Elliptic curve data - 413712.be4

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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': '413712be', 'Clabel': '413712be1', 'Cnumber': 1, 'abc_quality': 0.85449985979477, 'absD': 2446251381010464768, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5304, 'ainvs': [0, 0, 0, 206349, 66037426], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 413712, 'degree': 4128768, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2122292702331656805277062265', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 30, 'isogeny_degrees': [1, 2, 4], 'jinv': [67419143, 169728], 'lmfdb_iso': '413712.be', 'lmfdb_label': '413712.be4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 9, 21], 'min_quad_twist_disc': 156, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.1', '104.12.0.?', '136.12.0.?', '312.24.0.?', '408.24.0.?', '884.12.0.?', '1326.6.0.?', '1768.24.0.?', '2652.24.0.?', '5304.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 3, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.1478699466039037183339682856', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.31269873339160284261389223420', 'prec': 107}, 'szpiro_ratio': 3.8301164325979546, '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, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], 'aplist': [0, 0, -2, 0, 0, 0, -1, 0, 0, 2, 8, -10, -6, 4, 8, 2, 4, -10, 8, 12, -6, 8, -12, -10, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 413712, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '413712.be', 'trace_hash': 942896498625729045}
• 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': '0.011980696607277666146554357417', 'prec': 107}, 'conductor': 413712, 'gens': [[-130, 6084, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1478699466039037183339682856', 'prec': 100}], 'lmfdb_label': '413712.be4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.18015725939754319020900901519', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.1912698099601075731508080937471241104', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-247, 0, 1]], 'xcoord_integral_points': [-247, -130, 3081]}
• lmfdb_label 413712.be4 does not appear in ec_iwasawa
• lmfdb_label 413712.be4 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: 10222078
    {'conductor': 413712, 'conductor_valuation': 4, 'discriminant_valuation': 20, 'j_denominator_valuation': 8, 'kodaira_symbol': -16, 'lmfdb_label': '413712.be4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10222079
    {'conductor': 413712, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '413712.be4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 10222080
    {'conductor': 413712, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '413712.be4', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 10222081
    {'conductor': 413712, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '413712.be4', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 4223164
    {'adelic_gens': [[667, 666, 2002, 4651], [1, 0, 8, 1], [7, 6, 5298, 5299], [1, 8, 0, 1], [3532, 5303, 1745, 5298], [1, 4, 4, 17], [655, 660, 658, 3313], [5297, 8, 5296, 9], [400, 5301, 4891, 5302], [2188, 1, 647, 6]], 'adelic_image': '5304.48.0.?', 'conductor': 413712, 'lmfdb_label': '413712.be4', 'prime': 0}
  • id: 1398804
    {'conductor': 413712, 'elladic_image': '4.6.0.1', 'lmfdb_label': '413712.be4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 413712.be does not appear in ec_padic