Elliptic curve data - 8330.b2

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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': '8330g', 'Clabel': '8330g1', 'Cnumber': 1, 'abc_quality': 1.0175814005597876, 'absD': 4689530500976562500, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1428, 'ainvs': [1, 1, 0, -632713, 219691193], 'analytic_rank': 1, 'bad_primes': [2, 5, 7, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 8330, 'degree': 161280, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3095909446881228427045334549', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-99166425177001, 16601562500], 'lmfdb_iso': '8330.b', 'lmfdb_label': '8330.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -12913, -642344], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '21.8.0-3.a.1.1', '68.2.0.a.1', '204.8.0.?', '1428.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0096016741141869008696473605', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 833], [3, 2, 1666], [5, 6, 1666], [7, 20, 170], [17, 18, 490]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.68799915380869508845007283536', 'prec': 103}, 'szpiro_ratio': 5.7535671956183325, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, -1, -2, 1, -3, -1, -5, 0, 1, 1, 1, 2, -2, -1], 'aplist': [-1, -1, -1, 0, -3, -5, 1, -2, 0, 6, 4, -4, -6, 8, 6, 9, 0, 4, 2, 9, 10, 5, 0, -9, 4], 'class_deg': 3, 'class_size': 2, 'conductor': 8330, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '8330.b', 'trace_hash': 570154192589923395}
• 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': '0.0098608600364807565496452308946', 'prec': 110}, 'conductor': 8330, 'gens': [[-776, 16013, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0096016741141869008696473605', 'prec': 100}], 'lmfdb_label': '8330.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.23514685071918736952994429252', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8902060194718309274396570306390895168', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-776, 2957]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [3, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '8330.b2'}
• ec_torsion_growth •

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

  
  
  • id: 435410
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '8330.b2', 'torsion': [3]}
  • id: 435411
    {'degree': 3, 'field': [-20, 12, -1, 1], 'lmfdb_label': '8330.b2', 'torsion': [2]}
  • id: 435413
    {'degree': 6, 'field': [-15875, 8315, -678, 433, 78, -1, 1], 'lmfdb_label': '8330.b2', 'torsion': [3]}
  • id: 435414
    {'degree': 6, 'field': [92, 2, -10, 15, -5, -3, 1], 'lmfdb_label': '8330.b2', 'torsion': [6]}
  • id: 435412
    {'degree': 6, 'field': [272, 0, -72, 0, 1, 0, 1], 'lmfdb_label': '8330.b2', 'torsion': [2, 2]}
  • id: 435415
    {'degree': 12, 'field': [8, 140, -578, 896, -481, -70, 223, -42, 18, -28, 5, 0, 1], 'lmfdb_label': '8330.b2', 'torsion': [4]}
  • id: 435417
    {'degree': 12, 'field': [400, -1440, 2644, -3992, 5552, -5712, 3753, -1498, 463, -124, 19, -2, 1], 'lmfdb_label': '8330.b2', 'torsion': [2, 6]}
  • id: 435416
    {'degree': 12, 'field': [65691025, 14078385, -226237, -264024, 244857, -25389, 21778, -3045, -159, 12, -1, -3, 1], 'lmfdb_label': '8330.b2', 'torsion': [3, 3]}
  • id: 435419
    {'degree': 18, 'field': [-425259008, 1076719616, -1383631872, 1273173248, -984976832, 616378112, -281610908, 84752752, -16224544, 1841848, -425656, 217056, -42920, 5712, -644, -68, 0, 0, 1], 'lmfdb_label': '8330.b2', 'torsion': [6]}
  • id: 435418
    {'degree': 18, 'field': [105981016, 47661564, 122492686, 64027449, 108598091, 115769266, 51554322, 8778679, -1382526, -1274229, -375475, -22152, 21901, 6749, 284, -222, -40, 0, 1], 'lmfdb_label': '8330.b2', 'torsion': [9]}
• 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: 173296
    {'conductor': 8330, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8330.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 173297
    {'conductor': 8330, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '8330.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 173298
    {'conductor': 8330, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '8330.b2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 173299
    {'conductor': 8330, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8330.b2', 'prime': 17, '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: 1719038
    {'adelic_gens': [[4, 3, 9, 7], [834, 805, 1309, 1191], [1, 6, 0, 1], [1423, 6, 1422, 7], [715, 210, 105, 631], [3, 4, 8, 11], [1261, 210, 315, 631], [1019, 0, 0, 1427], [1, 0, 6, 1]], 'adelic_image': '1428.16.0.?', 'conductor': 8330, 'lmfdb_label': '8330.b2', 'prime': 0}
  • id: 40771
    {'conductor': 8330, 'elladic_image': '3.4.0.1', 'lmfdb_label': '8330.b2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 344525
    {'lmfdb_iso': '8330.b', 'p': 11, 'prec': 20, 'unit': 33998400409175018348, 'val': 1}
  • id: 344531
    {'lmfdb_iso': '8330.b', 'p': 13, 'prec': 20, 'unit': 866586988956546275161, 'val': 1}
  • id: 344533
    {'lmfdb_iso': '8330.b', 'p': 19, 'prec': 20, 'unit': 87640984729556029730705, 'val': 1}
  • id: 344530
    {'lmfdb_iso': '8330.b', 'p': 29, 'prec': 20, 'unit': 1391456820813034344350265258, 'val': 1}
  • id: 344539
    {'lmfdb_iso': '8330.b', 'p': 31, 'prec': 20, 'unit': 11283987161026292131156493104, 'val': 1}
  • id: 344526
    {'lmfdb_iso': '8330.b', 'p': 37, 'prec': 20, 'unit': 542288831377319439145145715615, 'val': 1}
  • id: 344528
    {'lmfdb_iso': '8330.b', 'p': 41, 'prec': 20, 'unit': 4039737949138669759526080014998, 'val': 1}
  • id: 344529
    {'lmfdb_iso': '8330.b', 'p': 43, 'prec': 20, 'unit': 5236497409046659140192791586515, 'val': 1}
  • id: 344532
    {'lmfdb_iso': '8330.b', 'p': 47, 'prec': 20, 'unit': 5939982146918959670251966369256, 'val': 1}
  • id: 344534
    {'lmfdb_iso': '8330.b', 'p': 53, 'prec': 20, 'unit': 94624947498332484947513374196146, 'val': 1}
  • id: 344538
    {'lmfdb_iso': '8330.b', 'p': 61, 'prec': 20, 'unit': 3888814581981407775161017315035225, 'val': 1}
  • id: 344524
    {'lmfdb_iso': '8330.b', 'p': 67, 'prec': 20, 'unit': 1097780448801718063643303103042980, 'val': 1}
  • id: 344527
    {'lmfdb_iso': '8330.b', 'p': 71, 'prec': 20, 'unit': 34760237809608191370099098543204701, 'val': 1}
  • id: 344535
    {'lmfdb_iso': '8330.b', 'p': 73, 'prec': 20, 'unit': 242935201866870684080465605470534432, 'val': 1}
  • id: 344537
    {'lmfdb_iso': '8330.b', 'p': 79, 'prec': 20, 'unit': 102385680765407340339903868597734622, 'val': 1}
  • id: 344536
    {'lmfdb_iso': '8330.b', 'p': 89, 'prec': 20, 'unit': 9413654499400882680420104897703817231, 'val': 1}
  • id: 344523
    {'lmfdb_iso': '8330.b', 'p': 97, 'prec': 20, 'unit': 42443273665286565625181619875174850973, 'val': 1}