Elliptic curve data - 11760.bx5

Formats: - HTML - YAML - JSON - 2025-10-08T19:15:21.705891

• 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': '11760ch', 'Clabel': '11760ch3', 'Cnumber': 3, 'abc_quality': 1.0288195344460926, 'absD': 585740676326400000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 1680, 'ainvs': [0, 1, 0, -5919216, -5421281580], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 11760, 'degree': 589824, 'elladic_images': ['8.96.0.89'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7673844914232196995057146191', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 49, 'isogeny_degrees': [1, 2, 4], 'jinv': [47595748626367201, 1215506250000], 'lmfdb_iso': '11760.bx', 'lmfdb_label': '11760.bx5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -7550, -247500], 'min_quad_twist_disc': 28, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0.b.1', '8.96.0-8.c.1.2', '24.192.1-24.w.2.10', '28.48.0-4.b.1.1', '56.192.1-56.x.1.3', '80.192.2.?', '168.384.5.?', '240.384.5.?', '560.384.5.?', '1680.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 3920], [5, 6, 2352], [7, 32, 240]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1012822363356177375358061259', 'prec': 100}, 'szpiro_ratio': 6.230461559649005, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, 0, 0, 1, 0, 4, 0, 2, 0, -1, 0, -2, 0, 4, 0], 'aplist': [0, 1, -1, 0, 4, 2, -2, 4, 8, -2, 0, 6, 6, 4, 0, -10, 12, -14, 12, 8, -10, -16, -12, -10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 11760, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '11760.bx', 'trace_hash': 1274942468229796285}
• 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': '0.0039471203831846374569208723854', 'prec': 110}, 'conductor': 11760, 'gens': [], 'heights': [], 'lmfdb_label': '11760.bx5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.096941557368700781627369532376', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1021298357984250120758250360275824252', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-1230, 0, 1], [2802, 0, 1]], 'xcoord_integral_points': [-1573, -1230, 2802]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '11760.bx5'}
• ec_torsion_growth •

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

  
  
  • id: 608630
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 4]}
  • id: 608629
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 4]}
  • id: 608631
    {'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [4, 4]}
  • id: 608632
    {'degree': 4, 'field': [16, 0, 6, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 8]}
  • id: 608633
    {'degree': 4, 'field': [81, 0, -24, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 8]}
  • id: 608634
    {'degree': 4, 'field': [81, 0, 24, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 8]}
  • id: 608638
    {'degree': 8, 'field': [-327, 30, 492, -20, -304, 58, 22, -4, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 6]}
  • id: 608635
    {'degree': 8, 'field': [16, 0, 0, 0, 1, 0, 0, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [4, 8]}
  • id: 608636
    {'degree': 8, 'field': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [4, 8]}
  • id: 608637
    {'degree': 8, 'field': [106, 148, -106, -92, 67, -28, 14, -4, 1], 'lmfdb_label': '11760.bx5', 'torsion': [4, 8]}
  • id: 608639
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [8, 8]}
  • id: 608643
    {'degree': 16, 'field': [318416, 769552, -503852, -780352, 1040096, -857472, 416392, -114256, 31013, -1024, -156, -136, 326, -168, 44, -8, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 12]}
  • id: 608642
    {'degree': 16, 'field': [844561, 0, -2800448, 0, 11144392, 0, -1571528, 0, 240958, 0, -20384, 0, 1288, 0, -56, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 16]}
  • id: 608644
    {'degree': 16, 'field': [3111696, 0, -3556224, 0, 1016064, 0, -140287, 0, 50666, 0, 1673, 0, 49, 0, -14, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 12]}
  • id: 608641
    {'degree': 16, 'field': [4494400, 0, -5329280, 0, 839344, 0, 265936, 0, -4751, 0, -6908, 0, 646, 0, -44, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 16]}
  • id: 608640
    {'degree': 16, 'field': [429981696, 0, 232906752, 0, 60559488, 0, -9642240, 0, -277344, 0, 8640, 0, 4338, 0, -132, 0, 1], 'lmfdb_label': '11760.bx5', 'torsion': [2, 16]}
• 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: 253292
    {'conductor': 11760, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '11760.bx5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 253293
    {'conductor': 11760, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '11760.bx5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 253294
    {'conductor': 11760, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '11760.bx5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 253295
    {'conductor': 11760, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '11760.bx5', 'prime': 7, '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: 1741949
    {'adelic_gens': [[225, 16, 1004, 805], [1, 16, 0, 1], [1439, 1668, 0, 1679], [1455, 1672, 1352, 1505], [1, 8, 0, 1], [1, 16, 8, 129], [1353, 8, 664, 1673], [9, 16, 124, 905], [1, 0, 16, 1], [1665, 16, 1664, 17]], 'adelic_image': '1680.768.13.?', 'conductor': 11760, 'lmfdb_label': '11760.bx5', 'prime': 0}
  • id: 56290
    {'conductor': 11760, 'elladic_image': '8.96.0.89', 'lmfdb_label': '11760.bx5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 11760.bx does not appear in ec_padic