Elliptic curve data - 13248.bj1

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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': '13248be', 'Clabel': '13248be4', 'Cnumber': 4, 'abc_quality': 1.0646600114779046, 'absD': 57676024774656, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 552, 'ainvs': [0, 0, 0, -142284, 20654480], 'analytic_rank': 1, 'bad_primes': [2, 3, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 13248, 'degree': 49152, 'elladic_images': ['8.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6440411685511626598234718066', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 35, 'isogeny_degrees': [1, 2, 4], 'jinv': [1666957239793, 301806], 'lmfdb_iso': '13248.bj', 'lmfdb_label': '13248.bj1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -247, 1391], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.p.1', '12.12.0-4.c.1.1', '24.24.0-8.p.1.6', '184.24.0.?', '552.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2347419843739665618361066832', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 207], [3, 8, 1472], [23, 24, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.055014253377189850000001005952', 'prec': 107}, 'szpiro_ratio': 4.973906898342076, '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, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, -8, 0], 'aplist': [0, 0, 2, 0, 0, 2, -2, -8, -1, -2, 8, -2, -10, 8, 8, 2, 4, -2, 8, 0, -6, -8, 16, -18, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 13248, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '13248.bj', 'trace_hash': 453020480165577698}
• 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': '0.037325358264035752059229804764', 'prec': 107}, 'conductor': 13248, 'gens': [[370, 4320, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2347419843739665618361066832', 'prec': 100}], 'lmfdb_label': '13248.bj1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.60736354287490503513403504931', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4292032361626719917621927941498217319', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[220, 0, 1]], 'xcoord_integral_points': [220, 370]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [3, 1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '13248.bj1'}
• ec_torsion_growth •

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

  
  
  • id: 683499
    {'degree': 2, 'field': [-138, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [4]}
  • id: 683497
    {'degree': 2, 'field': [-46, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [2, 2]}
  • id: 683498
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [4]}
  • id: 683500
    {'degree': 4, 'field': [529, 0, -92, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [2, 4]}
  • id: 683504
    {'degree': 8, 'field': [-6912, 0, 0, 0, 288, 0, -14, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [6]}
  • id: 683502
    {'degree': 8, 'field': [529, 0, -1380, 0, 404, 0, -36, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [8]}
  • id: 683501
    {'degree': 8, 'field': [33856, 0, 0, 0, 184, 0, 0, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [2, 4]}
  • id: 683503
    {'degree': 8, 'field': [38416, 0, -1960, 0, 624, 0, -10, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [8]}
  • id: 683509
    {'degree': 16, 'field': [2304, 0, -5376, 0, 16912, 0, -2688, 0, -8736, 0, 1456, 0, -336, 0, 0, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [12]}
  • id: 683507
    {'degree': 16, 'field': [14641, 0, -64372, 0, 105800, 0, -83064, 0, 34271, 0, -7704, 0, 920, 0, -52, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [2, 8]}
  • id: 683508
    {'degree': 16, 'field': [1048576, 0, -7206912, 0, 2848768, 0, -748544, 0, 42624, 0, 1504, 0, 496, 0, 18, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [2, 6]}
  • id: 683506
    {'degree': 16, 'field': [1708425, -1464120, -133032, 259920, 901378, -285936, 59700, 139776, -9357, -7920, -956, 96, 510, -24, -36, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [2, 8]}
  • id: 683505
    {'degree': 16, 'field': [4879681, 0, 1210532, 0, 83822, 0, 71376, 0, 9587, 0, -1488, 0, -82, 0, -4, 0, 1], 'lmfdb_label': '13248.bj1', 'torsion': [4, 4]}
  • id: 683510
    {'degree': 16, 'field': [109746576, 0, -824131584, 0, 230488416, 0, -23175936, 0, 1127304, 0, -47808, 0, 1945, 0, -28, 0, 1], 'lmfdb_label': '13248.bj1', '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: 288822
    {'conductor': 13248, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '13248.bj1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 288823
    {'conductor': 13248, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '13248.bj1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 288824
    {'conductor': 13248, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '13248.bj1', '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: 1751971
    {'adelic_gens': [[296, 15, 87, 224], [344, 429, 111, 266], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [388, 369, 207, 190], [7, 6, 546, 547], [367, 0, 0, 551], [545, 8, 544, 9]], 'adelic_image': '552.48.0.?', 'conductor': 13248, 'lmfdb_label': '13248.bj1', 'prime': 0}
  • id: 62867
    {'conductor': 13248, 'elladic_image': '8.12.0.9', 'lmfdb_label': '13248.bj1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 584301
    {'lmfdb_iso': '13248.bj', 'p': 5, 'prec': 20, 'unit': 15648433328981, 'val': 1}
  • id: 584306
    {'lmfdb_iso': '13248.bj', 'p': 13, 'prec': 20, 'unit': 1210050750963480233823, 'val': 1}
  • id: 584308
    {'lmfdb_iso': '13248.bj', 'p': 17, 'prec': 20, 'unit': 29096405570893273181704, 'val': 1}
  • id: 584309
    {'lmfdb_iso': '13248.bj', 'p': 19, 'prec': 20, 'unit': 1585937351192686368228175, 'val': 1}
  • id: 584305
    {'lmfdb_iso': '13248.bj', 'p': 29, 'prec': 20, 'unit': 6014970832994848704202997845, 'val': 1}
  • id: 584302
    {'lmfdb_iso': '13248.bj', 'p': 31, 'prec': 20, 'unit': 4521716116521494931815874712, 'val': 1}
  • id: 584316
    {'lmfdb_iso': '13248.bj', 'p': 37, 'prec': 20, 'unit': 24213544873768986414249981212, 'val': 1}
  • id: 584303
    {'lmfdb_iso': '13248.bj', 'p': 41, 'prec': 20, 'unit': 2177508795133109758732904618389, 'val': 1}
  • id: 584304
    {'lmfdb_iso': '13248.bj', 'p': 43, 'prec': 20, 'unit': 2035082140716329666197694122427, 'val': 1}
  • id: 584314
    {'lmfdb_iso': '13248.bj', 'p': 47, 'prec': 20, 'unit': 50251906422375626703933716329618, 'val': 1}
  • id: 584310
    {'lmfdb_iso': '13248.bj', 'p': 53, 'prec': 20, 'unit': 477802884322537139746310905938740, 'val': 1}
  • id: 584311
    {'lmfdb_iso': '13248.bj', 'p': 59, 'prec': 20, 'unit': 2885607913584998909929265629025423, 'val': 1}
  • id: 584315
    {'lmfdb_iso': '13248.bj', 'p': 61, 'prec': 20, 'unit': 3514081202346530820966567163598168, 'val': 1}
  • id: 584300
    {'lmfdb_iso': '13248.bj', 'p': 67, 'prec': 20, 'unit': 32627011325499894006984369775338031, 'val': 1}
  • id: 584312
    {'lmfdb_iso': '13248.bj', 'p': 73, 'prec': 20, 'unit': 213765419620497966432834504570606903, 'val': 1}
  • id: 584307
    {'lmfdb_iso': '13248.bj', 'p': 79, 'prec': 20, 'unit': 809586810099024249148223867127994800, 'val': 1}
  • id: 584299
    {'lmfdb_iso': '13248.bj', 'p': 83, 'prec': 20, 'unit': 1676419462375654267711293027486525200, 'val': 1}
  • id: 584313
    {'lmfdb_iso': '13248.bj', 'p': 89, 'prec': 20, 'unit': 4566195179902529882529292355362911879, 'val': 1}
  • id: 584298
    {'lmfdb_iso': '13248.bj', 'p': 97, 'prec': 20, 'unit': 36056066271499950002726865485743638717, 'val': 1}