Elliptic curve data - 331056.bf1

Formats: - HTML - YAML - JSON - 2024-06-14T15:26:34.191287

• 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': '331056bf', 'Clabel': '331056bf2', 'Cnumber': 2, 'abc_quality': 0.8993750730672936, 'absD': 4579359446686464, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 228, 'ainvs': [0, 0, 0, -100551, -11832590], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 331056, 'degree': 1612800, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7708093953017203759955622602', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2], 'jinv': [340062928, 13851], 'lmfdb_iso': '331056.bf', 'lmfdb_label': '331056.bf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -92, 360], 'min_quad_twist_disc': -132, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '76.6.0.?', '228.12.0.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.43954250580481661467785356155', 'prec': 107}, 'szpiro_ratio': 3.6324711641151093, '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, -2, 0, 0, 0, 6, 0, -1, 0], 'aplist': [0, 0, -2, 0, 0, -2, 6, -1, 2, 4, 8, -2, -8, -8, 2, 4, 0, -2, -12, -4, -6, -16, -6, 0, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 331056, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '331056.bf', 'trace_hash': 414248028040271006}
• 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': '0.028966398574903107473711186472', 'prec': 107}, 'conductor': 331056, 'gens': [], 'heights': [], 'lmfdb_label': '331056.bf1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.26877741904793999419238751519', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.53755483809587998838477503038265598112', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-154, 0, 1]], 'xcoord_integral_points': [-154]}
• lmfdb_label 331056.bf1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13875260
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '331056.bf1', 'torsion': [2, 2]}
  • id: 13875261
    {'degree': 4, 'field': [2299, 0, 88, 0, 1], 'lmfdb_label': '331056.bf1', 'torsion': [4]}
  • id: 13875263
    {'degree': 8, 'field': [-1321415, 1188076, -259332, -34332, 14014, 276, -252, -4, 1], 'lmfdb_label': '331056.bf1', 'torsion': [2, 4]}
  • id: 13875264
    {'degree': 8, 'field': [-9162, 6146, 17131, 8550, 1595, -56, -63, -4, 1], 'lmfdb_label': '331056.bf1', 'torsion': [6]}
  • id: 13875262
    {'degree': 8, 'field': [2025, 7830, 28656, 6444, 1599, -420, -32, -2, 1], 'lmfdb_label': '331056.bf1', 'torsion': [2, 4]}
  • id: 13875266
    {'degree': 16, 'field': [419904, 0, -660592, 0, 786256, 0, -432384, 0, 33080, 0, 11272, 0, 672, 0, 29, 0, 1], 'lmfdb_label': '331056.bf1', 'torsion': [2, 6]}
  • id: 13875265
    {'degree': 16, 'field': [3757506537, 8025211044, 8293360494, 4875053376, 1604698678, 255385352, 16239050, 12129180, 5862238, 502060, -104558, -16448, 2830, 528, -34, -4, 1], 'lmfdb_label': '331056.bf1', 'torsion': [8]}
• 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: 8190348
    {'conductor': 331056, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '331056.bf1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 8190349
    {'conductor': 331056, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '331056.bf1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8190350
    {'conductor': 331056, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '331056.bf1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8190351
    {'conductor': 331056, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '331056.bf1', 'prime': 19, '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: 3734833
    {'adelic_gens': [[172, 61, 57, 172], [194, 1, 131, 0], [1, 4, 0, 1], [225, 4, 224, 5], [1, 0, 4, 1], [77, 4, 154, 9], [3, 4, 8, 11], [1, 2, 2, 5]], 'adelic_image': '228.12.0.?', 'conductor': 331056, 'lmfdb_label': '331056.bf1', 'prime': 0}
  • id: 1152075
    {'conductor': 331056, 'elladic_image': '2.3.0.1', 'lmfdb_label': '331056.bf1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 331056.bf does not appear in ec_padic