Elliptic curve data - 267696.bj6

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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': '267696bj', 'Clabel': '267696bj5', 'Cnumber': 5, 'abc_quality': 0.9847533288977478, 'absD': 4267770268952353792831488, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6864, 'ainvs': [0, 0, 0, 32634069, 68776825754], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 267696, 'degree': 44040192, 'elladic_images': ['16.24.0.14'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4125972328116559992199721366', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 35, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [266679605718863, 296110251723], 'lmfdb_iso': '267696.bj', 'lmfdb_label': '267696.bj6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1341, 18228], 'min_quad_twist_disc': 156, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '8.12.0.n.1', '12.12.0.g.1', '16.24.0-8.n.1.6', '24.24.0.bh.1', '48.48.0-24.bh.1.3', '52.12.0-4.c.1.2', '88.24.0.?', '104.24.0.?', '156.24.0.?', '176.48.0.?', '208.48.0.?', '264.48.0.?', '312.48.0.?', '528.96.0.?', '624.96.0.?', '1144.48.0.?', '2288.96.0.?', '3432.96.0.?', '6864.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.88766922918688747607837367590', 'prec': 103}, 'szpiro_ratio': 5.082269242309446, '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, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, -2, 0, 1, 0, 6, -4, -8, 10, 0, -6, 10, -4, -8, 10, 12, 14, -12, 0, 6, -8, -12, 2, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 267696, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '267696.bj', 'trace_hash': 1590688862603802376}
• 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': '0.0010860647186742638724767378515', 'prec': 110}, 'conductor': 267696, 'gens': [], 'heights': [], 'lmfdb_label': '267696.bj6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.051724118031513499530197840270', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6551717770084319849663308886449439534', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-1898, 0, 1]], 'xcoord_integral_points': [-1898]}
• lmfdb_label 267696.bj6 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11449287
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '267696.bj6', 'torsion': [4]}
  • id: 11449286
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '267696.bj6', 'torsion': [2, 2]}
  • id: 11449288
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '267696.bj6', 'torsion': [4]}
  • id: 11449289
    {'degree': 4, 'field': [9, 3, 4, -1, 1], 'lmfdb_label': '267696.bj6', 'torsion': [2, 4]}
  • id: 11449290
    {'degree': 4, 'field': [166, -64, 65, -2, 1], 'lmfdb_label': '267696.bj6', 'torsion': [8]}
  • id: 11449291
    {'degree': 4, 'field': [5710, 112, -111, -2, 1], 'lmfdb_label': '267696.bj6', 'torsion': [8]}
  • id: 11449295
    {'degree': 8, 'field': [-85683, 0, -109668, 0, 5850, 0, -143, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [6]}
  • id: 11449293
    {'degree': 8, 'field': [-3, 228, -180, -84, 13, 32, -6, -4, 1], 'lmfdb_label': '267696.bj6', 'torsion': [8]}
  • id: 11449292
    {'degree': 8, 'field': [10609, 0, 12766, 0, 3807, 0, -26, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [2, 4]}
  • id: 11449294
    {'degree': 8, 'field': [177775, -32110, 38581, -3514, 3174, -134, 97, -2, 1], 'lmfdb_label': '267696.bj6', 'torsion': [2, 8]}
  • id: 11449302
    {'degree': 16, 'field': [-4563, 51714, -248430, 639366, -889473, 559572, 14730, -161520, 27538, 7366, -602, -80, -290, 112, 4, -8, 1], 'lmfdb_label': '267696.bj6', 'torsion': [12]}
  • id: 11449297
    {'degree': 16, 'field': [22932, 58968, 42156, 24840, 47982, 25704, 12018, 10008, 6697, 492, 2158, -96, 336, -12, 28, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [2, 8]}
  • id: 11449298
    {'degree': 16, 'field': [10673289, 0, 0, 0, 548856, 0, 0, 0, -6069, 0, 0, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [16]}
  • id: 11449296
    {'degree': 16, 'field': [53904964, 60086928, 52721832, 33881760, 19288318, 2397252, -425952, -154110, -52545, -198, -8280, -1254, 265, 0, 12, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [4, 4]}
  • id: 11449303
    {'degree': 16, 'field': [3252078729, 0, 591138003, 0, -17505089, 0, -8727258, 0, 396291, 0, 18470, 0, -966, 0, 0, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [12]}
  • id: 11449301
    {'degree': 16, 'field': [7341576489, 0, -650505336, 0, -29244098, 0, -7698288, 0, 1113879, 0, -15184, 0, 1014, 0, 0, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [2, 6]}
  • id: 11449299
    {'degree': 16, 'field': [522867825216, 0, 91508826816, 0, 8462636424, 0, -747170160, 0, 15034492, 0, -309760, 0, 8294, 0, -44, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [16]}
  • id: 11449300
    {'degree': 16, 'field': [30532100643396, 0, 4092831580464, 0, 313005088836, 0, 16433558856, 0, 543974013, 0, 10358568, 0, 106524, 0, 528, 0, 1], 'lmfdb_label': '267696.bj6', 'torsion': [16]}
• 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: 6635212
    {'conductor': 267696, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '267696.bj6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6635213
    {'conductor': 267696, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '267696.bj6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6635214
    {'conductor': 267696, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '267696.bj6', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6635215
    {'conductor': 267696, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '267696.bj6', 'prime': 13, '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: 3357489
    {'adelic_gens': [[6849, 16, 6848, 17], [1, 16, 0, 1], [4223, 6848, 6328, 6735], [15, 2, 6766, 6851], [1885, 16, 368, 6549], [5, 4, 6860, 6861], [2272, 6859, 45, 14], [1, 0, 16, 1], [13, 16, 1460, 1401], [5993, 6848, 4026, 4823]], 'adelic_image': '6864.192.1.?', 'conductor': 267696, 'lmfdb_label': '267696.bj6', 'prime': 0}
  • id: 957969
    {'conductor': 267696, 'elladic_image': '16.24.0.14', 'lmfdb_label': '267696.bj6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 267696.bj does not appear in ec_padic