, 389012, 221904, 14156, -129720, 25441, 20292, -2432, -3412, 714, 188, -44, -4, 1], 'lmfdb_label': '336336.bg1', 'torsion': [2, 8]}
  • id: 14083349
    {'degree': 16, 'field': [7100388, -7994592, 665376, 1703904, 1336504, -757936, -47920, -186048, 134088, -2912, 24416, 208, 1988, -8, 72, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [2, 8]}
  • id: 14083351
    {'degree': 16, 'field': [647142721, 0, 377790172, 0, 34741444, 0, 928212, 0, 623046, 0, -13548, 0, 580, 0, 28, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [12]}
  • id: 14083352
    {'degree': 16, 'field': [951599104, 0, -514192640, 0, 103025668, 0, -9101287, 0, 275678, 0, 7781, 0, -719, 0, 22, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [12]}
  • id: 14083347
    {'degree': 16, 'field': [170940075601, 0, 0, 0, 1129115740, 0, 0, 0, 5740566, 0, 0, 0, -2180, 0, 0, 0, 1], 'lmfdb_label': '336336.bg1', 'torsion': [4, 4]}
  • id: 14083350
    {'degree': 16, 'field': [71608456503684, 0, -93941738549508, 0, 3676450187809, 0, -79919493024, 0, 1366413300, 0, -16570078, 0, 119616, 0, -528, 0, 1], 'lmfdb_label': '336336.bg1', '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: 8323783
    {'conductor': 336336, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '336336.bg1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8323784
    {'conductor': 336336, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '336336.bg1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8323785
    {'conductor': 336336, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '336336.bg1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8323786
    {'conductor': 336336, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '336336.bg1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8323787
    {'conductor': 336336, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '336336.bg1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 3767062
    {'adelic_gens': [[92, 1057, 1519, 1590], [1, 0, 8, 1], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [232, 371, 1225, 1254], [316, 1057, 959, 1590], [293, 560, 406, 27], [263, 0, 0, 1847]], 'adelic_image': '1848.48.0.?', 'conductor': 336336, 'lmfdb_label': '336336.bg1', 'prime': 0}
  • id: 1168875
    {'conductor': 336336, 'elladic_image': '8.12.0.11', 'lmfdb_label': '336336.bg1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 336336.bg does not appear in ec_padic