Elliptic curve data - 136242.bj1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '136242e', 'Clabel': '136242e3', 'Cnumber': 3, 'abc_quality': 1.1259568215438134, 'absD': 55504153729152, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 14616, 'ainvs': [1, -1, 1, -905915, 332105131], 'analytic_rank': 1, 'bad_primes': [2, 3, 29], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 136242, 'degree': 1016064, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9530159938708771954224762669', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 7, 'intrinsic_torsion': 1, 'iso_nlabel': 35, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-189613868625, 128], 'lmfdb_iso': '136242.bj', 'lmfdb_label': '136242.bj1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -1077, 13877], 'min_quad_twist_disc': 29, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '21.64.1.a.4', '24.8.0.a.1', '56.16.0.a.1', '63.192.5.e.1', '87.8.0.?', '168.128.5.?', '504.384.21.?', '609.128.1.?', '696.16.0.?', '1827.384.5.?', '4872.256.5.?', '14616.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6945549537705728150319956801', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 68121], [3, 6, 58], [7, 2, 68121], [29, 422, 162]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27993806545641466386678236774', 'prec': 107}, 'szpiro_ratio': 4.4631083070808435, '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, 0, 1, 0, 0, 2, 1, 0, 0, -3, 0, 2, 2, 0, 1, -3, 0, 1, 0], 'aplist': [1, 0, 0, 2, -3, 2, -3, 1, 6, 0, 4, 4, 9, 1, -6, -12, -3, -8, 5, 12, -11, 4, -12, 6, -5], 'class_deg': 21, 'class_size': 4, 'conductor': 136242, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '136242.bj', 'trace_hash': 1949896678827953441}
• 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': '0.020120179994503060392028332814', 'prec': 107}, 'conductor': 136242, 'gens': [[689, 5542, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6945549537705728150319956801', 'prec': 100}], 'lmfdb_label': '136242.bj1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.52007280052836789244344236874', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.338087166393531074992943776758351922', 'prec': 130}, 'tamagawa_product': 14, 'torsion_generators': [], 'xcoord_integral_points': [689]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': [3, 1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': 'a', '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '136242.bj1'}
• ec_torsion_growth •

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

  
  
  • id: 6166173
    {'degree': 2, 'field': [-7, -1, 1], 'lmfdb_label': '136242.bj1', 'torsion': [3]}
  • id: 6166174
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '136242.bj1', 'torsion': [2]}
  • id: 6166177
    {'degree': 6, 'field': [-421568, 41832, 23436, -602, -315, 0, 1], 'lmfdb_label': '136242.bj1', 'torsion': [7]}
  • id: 6166175
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '136242.bj1', 'torsion': [2, 2]}
  • id: 6166178
    {'degree': 6, 'field': [199, -543, 156, 33, -24, -3, 1], 'lmfdb_label': '136242.bj1', 'torsion': [6]}
  • id: 6166176
    {'degree': 6, 'field': [1536, -576, 264, -9, -15, -3, 1], 'lmfdb_label': '136242.bj1', 'torsion': [3]}
  • id: 6166179
    {'degree': 12, 'field': [-230982704, 112322496, -39349788, 6550996, -1319490, 266688, -108102, 21546, -4221, 256, 12, -6, 1], 'lmfdb_label': '136242.bj1', 'torsion': [4]}
  • id: 6166182
    {'degree': 12, 'field': [1792, 112224, 74508, -199122, 17535, 60942, -11143, -7314, 1464, 372, -69, -6, 1], 'lmfdb_label': '136242.bj1', 'torsion': [21]}
  • id: 6166181
    {'degree': 12, 'field': [12689, 18438, 11541, -51530, 5730, 21198, -2487, -3606, 510, 250, -39, -6, 1], 'lmfdb_label': '136242.bj1', 'torsion': [2, 6]}
  • id: 6166180
    {'degree': 12, 'field': [47524, 0, -63576, 0, 35520, 0, -8581, 0, 975, 0, -51, 0, 1], 'lmfdb_label': '136242.bj1', 'torsion': [3, 3]}
  • id: 6166185
    {'degree': 18, 'field': [-1485264238742528, -213018826013184, -63338426981376, 677153246720, 16549560829968, 1830835225752, -407443924860, -167897887470, -5892813048, 2264171619, 600347157, 28721268, -7693336, 102054, 32478, -1310, -120, -9, 1], 'lmfdb_label': '136242.bj1', 'torsion': [14]}
  • id: 6166183
    {'degree': 18, 'field': [51568516, -52267392, -41935716, 46869894, 22239126, -23360058, -7412577, 7508250, 1359252, -1515735, -117648, 187146, 921, -13644, 630, 540, -45, -9, 1], 'lmfdb_label': '136242.bj1', 'torsion': [9]}
  • id: 6166184
    {'degree': 18, 'field': [1610612736, -1811939328, 1509949440, -736100352, 233570304, -41287680, 279552, -5390208, 3971088, -1026054, -22158, 119880, -30924, 1044, 456, -9, 21, -9, 1], 'lmfdb_label': '136242.bj1', 'torsion': [6]}
• 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: 3360623
    {'conductor': 136242, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '136242.bj1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 3360624
    {'conductor': 136242, 'conductor_valuation': 4, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '136242.bj1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3360625
    {'conductor': 136242, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '136242.bj1', 'prime': 29, '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: 2549752
    {'adelic_gens': [[11369, 12992, 1624, 12993], [1, 0, 4032, 1], [10585, 4032, 10584, 10585], [2089, 1914, 0, 1], [13399, 6090, 4263, 1219], [12181, 6090, 12789, 6091], [1, 9744, 0, 1], [1, 0, 2436, 1], [8527, 3306, 2436, 13399], [3046, 6873, 12789, 9745], [1, 7482, 6090, 7309], [1, 0, 8526, 1], [10583, 0, 0, 14615], [1, 0, 9744, 1], [465, 1450, 6496, 12297], [1, 6264, 0, 1], [4873, 9744, 4872, 9745]], 'adelic_image': '14616.768.21.?', 'conductor': 136242, 'lmfdb_label': '136242.bj1', 'prime': 0}
  • id: 527513
    {'conductor': 136242, 'elladic_image': '8.2.0.1', 'lmfdb_label': '136242.bj1', 'modell_image': '2G', 'prime': 2}
  • id: 527514
    {'conductor': 136242, 'elladic_image': '3.4.0.1', 'lmfdb_label': '136242.bj1', 'modell_image': '3B', 'prime': 3}
  • id: 527515
    {'conductor': 136242, 'elladic_image': '7.8.0.1', 'lmfdb_label': '136242.bj1', 'modell_image': '7B', 'prime': 7}
• lmfdb_iso 136242.bj does not appear in ec_padic