Elliptic curve data - 12936.d1

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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': '12936t', 'Clabel': '12936t4', 'Cnumber': 4, 'abc_quality': 1.0688986020632145, 'absD': 515451795167232, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 616, 'ainvs': [0, -1, 0, -1863584, 979821228], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 12936, 'degree': 196608, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1348770652301966999426458163', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [2970658109581346, 2139291], 'lmfdb_iso': '12936.d', 'lmfdb_label': '12936.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -38032, -2867488], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '28.12.0-4.c.1.1', '56.24.0-56.z.1.10', '88.24.0.?', '616.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '5.9833032208257049232069806973', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.52653707518925684709083999991', 'prec': 103}, 'szpiro_ratio': 5.801539672279672, '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, 0, -1, 0, -2, 0, 0, 0, 1, 0, 1, 0, -6, 0, 2, 0, -6, 0, 0, 0], 'aplist': [0, -1, -2, 0, 1, -6, -6, 0, -8, -2, -4, -2, 2, -12, -12, 6, -4, -6, 4, 0, 2, 8, 0, 6, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 12936, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '12936.d', 'trace_hash': 76387630334713929}
• 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': '0.013985221270571923398476286361', 'prec': 107}, 'conductor': 12936, 'gens': [[-583, 43218, 1], [677, 5292, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3464404694442676225623075931', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.5960482465655427956622347091', 'prec': 100}], 'lmfdb_label': '12936.d1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.43292934330201703421095312834', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1806950683378316869089731408003300946', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[789, 0, 1]], 'xcoord_integral_points': [-583, 677, 789, 793, 889]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [4, 0], '7': 'a', '11': [3, 0], '13': [2, 0], '17': [2, 0], '19': [2, 2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '12936.d1'}
• ec_torsion_growth •

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

  
  
  • id: 667127
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [4]}
  • id: 667126
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [2, 2]}
  • id: 667128
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [4]}
  • id: 667129
    {'degree': 4, 'field': [225, 0, -58, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [2, 4]}
  • id: 667130
    {'degree': 4, 'field': [550, 0, -88, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [8]}
  • id: 667134
    {'degree': 8, 'field': [-368122, -135092, -25462, -6722, 848, -158, 58, -4, 1], 'lmfdb_label': '12936.d1', 'torsion': [6]}
  • id: 667132
    {'degree': 8, 'field': [49, 0, 21, 0, 4, 0, -3, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [8]}
  • id: 667133
    {'degree': 8, 'field': [1089, 0, -2420, 0, 1056, 0, -132, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [2, 8]}
  • id: 667131
    {'degree': 8, 'field': [7672, -1792, 1640, 296, -127, -28, 14, -4, 1], 'lmfdb_label': '12936.d1', 'torsion': [2, 4]}
  • id: 667136
    {'degree': 16, 'field': [3364, -8816, 11552, -16632, 42112, -56920, 45672, -21284, 2325, 3508, -2136, 668, 10, -84, 32, -8, 1], 'lmfdb_label': '12936.d1', 'torsion': [2, 8]}
  • id: 667135
    {'degree': 16, 'field': [272484, 0, 521424, 0, 330196, 0, 46512, 0, -4627, 0, 12, 0, 158, 0, -12, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [4, 4]}
  • id: 667140
    {'degree': 16, 'field': [628605184, 0, -271514624, 0, 24327424, 0, -4955520, 0, 254304, 0, -28992, 0, 928, 0, -56, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [12]}
  • id: 667138
    {'degree': 16, 'field': [88889844736, 0, -8080894976, 0, 183656704, 0, -60821376, 0, -6992832, 0, 118272, 0, 7744, 0, -176, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [2, 6]}
  • id: 667137
    {'degree': 16, 'field': [105478800625, 0, -31981631000, 0, -1190106148, 0, -762943720, 0, 103353404, 0, 166936, 0, -12628, 0, -88, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [16]}
  • id: 667139
    {'degree': 16, 'field': [5083735221796, 0, -2912630526344, 0, 360549910204, 0, -17874456864, 0, 472106184, 0, -7340388, 0, 68728, 0, -374, 0, 1], 'lmfdb_label': '12936.d1', 'torsion': [12]}
• 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: 280997
    {'conductor': 12936, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '12936.d1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 280998
    {'conductor': 12936, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12936.d1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 280999
    {'conductor': 12936, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '12936.d1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 281000
    {'conductor': 12936, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12936.d1', 'prime': 11, '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: 1749798
    {'adelic_gens': [[232, 547, 81, 110], [456, 3, 285, 2], [1, 0, 8, 1], [1, 8, 0, 1], [80, 393, 105, 152], [1, 4, 4, 17], [609, 8, 608, 9], [263, 608, 436, 583], [7, 6, 610, 611]], 'adelic_image': '616.48.0.?', 'conductor': 12936, 'lmfdb_label': '12936.d1', 'prime': 0}
  • id: 61422
    {'conductor': 12936, 'elladic_image': '8.12.0.6', 'lmfdb_label': '12936.d1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 568354
    {'lmfdb_iso': '12936.d', 'p': 5, 'prec': 20, 'unit': 2532363629087, 'val': 3}
  • id: 568359
    {'lmfdb_iso': '12936.d', 'p': 13, 'prec': 20, 'unit': 392771904185609902104, 'val': 2}
  • id: 568361
    {'lmfdb_iso': '12936.d', 'p': 17, 'prec': 20, 'unit': 226858177709473873692139, 'val': 2}
  • id: 568365
    {'lmfdb_iso': '12936.d', 'p': 23, 'prec': 20, 'unit': 16249223410650055571384322, 'val': 2}
  • id: 568358
    {'lmfdb_iso': '12936.d', 'p': 29, 'prec': 20, 'unit': 3555095643637989468413687999, 'val': 2}
  • id: 568355
    {'lmfdb_iso': '12936.d', 'p': 31, 'prec': 20, 'unit': 13252796356611482348434573643, 'val': 2}
  • id: 568369
    {'lmfdb_iso': '12936.d', 'p': 37, 'prec': 20, 'unit': 453589479962379820256693402126, 'val': 2}
  • id: 568356
    {'lmfdb_iso': '12936.d', 'p': 41, 'prec': 20, 'unit': 3175534357591856006881458705326, 'val': 2}
  • id: 568357
    {'lmfdb_iso': '12936.d', 'p': 43, 'prec': 20, 'unit': 3112776402481820389484571036645, 'val': 2}
  • id: 568367
    {'lmfdb_iso': '12936.d', 'p': 47, 'prec': 20, 'unit': 636131930622733743740574395360, 'val': 2}
  • id: 568362
    {'lmfdb_iso': '12936.d', 'p': 53, 'prec': 20, 'unit': 9683051164566717328034399345969, 'val': 2}
  • id: 568363
    {'lmfdb_iso': '12936.d', 'p': 59, 'prec': 20, 'unit': 2221065940098064212479857185568996, 'val': 2}
  • id: 568368
    {'lmfdb_iso': '12936.d', 'p': 61, 'prec': 20, 'unit': 4278338493337469477099120524288413, 'val': 2}
  • id: 568353
    {'lmfdb_iso': '12936.d', 'p': 67, 'prec': 20, 'unit': 16124967581893497076506238411137443, 'val': 2}
  • id: 568364
    {'lmfdb_iso': '12936.d', 'p': 73, 'prec': 20, 'unit': 209984711434294543775753603508618212, 'val': 2}
  • id: 568360
    {'lmfdb_iso': '12936.d', 'p': 79, 'prec': 20, 'unit': 615370433067665941789780259451426710, 'val': 2}
  • id: 568366
    {'lmfdb_iso': '12936.d', 'p': 89, 'prec': 20, 'unit': 2489994079036444662398474178167503871, 'val': 2}
  • id: 568352
    {'lmfdb_iso': '12936.d', 'p': 97, 'prec': 20, 'unit': 12752560364135244514175656399688890892, 'val': 2}