Elliptic curve data - 413712.bk2

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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': '413712bk', 'Clabel': '413712bk2', 'Cnumber': 2, 'abc_quality': 0.9326517624097936, 'absD': 9269099110659922350336, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1768, 'ainvs': [0, 0, 0, 4008849, 3451333210], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 413712, 'degree': 18579456, 'elladic_images': ['8.12.0.38'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9009801602188904083074754373', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 36, 'isogeny_degrees': [1, 2], 'jinv': [7909612346288, 10289870721], 'lmfdb_iso': '413712.bk', 'lmfdb_label': '413712.bk2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 2636, 57304], 'min_quad_twist_disc': 156, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '8.12.0-4.a.1.2', '52.12.0.d.1', '104.24.0.?', '1768.48.0.?'], '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, 'serre_invariants': [[2, 2, 1521], [3, 2, 45968], [13, 98, 2448], [17, 18, 24336]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.60710121678077032163828768375', 'prec': 103}, 'szpiro_ratio': 4.441933809016545, '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, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0], 'aplist': [0, 0, -2, 2, 2, 0, 1, 2, -4, -10, -2, -2, -2, -12, -2, 10, 6, 6, 2, 6, -2, -8, -6, -2, -18], 'class_deg': 2, 'class_size': 2, 'conductor': 413712, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '413712.bk', 'trace_hash': 2204000694742606889}
• 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': '0.0030216255813613960641357344903', 'prec': 110}, 'conductor': 413712, 'gens': [], 'heights': [], 'lmfdb_label': '413712.bk2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.087256926993167357278232420441', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.69805541594533885822585936353045584555', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-754, 0, 1]], 'xcoord_integral_points': [-754]}
• lmfdb_label 413712.bk2 does not appear in ec_iwasawa
• lmfdb_label 413712.bk2 does not appear in ec_torsion_growth
• 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: 10222150
    {'conductor': 413712, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '413712.bk2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 10222151
    {'conductor': 413712, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '413712.bk2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 10222152
    {'conductor': 413712, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '413712.bk2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 10222153
    {'conductor': 413712, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '413712.bk2', 'prime': 17, '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: 4223179
    {'adelic_gens': [[3, 8, 10, 27], [1, 0, 8, 1], [1, 8, 0, 1], [1761, 8, 1760, 9], [105, 4, 0, 1], [1767, 1760, 1766, 1751], [885, 8, 2, 17], [5, 8, 48, 77], [1325, 1764, 663, 1767], [271, 1762, 0, 1767]], 'adelic_image': '1768.48.0.?', 'conductor': 413712, 'lmfdb_label': '413712.bk2', 'prime': 0}
  • id: 1398818
    {'conductor': 413712, 'elladic_image': '8.12.0.38', 'lmfdb_label': '413712.bk2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 413712.bk does not appear in ec_padic