Elliptic curve data - 82110.bs8

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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': '82110bt5', 'Cnumber': 5, 'abc_quality': 1.0168811917145575, 'absD': 4540848316592979232425603600, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 1313760, 'ainvs': [1, 0, 0, 352354920, -2007529902000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 17, 23], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 82110, 'degree': 58720256, 'elladic_images': ['16.96.0.25'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9941002091891954044324058131', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4837987390362436347081585367679, 4540848316592979232425603600], 'lmfdb_iso': '82110.bs', 'lmfdb_label': '82110.bs8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 352354920, -2007529902000], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '8.48.0-8.q.1.2', '16.96.0-16.j.1.2', '120.96.0.?', '240.192.1.?', '1288.96.0.?', '2576.192.1.?', '3808.192.2.?', '12512.192.2.?', '19320.192.1.?', '38640.384.5.?', '57120.384.5.?', '87584.384.5.?', '187680.384.5.?', '1313760.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.1394609687263747860865505011', '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': '3.9941002091891954044324058131', 'prec': 100}, 'szpiro_ratio': 6.243832285107038, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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': '0.00033944439193796220823532525344', 'prec': 113}, 'conductor': 82110, 'gens': [[7350, 985950, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '8.1394609687263747860865505011', 'prec': 100}], 'lmfdb_label': '82110.bs8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.023806154905303724018461847073', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.401233194699109664652645957408794859', 'prec': 130}, 'tamagawa_product': 1024, 'torsion_generators': [[26160, 4998180, 1]], 'xcoord_integral_points': [7350, 26160]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 3], '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.bs8'}
• ec_torsion_growth •

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

  
  
  • id: 3860461
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [8]}
  • id: 3860460
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [2, 4]}
  • id: 3860462
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '82110.bs8', 'torsion': [8]}
  • id: 3860466
    {'degree': 4, 'field': [-1799, -338, -6, -2, 1], 'lmfdb_label': '82110.bs8', 'torsion': [16]}
  • id: 3860465
    {'degree': 4, 'field': [16, 0, -7, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [2, 8]}
  • id: 3860467
    {'degree': 4, 'field': [2940, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [16]}
  • id: 3860464
    {'degree': 4, 'field': [25921, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [2, 8]}
  • id: 3860463
    {'degree': 4, 'field': [5832225, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [4, 4]}
  • id: 3860471
    {'degree': 8, 'field': [-196608, 0, -777232, 0, -1536, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [12]}
  • id: 3860469
    {'degree': 8, 'field': [287296, -94336, 15488, -1600, 1081, -170, 2, -2, 1], 'lmfdb_label': '82110.bs8', 'torsion': [2, 16]}
  • id: 3860470
    {'degree': 8, 'field': [538756, 0, 8824, 0, -1464, 0, 4, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [2, 16]}
  • id: 3860468
    {'degree': 8, 'field': [672339154, 1140268, -1088330, -103892, 51987, -52, 22, -4, 1], 'lmfdb_label': '82110.bs8', 'torsion': [4, 8]}
  • id: 3860478
    {'degree': 16, 'field': [150994944, 0, 0, 0, 9429462532, 0, 0, 0, 122880, 0, 0, 0, 768, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [2, 12]}
  • id: 3860475
    {'degree': 16, 'field': [1852816594276, 1269603967168, 184612780832, -5006087736, 11525291096, 495848408, -97615160, -104031348, 65510149, -7184544, 236080, 16576, -1774, 72, 8, -4, 1], 'lmfdb_label': '82110.bs8', 'torsion': [4, 16]}
  • id: 3860480
    {'degree': 16, 'field': [8506571118336, -5092898848128, 5707331295984, -1231717380480, 623066483520, -8862247296, 3304308064, -290985248, 61217745, 7714040, -1570660, 14568, -1882, -280, 60, -8, 1], 'lmfdb_label': '82110.bs8', 'torsion': [24]}
  • id: 3860472
    {'degree': 16, 'field': [34607924122500, 0, 4997180790000, 0, 194258655000, 0, 1434510000, 0, 11968200, 0, -1449000, 0, 900, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [4, 8]}
  • id: 3860479
    {'degree': 16, 'field': [147624030903969, 0, -19398005478168, 0, 642281810140, 0, 6644680824, 0, -285860250, 0, -1835624, 0, 3228, 0, -120, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [24]}
  • id: 3860474
    {'degree': 16, 'field': [3873359776087684, 0, 11783575757296, 0, 9210975512, 0, 1388464, 0, 124472648, 0, -315560, 0, 4, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [2, 16]}
  • id: 3860477
    {'degree': 16, 'field': [3287084887661189529600, 0, 0, 0, 80979400110067200, 0, 0, 0, 662467001280, 0, 0, 0, 1156680, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [32]}
  • id: 3860476
    {'degree': 16, 'field': [5463009796532820537600, 0, 0, 0, 2947991336590003200, 0, 0, 0, 3400008574020, 0, 0, 0, -5818080, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', 'torsion': [32]}
  • id: 3860473
    {'degree': 16, 'field': [9926997138383756115391876, 0, 134222296204804374000, 0, 466305635092504, 0, 312404400, 0, 6301427501256, 0, -71001000, 0, 4, 0, 0, 0, 1], 'lmfdb_label': '82110.bs8', '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: 2000561
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '82110.bs8', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2000562
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.bs8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2000563
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.bs8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2000564
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.bs8', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2000565
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '82110.bs8', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 2000566
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.bs8', '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: 2205384
    {'adelic_gens': [[25, 16, 1312024, 1312649], [1, 0, 32, 1], [1199549, 24, 631806, 2885], [1, 32, 0, 1], [563069, 8, 374334, 1313477], [437945, 32, 441302, 4329], [1236481, 16, 0, 1], [25, 32, 266134, 4329], [25, 16, 1312374, 1148653], [1313729, 32, 1313728, 33], [1, 32, 4, 129], [25, 16, 942879, 81223]], 'adelic_image': '1313760.768.13.?', 'conductor': 82110, 'lmfdb_label': '82110.bs8', 'prime': 0}
  • id: 336422
    {'conductor': 82110, 'elladic_image': '16.96.0.25', 'lmfdb_label': '82110.bs8', 'modell_image': '2B', '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}