Elliptic curve data - 102.a2

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

  
  {'Ciso': '102a', 'Clabel': '102a2', 'Cnumber': 2, 'abc_quality': 0.9489425211495345, 'absD': 46818, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 136, 'ainvs': [1, 1, 0, 8, 10], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 102, 'degree': 16, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.41695460028833387085356737217', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [46268279, 46818], 'lmfdb_iso': '102.a', 'lmfdb_label': '102.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 8, 10], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '68.6.0.c.1', '136.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.28650778588176014295254882606', 'prec': 103}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.41695460028833387085356737217', 'prec': 107}, 'szpiro_ratio': 3.8162315494631627, '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, -1, 1, -4, 1, -2, -1, 1, 4, 0, -1, -6, 2, 4, 1, -1, -1, 4, -4], 'aplist': [-1, -1, -4, -2, 0, -6, -1, 4, 6, -4, -6, -4, -10, -4, 4, -2, 12, -4, -12, -6, 2, 10, -12, -2, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 102, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '102.a', 'trace_hash': 339864609346769676}
• 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': '2.3023013291376976296878093022', 'prec': 100}, 'conductor': 102, 'gens': [[1, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.28650778588176014295254882606', 'prec': 103}], 'lmfdb_label': '102.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.3639319117707327559988779793', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.67728489801666901020123734615344300121', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-5, 5, 2]], 'xcoord_integral_points': [-1, 1, 3, 37]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 1], '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '102.a2'}
• ec_torsion_growth •

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

  
  
  • id: 3758
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '102.a2', 'torsion': [2, 2]}
  • id: 3759
    {'degree': 4, 'field': [-2, 0, 3, 0, 1], 'lmfdb_label': '102.a2', 'torsion': [4]}
  • id: 3762
    {'degree': 8, 'field': [-122, 137, -38, -3, 33, -21, 13, -4, 1], 'lmfdb_label': '102.a2', 'torsion': [6]}
  • id: 3760
    {'degree': 8, 'field': [4, 0, 16, 0, 14, 0, -8, 0, 1], 'lmfdb_label': '102.a2', 'torsion': [2, 4]}
  • id: 3761
    {'degree': 8, 'field': [81, 0, 54, 0, 10, 0, 6, 0, 1], 'lmfdb_label': '102.a2', 'torsion': [2, 4]}
  • id: 3763
    {'degree': 16, 'field': [256, 0, -304256, 0, -246064, 0, -72144, 0, -7828, 0, 696, 0, 278, 0, 28, 0, 1], 'lmfdb_label': '102.a2', 'torsion': [8]}
  • id: 3764
    {'degree': 16, 'field': [1024, 0, 16288, 0, -5468, 0, -1968, 0, -912, 0, 372, 0, 136, 0, 16, 0, 1], 'lmfdb_label': '102.a2', 'torsion': [2, 6]}
• 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: 631
    {'conductor': 102, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '102.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 632
    {'conductor': 102, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '102.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 633
    {'conductor': 102, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '102.a2', 'prime': 17, '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: 1666176
    {'adelic_gens': [[133, 4, 132, 5], [2, 1, 67, 0], [1, 4, 0, 1], [52, 89, 17, 120], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [105, 4, 74, 9]], 'adelic_image': '136.12.0.?', 'conductor': 102, 'lmfdb_label': '102.a2', 'prime': 0}
  • id: 359
    {'conductor': 102, 'elladic_image': '8.6.0.5', 'lmfdb_label': '102.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 369
    {'lmfdb_iso': '102.a', 'p': 5, 'prec': 20, 'unit': 436930634868, 'val': -1}
  • id: 370
    {'lmfdb_iso': '102.a', 'p': 7, 'prec': 20, 'unit': 5903891214289909, 'val': 1}
  • id: 375
    {'lmfdb_iso': '102.a', 'p': 13, 'prec': 20, 'unit': 833374363184066115561, 'val': 1}
  • id: 378
    {'lmfdb_iso': '102.a', 'p': 19, 'prec': 20, 'unit': 709218139591982838819525, 'val': 1}
  • id: 381
    {'lmfdb_iso': '102.a', 'p': 23, 'prec': 20, 'unit': 3055714762204626565792620, 'val': 2}
  • id: 374
    {'lmfdb_iso': '102.a', 'p': 29, 'prec': 20, 'unit': 2963995383933126806454481322, 'val': 1}
  • id: 371
    {'lmfdb_iso': '102.a', 'p': 31, 'prec': 20, 'unit': 11715460840502308405714364286, 'val': 1}
  • id: 386
    {'lmfdb_iso': '102.a', 'p': 37, 'prec': 20, 'unit': 621804333120416984730686780456, 'val': 1}
  • id: 372
    {'lmfdb_iso': '102.a', 'p': 41, 'prec': 20, 'unit': 1381557870751276458290741586375, 'val': 1}
  • id: 373
    {'lmfdb_iso': '102.a', 'p': 43, 'prec': 20, 'unit': 3884466227172912935978734982947, 'val': 1}
  • id: 384
    {'lmfdb_iso': '102.a', 'p': 47, 'prec': 20, 'unit': 5416024325319611894389770906930, 'val': 1}
  • id: 379
    {'lmfdb_iso': '102.a', 'p': 53, 'prec': 20, 'unit': 395836404967630289056743391733287, 'val': 1}
  • id: 377
    {'lmfdb_iso': '102.a', 'p': 59, 'prec': 20, 'unit': 1986895300269038256367898232819907, 'val': 1}
  • id: 385
    {'lmfdb_iso': '102.a', 'p': 61, 'prec': 20, 'unit': 4726258474754627792820382531934452, 'val': 1}
  • id: 368
    {'lmfdb_iso': '102.a', 'p': 67, 'prec': 20, 'unit': 22292603184079204532869060884854514, 'val': 1}
  • id: 383
    {'lmfdb_iso': '102.a', 'p': 71, 'prec': 20, 'unit': 57047609959158003854202123232995090, 'val': 1}
  • id: 380
    {'lmfdb_iso': '102.a', 'p': 73, 'prec': 20, 'unit': 244476180777129440497087435782047615, 'val': 1}
  • id: 376
    {'lmfdb_iso': '102.a', 'p': 79, 'prec': 20, 'unit': 619345698114445642042221520215670969, 'val': 1}
  • id: 367
    {'lmfdb_iso': '102.a', 'p': 83, 'prec': 20, 'unit': 857787593187156920001810616487473081, 'val': 1}
  • id: 382
    {'lmfdb_iso': '102.a', 'p': 89, 'prec': 20, 'unit': 7488092338239552792558621613513941620, 'val': 1}
  • id: 366
    {'lmfdb_iso': '102.a', 'p': 97, 'prec': 20, 'unit': 42973304265069156775964034952178338741, 'val': 1}