Elliptic curve data - 392784.bf1

Formats: - HTML - YAML - JSON - 2024-04-27T15:45:21.588358

• 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': '392784bf', 'Clabel': '392784bf1', 'Cnumber': 1, 'abc_quality': 0.9096373723091602, 'absD': 207579393294336, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 28056, 'ainvs': [0, -1, 0, -44424, 3551472], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 167], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 392784, 'degree': 2350080, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5361649204188712971232327362', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1], 'jinv': [6901323756319, 147750912], 'lmfdb_iso': '392784.bf', 'lmfdb_label': '392784.bf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2777, -55492], 'min_quad_twist_disc': -4, 'modell_images': [], 'modm_images': ['28056.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0377884814063596315683165225', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.35654020259509766142966242888', 'prec': 103}, 'szpiro_ratio': 3.394005096617493, '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, 0, -1, 0, 3, 0, 0, 0, 1, 0, -6, 0, -4, 0, -3, 0, 0, 0, -2, 0], 'aplist': [0, -1, 3, 0, -6, -4, 0, -2, -8, -5, -5, -5, 6, -10, -2, 0, -8, -7, 4, 6, 15, 13, -14, 1, 6], 'class_deg': 1, 'class_size': 1, 'conductor': 392784, 'isogeny_matrix': [[1]], 'lmfdb_iso': '392784.bf', 'trace_hash': 862420784111296312}
• 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': '0.046313126848009324863811005193', 'prec': 107}, 'conductor': 392784, 'gens': [[404, 7168, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0377884814063596315683165225', 'prec': 100}], 'lmfdb_label': '392784.bf1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.56260576946752023538098857202', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6709262970092342168946346415843670795', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [154, 404]}
• lmfdb_label 392784.bf1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16227473
    {'degree': 3, 'field': [88, -40, -1, 1], 'lmfdb_label': '392784.bf1', 'torsion': [2]}
  • id: 16227474
    {'degree': 6, 'field': [3376, -3728, 50, 856, -175, -2, 1], 'lmfdb_label': '392784.bf1', 'torsion': [2, 2]}
  • id: 16227475
    {'degree': 8, 'field': [-849072, 0, -108143, 0, -3192, 0, 0, 0, 1], 'lmfdb_label': '392784.bf1', 'torsion': [3]}
  • id: 16227476
    {'degree': 12, 'field': [7181404344, 3645847984, 364491294, -199101128, -27588743, -8411880, -792596, 198616, 20802, -1112, -194, 0, 1], 'lmfdb_label': '392784.bf1', 'torsion': [4]}
• 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: 9718002
    {'conductor': 392784, 'conductor_valuation': 4, 'discriminant_valuation': 27, 'j_denominator_valuation': 15, 'kodaira_symbol': -23, 'lmfdb_label': '392784.bf1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9718003
    {'conductor': 392784, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '392784.bf1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9718004
    {'conductor': 392784, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '392784.bf1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9718005
    {'conductor': 392784, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '392784.bf1', 'prime': 167, '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

  
  {'adelic_gens': [[1, 1, 28055, 0], [7015, 2, 7015, 3], [28055, 2, 28054, 3], [1, 0, 2, 1], [1, 2, 0, 1], [9353, 2, 9353, 3], [16033, 2, 16033, 3], [14029, 2, 14029, 3], [673, 2, 673, 3]], 'adelic_image': '28056.2.0.?', 'conductor': 392784, 'lmfdb_label': '392784.bf1', 'prime': 0}
• lmfdb_iso 392784.bf does not appear in ec_padic