Elliptic curve data - 219912.bs1

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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': '219912bj', 'Clabel': '219912bj2', 'Cnumber': 2, 'abc_quality': 0.8841428566887771, 'absD': 361310025517056, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4488, 'ainvs': [0, 1, 0, -40392, 2974320], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 219912, 'degree': 829440, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5524393094303764136820341202', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2], 'jinv': [30248395634, 1499553], 'lmfdb_iso': '219912.bs', 'lmfdb_label': '219912.bs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -824, -8436], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '132.6.0.?', '136.6.0.?', '4488.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 833], [3, 4, 73304], [7, 26, 4488], [11, 12, 19992], [17, 18, 12936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055900680610563439169771696193', 'prec': 110}, 'szpiro_ratio': 3.5308389388777863, '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, 1, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 1, 0, -2, 0], 'aplist': [0, 1, 2, 0, -1, 0, 1, -2, 2, 10, -8, -6, -2, 2, 0, -12, -10, -10, -4, 6, 0, -10, 4, 10, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 219912, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '219912.bs', 'trace_hash': 2242371204190673163}
• 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': '0.044829959740617515636648592433', 'prec': 107}, 'conductor': 219912, 'gens': [], 'heights': [], 'lmfdb_label': '219912.bs1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.53084674378764867998262416839', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1850804627258920798957450103664161501', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[135, 0, 1]], 'xcoord_integral_points': [135]}
• lmfdb_label 219912.bs1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9575500
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 2]}
  • id: 9575501
    {'degree': 4, 'field': [6664, 0, -203, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [4]}
  • id: 9575504
    {'degree': 8, 'field': [-80514, 18144, 54378, 11190, 5370, 42, 142, -2, 1], 'lmfdb_label': '219912.bs1', 'torsion': [6]}
  • id: 9575503
    {'degree': 8, 'field': [40857664, 0, -591872, 0, 33320, 0, -272, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 4]}
  • id: 9575502
    {'degree': 8, 'field': [43848814, -5737636, -3918866, 54544, 76199, 544, -494, -4, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 4]}
  • id: 9575505
    {'degree': 16, 'field': [251127267876, 0, -112145985288, 0, 18406357980, 0, -1375013448, 0, 49938061, 0, -1180174, 0, 21438, 0, -238, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [8]}
  • id: 9575506
    {'degree': 16, 'field': [28362995278864, 0, -2011835139296, 0, 34234255648, 0, -55733072, 0, -9199448, 0, 294712, 0, -5780, 0, -68, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 6]}
• 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: 5453126
    {'conductor': 219912, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '219912.bs1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5453127
    {'conductor': 219912, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '219912.bs1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 5453128
    {'conductor': 219912, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '219912.bs1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5453129
    {'conductor': 219912, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '219912.bs1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5453130
    {'conductor': 219912, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '219912.bs1', '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: 3068618
    {'adelic_gens': [[1, 0, 4, 1], [409, 4, 818, 9], [2993, 4, 1498, 9], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 2243, 0], [2114, 1, 3431, 0], [3929, 562, 560, 3927], [4485, 4, 4484, 5]], 'adelic_image': '4488.12.0.?', 'conductor': 219912, 'lmfdb_label': '219912.bs1', 'prime': 0}
  • id: 807129
    {'conductor': 219912, 'elladic_image': '2.3.0.1', 'lmfdb_label': '219912.bs1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 219912.bs does not appear in ec_padic