Elliptic curve data - 12696.p2

Formats: - HTML - YAML - JSON - 2025-09-21T19:57:10.072148

• 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': '12696s', 'Clabel': '12696s1', 'Cnumber': 1, 'abc_quality': 1.004043405683459, 'absD': 183922990848, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [0, 1, 0, -7444, 245600], 'analytic_rank': 2, 'bad_primes': [2, 3, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12696, 'degree': 23040, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0180724548040813968673175152', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [-14647977776, 59049], 'lmfdb_iso': '12696.p', 'lmfdb_label': '12696.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -7444, 245600], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.f.1', '46.6.0.a.1', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 33, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.31427839121311471278079345091', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 23], [3, 4, 4232], [5, 2, 4232], [23, 156, 24]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.22789921955150289877919210706', 'prec': 107}, 'szpiro_ratio': 4.060323673752532, '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, -2, 0, 1, 0, -4, 0, -6, 0, -2, 0, -6, 0, -6, 0], 'aplist': [0, 1, -2, -2, -4, -6, -6, -6, 0, -6, 8, -8, -6, 10, 4, 2, 8, -8, -10, -8, -10, -6, -12, -18, 12], 'class_deg': 2, 'class_size': 2, 'conductor': 12696, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12696.p', 'trace_hash': 1719359402156620589}
• 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': '0.13053095078049441928685099588', 'prec': 103}, 'conductor': 12696, 'gens': [[38, 138, 1], [8, 432, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.25523717779946072314203644081', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.2339674513063001259010704894', 'prec': 100}], 'lmfdb_label': '12696.p2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.0160969965156070809275590632', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.3867465876280563870394107373782985934', 'prec': 130}, 'tamagawa_product': 80, 'torsion_generators': [[-100, 0, 1]], 'xcoord_integral_points': [-100, -82, -46, -8, 8, 38, 44, 47, 50, 62, 107, 143, 194, 314, 478, 1142, 1352]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [4, 0], '7': [4, 0], '11': [2, 0], '13': [2, 0], '17': [2, 0], '19': [2, 0], '23': 'a', '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '12696.p2'}
• ec_torsion_growth •

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

  
  
  • id: 655294
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '12696.p2', 'torsion': [2, 2]}
  • id: 655295
    {'degree': 4, 'field': [-15, 33, -14, -1, 1], 'lmfdb_label': '12696.p2', 'torsion': [4]}
  • id: 655296
    {'degree': 8, 'field': [9, 63, 159, 84, -8, -12, 7, -3, 1], 'lmfdb_label': '12696.p2', 'torsion': [2, 4]}
  • id: 655298
    {'degree': 8, 'field': [81, 0, -108, -138, -84, -46, -12, 0, 1], 'lmfdb_label': '12696.p2', 'torsion': [6]}
  • id: 655297
    {'degree': 8, 'field': [324, 0, -300, 0, 85, 0, -9, 0, 1], 'lmfdb_label': '12696.p2', 'torsion': [2, 4]}
  • id: 655300
    {'degree': 16, 'field': [36, 0, 29256, 0, -27980, 0, 19596, 0, -4380, 0, 736, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '12696.p2', 'torsion': [2, 6]}
  • id: 655299
    {'degree': 16, 'field': [6889, 0, 467344, 0, -343214, 0, 82804, 0, -14333, 0, 1348, 0, -98, 0, 4, 0, 1], 'lmfdb_label': '12696.p2', 'torsion': [8]}
• 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: 275336
    {'conductor': 12696, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '12696.p2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 275337
    {'conductor': 12696, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '12696.p2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 275338
    {'conductor': 12696, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '12696.p2', 'prime': 23, 'reduction_type': 0, '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: 1748279
    {'adelic_gens': [[1, 0, 4, 1], [185, 4, 94, 9], [3, 4, 8, 11], [1, 2, 2, 5], [112, 1, 179, 0], [1, 4, 0, 1], [273, 4, 272, 5], [209, 70, 68, 207]], 'adelic_image': '276.12.0.?', 'conductor': 12696, 'lmfdb_label': '12696.p2', 'prime': 0}
  • id: 60387
    {'conductor': 12696, 'elladic_image': '2.3.0.1', 'lmfdb_label': '12696.p2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 557486
    {'lmfdb_iso': '12696.p', 'p': 5, 'prec': 20, 'unit': 677605688267, 'val': 2}
  • id: 557487
    {'lmfdb_iso': '12696.p', 'p': 7, 'prec': 20, 'unit': 83208045817244, 'val': 4}
  • id: 557488
    {'lmfdb_iso': '12696.p', 'p': 11, 'prec': 20, 'unit': 7971649503332458595, 'val': 2}
  • id: 557489
    {'lmfdb_iso': '12696.p', 'p': 13, 'prec': 20, 'unit': 1078843475712997404783, 'val': 2}
  • id: 557490
    {'lmfdb_iso': '12696.p', 'p': 17, 'prec': 20, 'unit': 235706680875237648815583, 'val': 2}
  • id: 557491
    {'lmfdb_iso': '12696.p', 'p': 19, 'prec': 20, 'unit': 1881230445990079331922035, 'val': 2}
  • id: 557492
    {'lmfdb_iso': '12696.p', 'p': 29, 'prec': 20, 'unit': 3514967488332672974991753856, 'val': 2}
  • id: 557493
    {'lmfdb_iso': '12696.p', 'p': 31, 'prec': 20, 'unit': 18072687288210188120565817523, 'val': 2}
  • id: 557494
    {'lmfdb_iso': '12696.p', 'p': 37, 'prec': 20, 'unit': 273401882979432957059559023972, 'val': 2}
  • id: 557495
    {'lmfdb_iso': '12696.p', 'p': 41, 'prec': 20, 'unit': 1430521409046173585321229726709, 'val': 2}
  • id: 557496
    {'lmfdb_iso': '12696.p', 'p': 43, 'prec': 20, 'unit': 10103778443983527673676706398401, 'val': 2}
  • id: 557497
    {'lmfdb_iso': '12696.p', 'p': 47, 'prec': 20, 'unit': 46521753340916081316954633559742, 'val': 2}
  • id: 557498
    {'lmfdb_iso': '12696.p', 'p': 53, 'prec': 20, 'unit': 530259992619889587393460614554799, 'val': 2}
  • id: 557499
    {'lmfdb_iso': '12696.p', 'p': 59, 'prec': 20, 'unit': 3223256140876324302867187761590396, 'val': 2}
  • id: 557500
    {'lmfdb_iso': '12696.p', 'p': 61, 'prec': 20, 'unit': 4970033354342182964642907998933038, 'val': 2}
  • id: 557501
    {'lmfdb_iso': '12696.p', 'p': 67, 'prec': 20, 'unit': 2625407438754758746131315881031342, 'val': 2}
  • id: 557502
    {'lmfdb_iso': '12696.p', 'p': 71, 'prec': 20, 'unit': 136109912964065237542312538298376160, 'val': 2}
  • id: 557503
    {'lmfdb_iso': '12696.p', 'p': 73, 'prec': 20, 'unit': 199753933367853296154163186894240180, 'val': 2}
  • id: 557504
    {'lmfdb_iso': '12696.p', 'p': 79, 'prec': 20, 'unit': 709552391724921657400365184725737316, 'val': 2}
  • id: 557505
    {'lmfdb_iso': '12696.p', 'p': 83, 'prec': 20, 'unit': 987516279009891635842511382376339774, 'val': 2}
  • id: 557506
    {'lmfdb_iso': '12696.p', 'p': 89, 'prec': 20, 'unit': 3534886005966466581694967914237148928, 'val': 2}
  • id: 557507
    {'lmfdb_iso': '12696.p', 'p': 97, 'prec': 20, 'unit': 37998249345469495113907742178903139761, 'val': 2}