Elliptic curve data - 45760.bc2

Formats: - HTML - YAML - JSON - 2025-09-26T00:25:07.171227

• 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': '45760e', 'Clabel': '45760e3', 'Cnumber': 3, 'abc_quality': 1.0322408901773137, 'absD': 213907243780658954240000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5720, 'ainvs': [0, 0, 0, -59194028, 173875052848], 'analytic_rank': 0, 'bad_primes': [2, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 45760, 'degree': 5160960, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2979238467590124387236140406', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 4], 'jinv': [87501897507774086005761, 815991377947460000], 'lmfdb_iso': '45760.bc', 'lmfdb_label': '45760.bc2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -924907, 339830939], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '52.12.0-4.c.1.1', '104.24.0.?', '440.24.0.?', '5720.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 13], [3, 2, 4160], [5, 6, 9152], [11, 12, 4160], [13, 14, 3520]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2582030759190944745977658584', 'prec': 100}, 'szpiro_ratio': 6.0853218520214165, '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, 0, 0, -1, 0, 0, 0, -3, 0, 1, 0, -1, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, -1, 0, 1, -1, 2, -4, 8, -10, 8, -6, -2, 12, -4, 6, 4, -10, -4, 0, -14, -8, -12, -14, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 45760, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '45760.bc', 'trace_hash': 1800872682865484547}
• 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': '0.0013660284463111783759819358756', 'prec': 110}, 'conductor': 45760, 'gens': [], 'heights': [], 'lmfdb_label': '45760.bc2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.10033332561360381346495278038', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2039999073632457615794333645897525901', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-8876, 0, 1]], 'xcoord_integral_points': [-8876]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 2, 0], '5': [0, 0], '11': [1, 0], '13': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '45760.bc2'}
• ec_torsion_growth •

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

  
  
  • id: 2234707
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [2, 2]}
  • id: 2234708
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [4]}
  • id: 2234709
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [4]}
  • id: 2234710
    {'degree': 4, 'field': [49, 0, -12, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [2, 4]}
  • id: 2234714
    {'degree': 8, 'field': [-48, 0, -66, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [6]}
  • id: 2234711
    {'degree': 8, 'field': [484, 0, -656, 0, -28, 0, -8, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [2, 4]}
  • id: 2234712
    {'degree': 8, 'field': [1936, 0, -704, 0, 97, 0, -6, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [8]}
  • id: 2234713
    {'degree': 8, 'field': [8281, 0, 321100, 0, 17082, 0, 260, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [8]}
  • id: 2234718
    {'degree': 16, 'field': [-55208, -110288, -216543, -337000, -275260, -259782, -89195, -31196, 5025, 1390, 3367, 444, 197, -70, 6, -8, 1], 'lmfdb_label': '45760.bc2', 'torsion': [2, 6]}
  • id: 2234719
    {'degree': 16, 'field': [4225, 0, 16900, 0, 16900, 0, -1268, 0, -1658, 0, 268, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [12]}
  • id: 2234715
    {'degree': 16, 'field': [28561, 0, 0, 0, 0, 0, 0, 0, 5746, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [4, 4]}
  • id: 2234717
    {'degree': 16, 'field': [618596, -332816, 1886608, -2242288, 2355436, -1580664, 923708, -432456, 186397, -64784, 22266, -6196, 1575, -268, 58, -4, 1], 'lmfdb_label': '45760.bc2', 'torsion': [2, 8]}
  • id: 2234720
    {'degree': 16, 'field': [10673289, 0, 2087856, 0, 3012228, 0, 1530576, 0, 304830, 0, 28944, 0, 1476, 0, 48, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [12]}
  • id: 2234716
    {'degree': 16, 'field': [13376055414241, 0, 148230219072, 0, 59488678704, 0, 131609088, 0, 9191234, 0, 32448, 0, 8112, 0, 0, 0, 1], 'lmfdb_label': '45760.bc2', 'torsion': [2, 8]}
• 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: 1090443
    {'conductor': 45760, 'conductor_valuation': 6, 'discriminant_valuation': 23, 'j_denominator_valuation': 5, 'kodaira_symbol': -17, 'lmfdb_label': '45760.bc2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1090444
    {'conductor': 45760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '45760.bc2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1090445
    {'conductor': 45760, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '45760.bc2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1090446
    {'conductor': 45760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '45760.bc2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1969013
    {'adelic_gens': [[2144, 4997, 711, 682], [1, 0, 8, 1], [1, 8, 0, 1], [3968, 3, 1765, 2], [1, 4, 4, 17], [3579, 3576, 738, 3581], [4577, 8, 1148, 33], [5713, 8, 5712, 9], [2081, 8, 2604, 33], [7, 6, 5714, 5715]], 'adelic_image': '5720.48.0.?', 'conductor': 45760, 'lmfdb_label': '45760.bc2', 'prime': 0}
  • id: 198301
    {'conductor': 45760, 'elladic_image': '8.12.0.7', 'lmfdb_label': '45760.bc2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 45760.bc does not appear in ec_padic