Elliptic curve data - 397488.jd2

Formats: - HTML - YAML - JSON - 2025-11-07T08:50:10.960731

• 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': '397488jd', 'Clabel': '397488jd3', 'Cnumber': 3, 'abc_quality': 1.065057693637064, 'absD': 3330423121420222464, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 5460, 'ainvs': [0, 1, 0, -3478232, 2497196820], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 397488, 'degree': 10368000, 'elladic_images': ['2.3.0.1', '5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4895345181803986498898437704', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 5, 'iso_nlabel': 237, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [-4395631034341, 3145728], 'lmfdb_iso': '397488.jd', 'lmfdb_label': '397488.jd2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -4437, 113440], 'min_quad_twist_disc': 28, 'modell_images': ['2B', '5B'], 'modm_images': ['2.3.0.a.1', '5.6.0.a.1', '10.18.0.a.1', '12.6.0.f.1', '20.36.0.b.2', '30.36.0.c.1', '52.6.0.c.1', '60.72.1.dt.1', '65.12.0.a.1', '78.6.0.?', '130.36.0.?', '156.12.0.?', '260.72.1.?', '390.72.1.?', '780.144.5.?', '1820.144.1.?', '5460.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '13.042406843247347307880899864', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1911], [3, 4, 132496], [7, 26, 8112], [13, 50, 2352]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18219492372741250390656341683', 'prec': 103}, 'szpiro_ratio': 4.405591838145198, '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, 0, 0, 0, 0, 2, 0, -2, 0, 6, 0], 'aplist': [0, 1, 2, 0, 0, 0, -2, 6, 4, -10, -10, 8, 10, 4, -12, -6, 4, -2, -2, 0, 4, 0, 4, 6, -12], 'class_deg': 10, 'class_size': 4, 'conductor': 397488, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '397488.jd', 'trace_hash': 2000324589606644137}
• 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': '0.0068804650395674740611559183293', 'prec': 110}, 'conductor': 397488, 'gens': [[32170693, 7742247695, 174]], 'heights': [{'__RealLiteral__': 0, 'data': '13.042406843247347307880899864', 'prec': 100}], 'lmfdb_label': '397488.jd2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.24896397869259492249871112771', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.988357997689547122052702962202055755', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-2154, 0, 1]], 'xcoord_integral_points': [-2154]}
• lmfdb_label 397488.jd2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16401848
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '397488.jd2', 'torsion': [2, 2]}
  • id: 16401849
    {'degree': 4, 'field': [-1911, 0, 91, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [4]}
  • id: 16401850
    {'degree': 4, 'field': [12740, 0, -455, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [10]}
  • id: 16401853
    {'degree': 8, 'field': [-1217307, 0, 463736, 0, -3822, 0, 0, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [6]}
  • id: 16401852
    {'degree': 8, 'field': [8100, 0, 1917, 0, 462, 0, -6, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [2, 4]}
  • id: 16401851
    {'degree': 8, 'field': [6492304, 0, 231868, 0, 5733, 0, 91, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [2, 4]}
  • id: 16401854
    {'degree': 8, 'field': [2596921600, 0, 27534325, 0, 136955, 0, 455, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [2, 10]}
  • id: 16401855
    {'degree': 16, 'field': [357634148, 474442144, 291621480, 110656912, 13242356, -7197768, -3615884, -915640, -58815, 58620, 13116, 2076, -159, -192, 6, -4, 1], 'lmfdb_label': '397488.jd2', 'torsion': [8]}
  • id: 16401857
    {'degree': 16, 'field': [2634375701776, 0, -658593925444, 0, 2326273677, 0, -1957023887, 0, 36519210, 0, 637637, 0, -8918, 0, -91, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [20]}
  • id: 16401856
    {'degree': 16, 'field': [28299119773206, -5286480569280, -856131713498, 344360875070, 10460206636, -967785130, -865768175, -54229552, 46494831, -4805268, 773256, -70330, -842, 14, 121, -4, 1], 'lmfdb_label': '397488.jd2', 'torsion': [2, 6]}
  • id: 16401858
    {'degree': 20, 'field': [106812886812349, -51511824952770, 75040794659285, 10375189886880, 22227508464525, 554760868458, 3528311137260, 7559476470, 321800512215, -45214260, 16948566936, -1739010, 505182405, 2730, 8695050, -66, 85995, 0, 455, 0, 1], 'lmfdb_label': '397488.jd2', 'torsion': [10]}
• 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: 9832861
    {'conductor': 397488, 'conductor_valuation': 4, 'discriminant_valuation': 32, 'j_denominator_valuation': 20, 'kodaira_symbol': -28, 'lmfdb_label': '397488.jd2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9832862
    {'conductor': 397488, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '397488.jd2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 9832863
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '397488.jd2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9832864
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '397488.jd2', 'prime': 13, '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: 4129915
    {'adelic_gens': [[3119, 0, 0, 5459], [11, 16, 5220, 5111], [3277, 3920, 0, 1], [2346, 3913, 175, 596], [1, 10, 10, 101], [5441, 20, 5440, 21], [2729, 1554, 0, 5459], [1, 0, 20, 1], [4502, 1575, 385, 4418], [1, 20, 0, 1]], 'adelic_image': '5460.288.5.?', 'conductor': 397488, 'lmfdb_label': '397488.jd2', 'prime': 0}
  • id: 1352486
    {'conductor': 397488, 'elladic_image': '2.3.0.1', 'lmfdb_label': '397488.jd2', 'modell_image': '2B', 'prime': 2}
  • id: 1352487
    {'conductor': 397488, 'elladic_image': '5.6.0.1', 'lmfdb_label': '397488.jd2', 'modell_image': '5B', 'prime': 5}
• lmfdb_iso 397488.jd does not appear in ec_padic