Elliptic curve data - 281775.bz5

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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': '281775bz', 'Clabel': '281775bz2', 'Cnumber': 2, 'abc_quality': 1.0179337433150557, 'absD': 10454669431766015625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 53040, 'ainvs': [1, 0, 1, -831026, 246553823], 'analytic_rank': 0, 'bad_primes': [3, 5, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 281775, 'degree': 5898240, 'elladic_images': ['8.24.0.23'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3710219251998741502734956669', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 51, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [168288035761, 27720225], 'lmfdb_iso': '281775.bz', 'lmfdb_label': '281775.bz5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -115, 392], 'min_quad_twist_disc': 85, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.i.1', '40.48.0.bc.2', '48.48.0.d.1', '104.48.0.?', '136.48.0.?', '208.96.2.?', '240.96.1.?', '260.24.0.?', '340.24.0.?', '520.96.1.?', '624.192.5.?', '680.96.0.?', '816.96.0.?', '884.24.0.?', '1040.192.5.?', '1768.96.0.?', '3120.384.13.?', '3536.192.2.?', '4080.192.1.?', '4420.48.0.?', '8840.192.1.?', '10608.384.5.?', '17680.384.5.?', '53040.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 7225], [3, 4, 93925], [5, 18, 11271], [13, 14, 21675], [17, 146, 975]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.14969629695471592284834869135', 'prec': 103}, 'szpiro_ratio': 4.184032094066166, '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, 1, 1, -1, 0, 1, 0, -3, 1, 0, -4, -1, -1, 0, 0, -1, 0, 1, -4, 0], 'aplist': [1, 1, 0, 0, -4, -1, 0, -4, 8, 2, 8, 6, 6, 4, 8, -6, -12, 2, 4, 0, -6, -16, 4, 10, 18], 'class_deg': 16, 'class_size': 8, 'conductor': 281775, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '281775.bz', 'trace_hash': 107483724118849064}
• 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': '0.0087208039396255778268584027385', 'prec': 110}, 'conductor': 281775, 'gens': [], 'heights': [], 'lmfdb_label': '281775.bz5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21816959394928477024157463325', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4907135031885563238651941319477448654', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[347, -174, 1], [687, -344, 1]], 'xcoord_integral_points': [347, 687]}
• lmfdb_label 281775.bz5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11994280
    {'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 4]}
  • id: 11994281
    {'degree': 4, 'field': [25, 0, 75, 0, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 4]}
  • id: 11994283
    {'degree': 4, 'field': [324, 0, -49, 0, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 8]}
  • id: 11994282
    {'degree': 4, 'field': [1156, 0, 153, 0, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 4]}
  • id: 11994286
    {'degree': 8, 'field': [-371619, -959751, 957042, 5417, -2705, -7, 7, -4, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 6]}
  • id: 11994285
    {'degree': 8, 'field': [909, 390, -304, -162, 57, 26, -4, -4, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 8]}
  • id: 11994284
    {'degree': 8, 'field': [1225, 0, 10005, 0, 1816, 0, 93, 0, 1], 'lmfdb_label': '281775.bz5', 'torsion': [4, 4]}
  • id: 11994289
    {'degree': 16, 'field': [20736, 0, 212544, 0, 444928, 0, 348516, 0, 124673, 0, 21852, 0, 1862, 0, 72, 0, 1], 'lmfdb_label': '281775.bz5', 'torsion': [4, 8]}
  • id: 11994287
    {'degree': 16, 'field': [2772225, 0, -10431900, 0, 15911830, 0, -3381040, 0, 481291, 0, -40976, 0, 2326, 0, -76, 0, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 8]}
  • id: 11994288
    {'degree': 16, 'field': [636855696, 0, -406455552, 0, 30834688, 0, 9337536, 0, 1187240, 0, 27456, 0, 1088, 0, 48, 0, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 8]}
  • id: 11994291
    {'degree': 16, 'field': [4580858421, 5750706384, -3652574349, -3863061174, 1124733871, 895854718, -181356562, -94103502, 15684787, 4969556, -739688, -134086, 18556, 1722, -226, -8, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 16]}
  • id: 11994292
    {'degree': 16, 'field': [35982384975, 14873207850, -12412361700, -4690727130, 1781615295, 638756180, -151561354, -49539568, 8655620, 2353250, -340102, -68192, 8878, 1120, -140, -8, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 12]}
  • id: 11994290
    {'degree': 16, 'field': [54760212081, 7651392273, 9859173876, 204873705, 905715900, -27947364, 65447821, -2591060, 3665676, -92353, 138254, -1674, 4037, -64, 84, -2, 1], 'lmfdb_label': '281775.bz5', 'torsion': [2, 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: 6980061
    {'conductor': 281775, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '281775.bz5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 6980062
    {'conductor': 281775, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '281775.bz5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 6980063
    {'conductor': 281775, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '281775.bz5', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6980064
    {'conductor': 281775, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '281775.bz5', 'prime': 17, '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: 3441585
    {'adelic_gens': [[53025, 16, 53024, 17], [1, 16, 0, 1], [31213, 3128, 49130, 9317], [3129, 3128, 26996, 37401], [28085, 6256, 28084, 17953], [1, 0, 16, 1], [18087, 46784, 11662, 24615], [18735, 3128, 16048, 20129], [1, 16, 4, 65], [40559, 0, 0, 53039]], 'adelic_image': '53040.768.13.?', 'conductor': 281775, 'lmfdb_label': '281775.bz5', 'prime': 0}
  • id: 1001906
    {'conductor': 281775, 'elladic_image': '8.24.0.23', 'lmfdb_label': '281775.bz5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 281775.bz does not appear in ec_padic