Elliptic curve data - 82110.bs5

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• 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': '82110bt', 'Clabel': '82110bt2', 'Cnumber': 2, 'abc_quality': 0.9923666812811367, 'absD': 363628103290905600000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 656880, 'ainvs': [1, 0, 0, -49423080, 130545230400], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 17, 23], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 82110, 'degree': 14680064, 'elladic_images': ['8.96.0.40'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3009530286292500950151736916', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13350979617415439280823624321, 363628103290905600000000], 'lmfdb_iso': '82110.bs', 'lmfdb_label': '82110.bs5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -49423080, 130545230400], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.96.0-8.l.2.2', '240.192.1.?', '644.48.0.?', '1288.192.1.?', '1904.192.2.?', '6256.192.2.?', '28560.384.5.?', '38640.384.5.?', '43792.384.5.?', '93840.384.5.?', '656880.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 36, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0348652421815936965216376253', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 27370], [5, 6, 16422], [7, 8, 11730], [17, 18, 4830], [23, 24, 3570]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.3009530286292500950151736916', 'prec': 100}, 'szpiro_ratio': 5.723086384275005, 'torsion': 16, 'torsion_primes': [2], 'torsion_structure': [2, 8]}
• 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, 1, 1, 4, 1], 'aplist': [1, 1, 1, -1, -4, -2, 1, 4, -1, -2, 0, -10, -6, 12, 0, -10, 12, -2, 4, 8, -6, 0, 4, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 82110, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '82110.bs', 'trace_hash': 1601533552796115024}
• 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': '0.0013577775677518488329413010138', 'prec': 110}, 'conductor': 82110, 'gens': [[3480, 24720, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0348652421815936965216376253', 'prec': 100}], 'lmfdb_label': '82110.bs5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.095224619621214896073847388293', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.401233194699109664652645957408794859', 'prec': 130}, 'tamagawa_product': 16384, 'torsion_generators': [[3536, -1768, 1], [3060, 87720, 1]], 'xcoord_integral_points': [-7440, -4080, -1938, -510, 960, 3060, 3480, 3536, 4560, 4760, 5100, 5712, 6480, 8160, 11310, 15810, 28560, 69360, 216240]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 1], '3': [2, 0], '5': [2, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '82110.bs5'}
• ec_torsion_growth •

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

  
  
  • id: 3860422
    {'degree': 4, 'field': [676, 0, 67, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [2, 16]}
  • id: 3860421
    {'degree': 4, 'field': [1600, 0, 81, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [4, 8]}
  • id: 3860423
    {'degree': 4, 'field': [8836, 0, -203, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [2, 16]}
  • id: 3860424
    {'degree': 8, 'field': [-196608, 0, -777232, 0, -1536, 0, 0, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [2, 24]}
  • id: 3860426
    {'degree': 16, 'field': [1061856055296, 0, 175731780096, 0, 2777633424, 0, -171145176, 0, 28638985, 0, -868596, 0, 20174, 0, -204, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [4, 16]}
  • id: 3860427
    {'degree': 16, 'field': [44307660960000, 0, 0, 0, 32852743200, 0, 0, 0, 2058481, 0, 0, 0, 338, 0, 0, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [4, 16]}
  • id: 3860425
    {'degree': 16, 'field': [188930962886656, 0, 18562783518976, 0, 625683863044, 0, 6492300540, 0, -35311383, 0, 388440, 0, 19174, 0, -164, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [8, 8]}
  • id: 3860428
    {'degree': 16, 'field': [348772656807936, 0, -394905427310592, 0, 1544197076502528, 0, 16222291278816, 0, 92124620560, 0, 306568976, 0, 714168, 0, 1118, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [2, 32]}
  • id: 3860429
    {'degree': 16, 'field': [5896975881323151360, -2064027274242785280, 331670513925757440, -3864720613340160, -1978467862337304, 99014238400872, 33553246522014, 2812083724242, -189755332583, -15440175402, 196300424, 17836566, 1038774, -2646, -2158, 0, 1], 'lmfdb_label': '82110.bs5', 'torsion': [2, 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: 2000543
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '82110.bs5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 2000544
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '82110.bs5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 2000545
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '82110.bs5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 2000546
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.bs5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2000547
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '82110.bs5', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2000548
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.bs5', 'prime': 23, '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: 2205381
    {'adelic_gens': [[199921, 16, 542646, 97], [15, 16, 74, 574849], [1, 16, 0, 1], [618249, 16, 68, 121], [437921, 8, 0, 1], [469209, 16, 187874, 345], [1, 16, 4, 65], [1, 0, 16, 1], [5, 16, 4, 492673], [131377, 8, 0, 1], [656865, 16, 656864, 17]], 'adelic_image': '656880.768.13.?', 'conductor': 82110, 'lmfdb_label': '82110.bs5', 'prime': 0}
  • id: 336419
    {'conductor': 82110, 'elladic_image': '8.96.0.40', 'lmfdb_label': '82110.bs5', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 4236030
    {'lmfdb_iso': '82110.bs', 'p': 11, 'prec': 20, 'unit': 32702201256068778573, 'val': 1}
  • id: 4236028
    {'lmfdb_iso': '82110.bs', 'p': 13, 'prec': 20, 'unit': 170422566261904553613, 'val': 1}
  • id: 4236031
    {'lmfdb_iso': '82110.bs', 'p': 19, 'prec': 20, 'unit': 626463097538166343515799, 'val': 1}
  • id: 4236029
    {'lmfdb_iso': '82110.bs', 'p': 29, 'prec': 20, 'unit': 1274550482482936693442952409, 'val': 1}
  • id: 4236024
    {'lmfdb_iso': '82110.bs', 'p': 37, 'prec': 20, 'unit': 153709385256265349528642532492, 'val': 1}
  • id: 4236026
    {'lmfdb_iso': '82110.bs', 'p': 41, 'prec': 20, 'unit': 4124505813912686061724912329002, 'val': 1}
  • id: 4236027
    {'lmfdb_iso': '82110.bs', 'p': 43, 'prec': 20, 'unit': 313794116651113313610543150545, 'val': 1}
  • id: 4236032
    {'lmfdb_iso': '82110.bs', 'p': 53, 'prec': 20, 'unit': 514079795423136305242908110955302, 'val': 1}
  • id: 4236035
    {'lmfdb_iso': '82110.bs', 'p': 59, 'prec': 20, 'unit': 1373180473342419009630894594773602, 'val': 1}
  • id: 4236036
    {'lmfdb_iso': '82110.bs', 'p': 61, 'prec': 20, 'unit': 7849164803061490415256332888441995, 'val': 1}
  • id: 4236023
    {'lmfdb_iso': '82110.bs', 'p': 67, 'prec': 20, 'unit': 20277641553557277290824445517887470, 'val': 1}
  • id: 4236025
    {'lmfdb_iso': '82110.bs', 'p': 71, 'prec': 20, 'unit': 73271211922403488414681125325869296, 'val': 1}
  • id: 4236033
    {'lmfdb_iso': '82110.bs', 'p': 73, 'prec': 20, 'unit': 185266699369358011617986951364440946, 'val': 1}
  • id: 4236022
    {'lmfdb_iso': '82110.bs', 'p': 83, 'prec': 20, 'unit': 2576603744706529038439982148985526394, 'val': 1}
  • id: 4236034
    {'lmfdb_iso': '82110.bs', 'p': 89, 'prec': 20, 'unit': 3214872213493159338462367919601441120, 'val': 1}
  • id: 4236021
    {'lmfdb_iso': '82110.bs', 'p': 97, 'prec': 20, 'unit': 55070366777344394997085987446012228866, 'val': 1}