Elliptic curve data - 258720.bj3

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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': '258720bj', 'Clabel': '258720bj1', 'Cnumber': 1, 'abc_quality': 1.0738612260109766, 'absD': 98447019360782400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, -1, 0, -270006, 51939000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 258720, 'degree': 2949120, 'elladic_images': ['8.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0228645661032380890482447865', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 35, 'isogeny_degrees': [1, 2], 'jinv': [289119478354624, 13074779025], 'lmfdb_iso': '258720.bj', 'lmfdb_label': '258720.bj3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -5510, 153000], 'min_quad_twist_disc': 28, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.1', '28.12.0-2.a.1.1', '56.24.0-56.a.1.2', '60.12.0.a.1', '120.24.0.?', '420.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 86240], [5, 6, 51744], [7, 32, 5280], [11, 12, 23520]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.70333590129560878178695235405', 'prec': 103}, 'szpiro_ratio': 3.9420867744983537, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 6, 0, 4, 0], 'aplist': [0, -1, -1, 0, 1, 2, 6, 4, 0, 2, 4, 10, 2, 12, 4, -2, 4, -14, 12, -16, 2, -8, -4, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 258720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '258720.bj', 'trace_hash': 768633617672411730}
• 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': '0.017496942419448023548490074383', 'prec': 107}, 'conductor': 258720, 'gens': [], 'heights': [], 'lmfdb_label': '258720.bj3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.33323639269955566834364514251', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6658911415964453467491611400766105144', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[250, 0, 1], [348, 0, 1]], 'xcoord_integral_points': [-597, 250, 348]}
• lmfdb_label 258720.bj3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11093502
    {'degree': 4, 'field': [9, 0, 8, 0, 1], 'lmfdb_label': '258720.bj3', 'torsion': [2, 4]}
  • id: 11093503
    {'degree': 4, 'field': [274, 26, -25, -2, 1], 'lmfdb_label': '258720.bj3', 'torsion': [2, 4]}
  • id: 11093501
    {'degree': 4, 'field': [574, 56, -55, -2, 1], 'lmfdb_label': '258720.bj3', 'torsion': [2, 4]}
  • id: 11093504
    {'degree': 8, 'field': [-42483, 0, -224, 0, -714, 0, 0, 0, 1], 'lmfdb_label': '258720.bj3', 'torsion': [2, 6]}
  • id: 11093505
    {'degree': 16, 'field': [67104, 169920, 51360, -60288, 76402, 48084, -37930, -16152, 13881, 840, -2630, 72, 360, -12, -28, 0, 1], 'lmfdb_label': '258720.bj3', 'torsion': [4, 4]}
  • id: 11093506
    {'degree': 16, 'field': [1552516, 0, 2546432, 0, 745360, 0, -596848, 0, 590284, 0, -190432, 0, 14920, 0, -232, 0, 1], 'lmfdb_label': '258720.bj3', 'torsion': [2, 8]}
  • id: 11093507
    {'degree': 16, 'field': [1133332225, 0, 1276752920, 0, 1201362316, 0, 373411752, 0, 46846758, 0, -447384, 0, 14476, 0, -40, 0, 1], 'lmfdb_label': '258720.bj3', 'torsion': [2, 8]}
  • id: 11093508
    {'degree': 16, 'field': [85583162116, 0, -114653108392, 0, 111675959200, 0, 3658576508, 0, 119009269, 0, 3055232, 0, 45070, 0, 332, 0, 1], 'lmfdb_label': '258720.bj3', 'torsion': [2, 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: 6411353
    {'conductor': 258720, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '258720.bj3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6411354
    {'conductor': 258720, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '258720.bj3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6411355
    {'conductor': 258720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '258720.bj3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6411356
    {'conductor': 258720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '258720.bj3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6411357
    {'conductor': 258720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '258720.bj3', 'prime': 11, 'reduction_type': 1, '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: 3303107
    {'adelic_gens': [[837, 4, 836, 5], [599, 836, 358, 831], [627, 838, 8, 5], [1, 4, 0, 1], [421, 4, 2, 9], [281, 2, 0, 1], [1, 0, 4, 1], [337, 2, 0, 1]], 'adelic_image': '840.48.0.?', 'conductor': 258720, 'lmfdb_label': '258720.bj3', 'prime': 0}
  • id: 928978
    {'conductor': 258720, 'elladic_image': '8.12.0.1', 'lmfdb_label': '258720.bj3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 258720.bj does not appear in ec_padic