Elliptic curve data - 136710.bb4

Formats: - HTML - YAML - JSON - 2024-05-19T18:30:00.974317

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '136710fb', 'Clabel': '136710fb1', 'Cnumber': 1, 'abc_quality': 1.1472356070759668, 'absD': 33224648946010583040, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 13020, 'ainvs': [1, -1, 0, 612540, -207180464], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 136710, 'degree': 4147200, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4317001179771663080865777450', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [296354077829711, 387386634240], 'lmfdb_iso': '136710.bb', 'lmfdb_label': '136710.bb4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1389, -22239], 'min_quad_twist_disc': 21, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '21.8.0-3.a.1.2', '30.24.0.b.1', '42.24.0-6.a.1.4', '124.6.0.?', '210.48.0.?', '372.24.0.?', '1860.48.1.?', '2604.48.0.?', '13020.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.766793330669042660659010875', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.90943889911545480983627875482', 'prec': 103}, 'szpiro_ratio': 4.382001168606046, '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, -1, 0, 0, -1, 0, 1, 0, 0, 4, 0, 0, 1, 6, 0, -8, -1], 'aplist': [-1, 0, -1, 0, 0, 4, 6, -8, 0, 0, -1, -4, -6, 8, -12, 6, -6, -2, 2, 6, -8, 8, 12, 0, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 136710, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '136710.bb', 'trace_hash': 741769663127163008}
• 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': '0.0077241751704231977095284573747', 'prec': 110}, 'conductor': 136710, 'gens': [[589160, 585564116, 31]], 'heights': [{'__RealLiteral__': 0, 'data': '10.766793330669042660659010875', 'prec': 100}], 'lmfdb_label': '136710.bb4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11069735033723462825230276494', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7674219733346891836377963086292531353', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[296, -148, 1]], 'xcoord_integral_points': [296]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [13, 0], '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [3, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '136710.bb4'}
• ec_torsion_growth •

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

  
  
  • id: 6186102
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '136710.bb4', 'torsion': [6]}
  • id: 6186101
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '136710.bb4', 'torsion': [2, 2]}
  • id: 6186103
    {'degree': 4, 'field': [-12, 204, 14, -2, 1], 'lmfdb_label': '136710.bb4', 'torsion': [4]}
  • id: 6186104
    {'degree': 4, 'field': [15, -15, 4, -1, 1], 'lmfdb_label': '136710.bb4', 'torsion': [2, 6]}
  • id: 6186105
    {'degree': 6, 'field': [29024, -14776, 2846, -371, 109, -1, 1], 'lmfdb_label': '136710.bb4', 'torsion': [6]}
  • id: 6186108
    {'degree': 8, 'field': [1089, 0, -2934, 0, 91, 0, -10, 0, 1], 'lmfdb_label': '136710.bb4', 'torsion': [12]}
  • id: 6186106
    {'degree': 8, 'field': [143991, -76221, 29124, -5517, 1104, -99, 36, -3, 1], 'lmfdb_label': '136710.bb4', 'torsion': [2, 4]}
  • id: 6186107
    {'degree': 8, 'field': [180244, -42532, 46254, -2170, 521, -434, 40, 0, 1], 'lmfdb_label': '136710.bb4', 'torsion': [2, 4]}
  • id: 6186110
    {'degree': 12, 'field': [6084, 0, 36003, 0, -8645, 0, -125, 0, 165, 0, 13, 0, 1], 'lmfdb_label': '136710.bb4', 'torsion': [2, 6]}
  • id: 6186109
    {'degree': 12, 'field': [515290000, 0, -9323500, 0, -1074675, 0, 48103, 0, -468, 0, 11, 0, 1], 'lmfdb_label': '136710.bb4', 'torsion': [3, 6]}
  • id: 6186112
    {'degree': 16, 'field': [2643876, 0, 1279656, 0, 157665, 0, -5916, 0, 8524, 0, -466, 0, -120, 0, -4, 0, 1], 'lmfdb_label': '136710.bb4', 'torsion': [2, 12]}
  • id: 6186113
    {'degree': 16, 'field': [2906100, -6750000, 6044280, -1964160, 496741, -297324, -109104, 87100, 4988, 16108, 1994, -332, 456, -84, 44, -4, 1], 'lmfdb_label': '136710.bb4', 'torsion': [2, 12]}
  • id: 6186111
    {'degree': 16, 'field': [3549776400, 0, 130094400, 0, -481722980, 0, 80939280, 0, -1243671, 0, -294064, 0, -3270, 0, 96, 0, 1], 'lmfdb_label': '136710.bb4', 'torsion': [8]}
  • id: 6186114
    {'degree': 18, 'field': [58983453, -214200261, 278879607, -152169570, 16684488, 11912526, 1813170, -4495878, 1354065, -77865, -82401, 41850, -416, -4008, 336, 224, -39, -3, 1], 'lmfdb_label': '136710.bb4', '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: 3372696
    {'conductor': 136710, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '136710.bb4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3372697
    {'conductor': 136710, 'conductor_valuation': 2, 'discriminant_valuation': 15, 'j_denominator_valuation': 9, 'kodaira_symbol': -13, 'lmfdb_label': '136710.bb4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3372698
    {'conductor': 136710, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '136710.bb4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3372699
    {'conductor': 136710, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '136710.bb4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3372700
    {'conductor': 136710, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '136710.bb4', 'prime': 31, '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: 2552560
    {'adelic_gens': [[1859, 0, 0, 13019], [9241, 11172, 8946, 1933], [10534, 9289, 12411, 20], [3879, 8218, 1106, 12881], [1, 0, 12, 1], [1870, 9303, 12621, 11152], [13009, 12, 13008, 13], [1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 12970, 13011]], 'adelic_image': '13020.96.1.?', 'conductor': 136710, 'lmfdb_label': '136710.bb4', 'prime': 0}
  • id: 529002
    {'conductor': 136710, 'elladic_image': '2.3.0.1', 'lmfdb_label': '136710.bb4', 'modell_image': '2B', 'prime': 2}
  • id: 529003
    {'conductor': 136710, 'elladic_image': '3.4.0.1', 'lmfdb_label': '136710.bb4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 136710.bb does not appear in ec_padic