Elliptic curve data - 263568.cb2

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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': '263568cb', 'Clabel': '263568cb4', 'Cnumber': 4, 'abc_quality': 1.0101536552434738, 'absD': 83723540801368891392, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 7752, 'ainvs': [0, 1, 0, -1932928, 1123502132], 'analytic_rank': 1, 'bad_primes': [2, 3, 17, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 263568, 'degree': 7962624, 'elladic_images': ['8.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5618294888181287553759430604', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 53, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-8078253774625, 846825858], 'lmfdb_iso': '263568.cb', 'lmfdb_label': '263568.cb2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -418, -3610], 'min_quad_twist_disc': -68, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.a.1', '24.24.0.p.1', '204.24.0.?', '228.24.0.?', '408.48.0.?', '456.48.1.?', '3876.48.0.?', '7752.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.5135132744373179258124044593', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 4624], [17, 146, 912], [19, 20, 13872]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.45207563623007540583394363000', 'prec': 103}, 'szpiro_ratio': 4.422643036016018, '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, 0, 0, -4, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, 0], 'aplist': [0, 1, 0, -4, 0, -4, 0, -1, -6, -6, 2, 4, -6, 4, -6, 6, 12, -14, -8, 0, -14, -10, 12, -6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 263568, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '263568.cb', 'trace_hash': 892050349999030549}
• 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': '0.0059541967159807712179370024368', 'prec': 110}, 'conductor': 263568, 'gens': [[436, 19074, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5135132744373179258124044593', 'prec': 100}], 'lmfdb_label': '263568.cb2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.18711303864038268537779744128', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2593931606662989077226036718166644919', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-1621, 0, 1]], 'xcoord_integral_points': [-1621, 436]}
• lmfdb_label 263568.cb2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11294334
    {'degree': 2, 'field': [-51, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [6]}
  • id: 11294333
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [2, 2]}
  • id: 11294335
    {'degree': 4, 'field': [-1148, 335, 57, -1, 1], 'lmfdb_label': '263568.cb2', 'torsion': [4]}
  • id: 11294336
    {'degree': 4, 'field': [625, 0, 52, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [2, 6]}
  • id: 11294337
    {'degree': 6, 'field': [5057, 1224, 867, -24, 51, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [6]}
  • id: 11294338
    {'degree': 8, 'field': [5329, 0, -524, 0, -88, 0, 4, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [2, 4]}
  • id: 11294340
    {'degree': 8, 'field': [22456, -40240, 27742, -8392, 420, 388, -77, -2, 1], 'lmfdb_label': '263568.cb2', 'torsion': [12]}
  • id: 11294339
    {'degree': 8, 'field': [146706, -154140, 69679, -14594, 929, 280, -43, -2, 1], 'lmfdb_label': '263568.cb2', 'torsion': [2, 4]}
  • id: 11294342
    {'degree': 12, 'field': [356409, 0, -356508, 0, 114075, 0, -13108, 0, 975, 0, -48, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [2, 6]}
  • id: 11294341
    {'degree': 12, 'field': [24019801, 0, 8623182, 0, 1246695, 0, 98284, 0, 4335, 0, 102, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [3, 6]}
  • id: 11294344
    {'degree': 16, 'field': [11100081, 9675312, -8678408, -2719368, 3214640, -2336960, 952136, -124544, 1017, 20512, -4516, 184, 30, -56, 28, -8, 1], 'lmfdb_label': '263568.cb2', 'torsion': [2, 12]}
  • id: 11294345
    {'degree': 16, 'field': [1028749252, 302879616, -246185976, -187666848, 30267688, 26833824, -5061516, -1656576, 1293837, 31536, -120864, 1440, 5146, -48, -108, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [2, 12]}
  • id: 11294343
    {'degree': 16, 'field': [30393040896, 0, -33494370048, 0, -6921203712, 0, -238780032, 0, 12618688, 0, 315188, 0, -5568, 0, 29, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [8]}
  • id: 11294346
    {'degree': 18, 'field': [-57862030915991, -60600824007582, 69110896811178, -7698125940140, -1159814416059, -265087407786, -93142102738, 3193265082, -3036213252, -129051530, 41015091, -2295858, -1357513, 18144, 23253, -86, -165, 0, 1], 'lmfdb_label': '263568.cb2', 'torsion': [18]}
• 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: 6535557
    {'conductor': 263568, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '263568.cb2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6535558
    {'conductor': 263568, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '263568.cb2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6535559
    {'conductor': 263568, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '263568.cb2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6535560
    {'conductor': 263568, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '263568.cb2', '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: 3333262
    {'adelic_gens': [[11, 2, 7702, 7743], [2585, 1836, 7378, 3265], [1378, 459, 7497, 6376], [5471, 0, 0, 7751], [1, 0, 12, 1], [1, 6, 6, 37], [1, 12, 0, 1], [6937, 1836, 3774, 3265], [7741, 12, 7740, 13], [1614, 6239, 5491, 4198]], 'adelic_image': '7752.96.1.?', 'conductor': 263568, 'lmfdb_label': '263568.cb2', 'prime': 0}
  • id: 945615
    {'conductor': 263568, 'elladic_image': '8.6.0.5', 'lmfdb_label': '263568.cb2', 'modell_image': '2B', 'prime': 2}
  • id: 945616
    {'conductor': 263568, 'elladic_image': '3.4.0.1', 'lmfdb_label': '263568.cb2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 263568.cb does not appear in ec_padic