Elliptic curve data - 139650.a1

Formats: - HTML - YAML - JSON - 2024-05-01T20:46:42.657048

• 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': '139650hj', 'Clabel': '139650hj1', 'Cnumber': 1, 'abc_quality': 0.9606554697165266, 'absD': 4916582592862500000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 168, 'ainvs': [1, 1, 0, -19058575, -32032722875], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 139650, 'degree': 8294400, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7710034065821606836524991018', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [-16658916431011465, 106983072], 'lmfdb_iso': '139650.a', 'lmfdb_label': '139650.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -15558, 740451], 'min_quad_twist_disc': -35, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '21.8.0-3.a.1.1', '24.8.0-3.a.1.7', '168.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.9818290413624165008128532232', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.72508972376510378136598317459', 'prec': 103}, 'szpiro_ratio': 5.225225640976666, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 1, 0, -1, 1, 0, -6, -1, -5, 0, 0, 1, 3, -1, -1, 0], 'aplist': [-1, -1, 0, 0, -6, -5, 3, -1, -3, 3, -5, -4, 3, -7, -6, -3, -3, 1, 8, 0, 4, -4, 3, -6, 4], 'class_deg': 3, 'class_size': 2, 'conductor': 139650, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '139650.a', 'trace_hash': 213695976948525804}
• 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': '0.0039186549339190028103979934568', 'prec': 110}, 'conductor': 139650, 'gens': [[321359, 169085017, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '7.9818290413624165008128532232', 'prec': 100}], 'lmfdb_label': '139650.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.036128238090648693121020938309', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3069553600415647912912671186595389474', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [1, 0], '5': 'a', '7': 'a', '11': [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': '139650.a1'}
• ec_torsion_growth •

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

  
  
  • id: 6315334
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '139650.a1', 'torsion': [3]}
  • id: 6315335
    {'degree': 3, 'field': [-38, 2, -1, 1], 'lmfdb_label': '139650.a1', 'torsion': [2]}
  • id: 6315337
    {'degree': 6, 'field': [-563, -1837, 1456, -379, 2, -3, 1], 'lmfdb_label': '139650.a1', 'torsion': [3]}
  • id: 6315338
    {'degree': 6, 'field': [44, -92, 65, -10, 10, -2, 1], 'lmfdb_label': '139650.a1', 'torsion': [6]}
  • id: 6315336
    {'degree': 6, 'field': [672, 0, 352, 0, 34, 0, 1], 'lmfdb_label': '139650.a1', 'torsion': [2, 2]}
  • id: 6315339
    {'degree': 12, 'field': [-131658, 714916, -446131, 270132, 140787, 2696, 2083, -800, 71, -120, 9, -4, 1], 'lmfdb_label': '139650.a1', 'torsion': [4]}
  • id: 6315341
    {'degree': 12, 'field': [12352, -3200, 4968, 1432, 426, -208, 645, -34, 9, -20, 15, -2, 1], 'lmfdb_label': '139650.a1', 'torsion': [2, 6]}
  • id: 6315340
    {'degree': 12, 'field': [2088025, 0, -36625, 0, -61650, 0, 3643, 0, -78, 0, 11, 0, 1], 'lmfdb_label': '139650.a1', 'torsion': [3, 3]}
  • id: 6315343
    {'degree': 18, 'field': [238319127, -525314757, 769939390, -332444953, 93227361, -754118, -7693643, 5410179, 661159, -695232, 383557, -104187, 14699, 622, -969, 225, -26, -3, 1], 'lmfdb_label': '139650.a1', 'torsion': [6]}
  • id: 6315342
    {'degree': 18, 'field': [1133280531530091, -88123056877800, 17586687259071, -4827660798681, 1339200690660, -24360789285, 27949935825, 2768491845, 392179725, -41578740, 16750251, -1005165, 325711, -17331, 1590, -461, 15, -6, 1], 'lmfdb_label': '139650.a1', 'torsion': [9]}
• 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: 3449510
    {'conductor': 139650, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '139650.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3449511
    {'conductor': 139650, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '139650.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3449512
    {'conductor': 139650, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '139650.a1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3449513
    {'conductor': 139650, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '139650.a1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3449514
    {'conductor': 139650, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '139650.a1', 'prime': 19, '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: 2571568
    {'adelic_gens': [[165, 166, 158, 161], [4, 3, 9, 7], [163, 6, 162, 7], [1, 6, 0, 1], [1, 0, 6, 1], [78, 97, 115, 54], [127, 6, 45, 19], [95, 162, 117, 149], [3, 4, 8, 11], [85, 6, 87, 19]], 'adelic_image': '168.16.0.?', 'conductor': 139650, 'lmfdb_label': '139650.a1', 'prime': 0}
  • id: 539874
    {'conductor': 139650, 'elladic_image': '3.4.0.1', 'lmfdb_label': '139650.a1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 139650.a does not appear in ec_padic