Elliptic curve data - 139656.l4

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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': '139656bf', 'Clabel': '139656bf1', 'Cnumber': 1, 'abc_quality': 0.9498719792755755, 'absD': 590576343861780144, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2024, 'ainvs': [0, -1, 0, 63833, 36427900], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 139656, 'degree': 1351680, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0903284445296550637331101337', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 4], 'jinv': [12144109568, 249338331], 'lmfdb_iso': '139656.l', 'lmfdb_label': '139656.l4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 121, -3036], 'min_quad_twist_disc': -23, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '22.6.0.a.1', '44.12.0.g.1', '88.24.0.?', '92.12.0.?', '184.24.0.?', '1012.24.0.?', '2024.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.4084978497872840524320166106', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29153227637843178185732301064', 'prec': 103}, 'szpiro_ratio': 4.08088624607432, '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, -2, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, -1, 2, 0, 1, -2, 2, 4, 0, 6, 0, -6, -6, -4, -8, 10, -4, 14, -4, 8, 2, 0, -4, -10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 139656, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '139656.l', 'trace_hash': 1922819729288946018}
• 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': '0.015288461444436313588583321646', 'prec': 107}, 'conductor': 139656, 'gens': [[-89021, 130141935, 29]], 'heights': [{'__RealLiteral__': 0, 'data': '8.4084978497872840524320166106', 'prec': 100}], 'lmfdb_label': '139656.l4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21689825719425384896152432390', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2951541169619712121691285299248655890', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-268, 0, 1]], 'xcoord_integral_points': [-268]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': 'a', '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '139656.l4'}
• ec_torsion_growth •

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

  
  
  • id: 6316490
    {'degree': 2, 'field': [-63, -1, 1], 'lmfdb_label': '139656.l4', 'torsion': [4]}
  • id: 6316489
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '139656.l4', 'torsion': [2, 2]}
  • id: 6316491
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '139656.l4', 'torsion': [4]}
  • id: 6316493
    {'degree': 4, 'field': [-539, 0, 11, 0, 1], 'lmfdb_label': '139656.l4', 'torsion': [8]}
  • id: 6316492
    {'degree': 4, 'field': [9, 0, 17, 0, 1], 'lmfdb_label': '139656.l4', 'torsion': [2, 4]}
  • id: 6316495
    {'degree': 8, 'field': [49, -112, 128, -124, 50, 8, 8, -4, 1], 'lmfdb_label': '139656.l4', 'torsion': [8]}
  • id: 6316496
    {'degree': 8, 'field': [17424, 0, -6776, 0, 957, 0, -33, 0, 1], 'lmfdb_label': '139656.l4', 'torsion': [2, 8]}
  • id: 6316494
    {'degree': 8, 'field': [131769, 7986, 23474, 3894, 1035, 62, -16, -4, 1], 'lmfdb_label': '139656.l4', 'torsion': [2, 4]}
  • id: 6316497
    {'degree': 8, 'field': [1245627, -1435992, 430270, 101040, -2076, -1504, -174, 0, 1], 'lmfdb_label': '139656.l4', 'torsion': [6]}
  • id: 6316499
    {'degree': 16, 'field': [178929, -43992, 5408, 76628, -33410, -15740, 21288, -12684, 1183, 2308, -1368, 380, 58, -84, 32, -8, 1], 'lmfdb_label': '139656.l4', 'torsion': [2, 8]}
  • id: 6316498
    {'degree': 16, 'field': [480249, 0, 1681416, 0, 1185250, 0, 388872, 0, 83315, 0, 11400, 0, 974, 0, 48, 0, 1], 'lmfdb_label': '139656.l4', 'torsion': [4, 4]}
  • id: 6316503
    {'degree': 16, 'field': [1722146196, -229981296, 248695004, -41848000, 32048444, -13579808, 4989400, -555056, 339201, -137856, 32508, -3608, 1390, -392, 76, -8, 1], 'lmfdb_label': '139656.l4', 'torsion': [12]}
  • id: 6316501
    {'degree': 16, 'field': [704798867529, 0, 111837895968, 0, 46718895268, 0, 422827584, 0, 8395230, 0, -133216, 0, -6348, 0, 0, 0, 1], 'lmfdb_label': '139656.l4', 'torsion': [2, 6]}
  • id: 6316500
    {'degree': 16, 'field': [5683756387969, 0, 364104862132, 0, 24236612906, 0, 233288000, 0, -33948541, 0, 323488, 0, 9482, 0, -220, 0, 1], 'lmfdb_label': '139656.l4', 'torsion': [16]}
  • id: 6316502
    {'degree': 16, 'field': [34336353636729, 0, 456393899640, 0, 80268642622, 0, 6350280720, 0, 26074839, 0, -2262400, 0, -25914, 0, 0, 0, 1], 'lmfdb_label': '139656.l4', '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: 3450215
    {'conductor': 139656, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '139656.l4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3450216
    {'conductor': 139656, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '139656.l4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3450217
    {'conductor': 139656, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '139656.l4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3450218
    {'conductor': 139656, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '139656.l4', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2572006
    {'adelic_gens': [[87, 2016, 348, 1991], [1108, 1, 1311, 6], [257, 256, 1278, 263], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 2018, 2019], [2017, 8, 2016, 9], [763, 762, 266, 1275]], 'adelic_image': '2024.48.0.?', 'conductor': 139656, 'lmfdb_label': '139656.l4', 'prime': 0}
  • id: 540168
    {'conductor': 139656, 'elladic_image': '8.12.0.6', 'lmfdb_label': '139656.l4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 139656.l does not appear in ec_padic