Elliptic curve data - 82110.bs6

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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': '82110bt1', 'Cnumber': 1, 'abc_quality': 0.9919472947720096, 'absD': 10116926999101440000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 1313760, 'ainvs': [1, 0, 0, -49095400, 132402324032], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 17, 23], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 82110, 'degree': 7340032, 'elladic_images': ['16.96.0.95'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9543794383492774403065576309', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [13087181362848921857775657601, 10116926999101440000], 'lmfdb_iso': '82110.bs', 'lmfdb_label': '82110.bs6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -49095400, 132402324032], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.bb.1.1', '16.96.0-16.v.1.2', '322.6.0.?', '480.192.1.?', '644.24.0.?', '1288.96.0.?', '2576.192.1.?', '3808.192.2.?', '12512.192.2.?', '28560.192.2.?', '57120.384.5.?', '77280.384.5.?', '87584.384.5.?', '93840.192.2.?', '187680.384.5.?', '656880.384.5.?', '1313760.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 13, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.0697304843631873930432752506', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 161], [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': '2.9543794383492774403065576309', 'prec': 100}, 'szpiro_ratio': 5.721322787719762, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [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': '0.0027155551355036976658826020275', 'prec': 110}, 'conductor': 82110, 'gens': [[4724, 74468, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.0697304843631873930432752506', 'prec': 100}], 'lmfdb_label': '82110.bs6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19044923924242979214769477659', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.401233194699109664652645957408794859', 'prec': 130}, 'tamagawa_product': 1024, 'torsion_generators': [[4064, 8, 1]], 'xcoord_integral_points': [4048, 4064, 4304, 4724, 5492, 8144, 54224]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 0], '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.bs6'}
• ec_torsion_growth •

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

  
  
  • id: 3860407
    {'degree': 2, 'field': [-1466, -1, 1], 'lmfdb_label': '82110.bs6', 'torsion': [16]}
  • id: 3860408
    {'degree': 2, 'field': [-446, -1, 1], 'lmfdb_label': '82110.bs6', 'torsion': [16]}
  • id: 3860406
    {'degree': 2, 'field': [-40, -1, 1], 'lmfdb_label': '82110.bs6', 'torsion': [2, 8]}
  • id: 3860409
    {'degree': 4, 'field': [164836, 0, -973, 0, 1], 'lmfdb_label': '82110.bs6', 'torsion': [2, 16]}
  • id: 3860414
    {'degree': 8, 'field': [-196608, 0, -777232, 0, -1536, 0, 0, 0, 1], 'lmfdb_label': '82110.bs6', 'torsion': [24]}
  • id: 3860410
    {'degree': 8, 'field': [8856576, 3952128, 881792, 60400, -4271, -1410, 2, -2, 1], 'lmfdb_label': '82110.bs6', 'torsion': [4, 8]}
  • id: 3860413
    {'degree': 8, 'field': [1345117456, -71393844, 89318048, -13867335, 610701, 16350, -1438, -3, 1], 'lmfdb_label': '82110.bs6', 'torsion': [32]}
  • id: 3860411
    {'degree': 8, 'field': [11932503696, 918893232, 35380872, 563364, -216791, -8494, 2, -2, 1], 'lmfdb_label': '82110.bs6', 'torsion': [2, 16]}
  • id: 3860412
    {'degree': 8, 'field': [2953552326226, -169626415650, -26707357729, 97851660, 26158281, -11730, -8899, 0, 1], 'lmfdb_label': '82110.bs6', 'torsion': [32]}
  • id: 3860418
    {'degree': 16, 'field': [6894506999808, 7556917690368, 2501445058560, -62671970304, -218228050944, -55942905600, -8169478144, -662868736, 99660736, 30595728, 1427476, -184337, -15832, 273, -73, -4, 1], 'lmfdb_label': '82110.bs6', 'torsion': [2, 24]}
  • id: 3860420
    {'degree': 16, 'field': [34218263912094684900, 0, 455715450355666815, 0, -10659488136489729, 0, -74373235976601, 0, 953496855495, 0, -3263953275, 0, 4935205, 0, -3451, 0, 1], 'lmfdb_label': '82110.bs6', 'torsion': [48]}
  • id: 3860415
    {'degree': 16, 'field': [156163135476069804096, -2200725616876351488, 15506839133356032, 67296410242022976, 170104925316592, 56290973654048, 13690072447520, 293920824064, 3176361084, 2738503696, 82986640, -1597228, 261477, 12674, 2, -2, 1], 'lmfdb_label': '82110.bs6', 'torsion': [4, 16]}
  • id: 3860416
    {'degree': 16, 'field': [962108000389909872640, 989424388102225920, -976346068868339200, -26169397681624960, 13116575730034976, -38193090253032, 12632493130460, 84277797690, -20840689649, -153599670, 31823146, -614570, 113136, -4970, 730, -8, 1], 'lmfdb_label': '82110.bs6', 'torsion': [2, 32]}
  • id: 3860417
    {'degree': 16, 'field': [1737472494335424004096, 0, -113312268579715046400, 0, 2023242359452276096, 0, -13997286861877500, 0, 38439759693996, 0, -49446095235, 0, 31188871, 0, -9165, 0, 1], 'lmfdb_label': '82110.bs6', 'torsion': [2, 32]}
  • id: 3860419
    {'degree': 16, 'field': [176929112778756448022784, 0, -266017601971495930368, 0, -1726580059384963040, 0, -1891724255984256, 0, 4201370442885, 0, 1054055356, 0, -4499922, 0, 0, 0, 1], 'lmfdb_label': '82110.bs6', 'torsion': [48]}
• 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: 2000537
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 32, 'j_denominator_valuation': 32, 'kodaira_symbol': 36, 'lmfdb_label': '82110.bs6', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 32}
  • id: 2000538
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '82110.bs6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2000539
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '82110.bs6', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2000540
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '82110.bs6', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2000541
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '82110.bs6', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2000542
    {'conductor': 82110, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '82110.bs6', 'prime': 23, '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: 2205382
    {'adelic_gens': [[1, 0, 32, 1], [1051031, 26, 260214, 1310891], [1, 32, 0, 1], [850103, 26, 619014, 875], [5, 28, 68, 381], [492663, 2, 492634, 1313743], [23, 18, 1311198, 1311755], [938432, 29, 753547, 2562], [742590, 31, 685289, 1313604], [1313729, 32, 1313728, 33], [875863, 26, 1311222, 1310891], [1231681, 32, 247290, 991]], 'adelic_image': '1313760.768.13.?', 'conductor': 82110, 'lmfdb_label': '82110.bs6', 'prime': 0}
  • id: 336420
    {'conductor': 82110, 'elladic_image': '16.96.0.95', 'lmfdb_label': '82110.bs6', '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}