Elliptic curve data - 187425.bc1

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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': '187425by', 'Clabel': '187425by1', 'Cnumber': 1, 'abc_quality': 0.6890595357104303, 'absD': 1447055126015625, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 7140, 'ainvs': [1, -1, 1, -36980, -2025978], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 187425, 'degree': 688128, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6181948107215793872236053323', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2], 'jinv': [328509, 85], 'lmfdb_iso': '187425.bc', 'lmfdb_label': '187425.bc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -272, -1214], 'min_quad_twist_disc': 105, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '84.6.0.?', '340.6.0.?', '3570.6.0.?', '7140.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.8056913707593175502339640824', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 6, 20825], [5, 18, 7497], [7, 20, 3825], [17, 18, 11025]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.92060982945398320175460020113', 'prec': 107}, 'szpiro_ratio': 3.5555142574108705, '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, -1, 0, -1, 0, 0, 0, 3, 0, 0, -4, 0, 2, 0, 0, -1, 1, 0, 8, 0], 'aplist': [-1, 0, 0, 0, -4, 2, 1, 8, 0, -2, 0, -6, -6, 6, -2, -6, -4, -6, -2, 0, -4, -2, 2, 14, 12], 'class_deg': 2, 'class_size': 2, 'conductor': 187425, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '187425.bc', 'trace_hash': 2090703372696415193}
• 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': '0.039305547140934696437701259528', 'prec': 107}, 'conductor': 187425, 'gens': [[228, 1050, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.8056913707593175502339640824', 'prec': 100}], 'lmfdb_label': '187425.bc1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.35086956245554864001866801842', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0740807820205523291740552118244094271', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-61, 30, 1]], 'xcoord_integral_points': [-61, 228]}
• lmfdb_label 187425.bc1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8263719
    {'degree': 2, 'field': [-446, -1, 1], 'lmfdb_label': '187425.bc1', 'torsion': [2, 2]}
  • id: 8263720
    {'degree': 4, 'field': [256, -32, 54, -2, 1], 'lmfdb_label': '187425.bc1', 'torsion': [4]}
  • id: 8263723
    {'degree': 8, 'field': [-235791, 130788, 61380, 13671, 1125, -231, -12, 0, 1], 'lmfdb_label': '187425.bc1', 'torsion': [6]}
  • id: 8263721
    {'degree': 8, 'field': [256, -2720, 9998, -14726, 7789, -514, 176, -4, 1], 'lmfdb_label': '187425.bc1', 'torsion': [2, 4]}
  • id: 8263722
    {'degree': 8, 'field': [126736, 0, -414677, 0, 10359, 0, 157, 0, 1], 'lmfdb_label': '187425.bc1', 'torsion': [2, 4]}
  • id: 8263724
    {'degree': 16, 'field': [14478105625, 0, 1230797500, 0, 50978150, 0, 7021900, 0, 562195, 0, 5900, 0, 794, 0, -16, 0, 1], 'lmfdb_label': '187425.bc1', 'torsion': [8]}
  • id: 8263725
    {'degree': 16, 'field': [53187890625, 0, -51041292750, 0, 1747858725, 0, -16460325, 0, 4333500, 0, -129255, 0, 3480, 0, 0, 0, 1], 'lmfdb_label': '187425.bc1', '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: 4638471
    {'conductor': 187425, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '187425.bc1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4638472
    {'conductor': 187425, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '187425.bc1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4638473
    {'conductor': 187425, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '187425.bc1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4638474
    {'conductor': 187425, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '187425.bc1', '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: 2868067
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [7137, 4, 7136, 5], [1, 4, 0, 1], [3064, 1, 1019, 0], [2384, 1, 4759, 0], [2522, 1, 5879, 0], [5714, 1, 4283, 0], [1789, 5356, 1784, 5355]], 'adelic_image': '7140.12.0.?', 'conductor': 187425, 'lmfdb_label': '187425.bc1', 'prime': 0}
  • id: 700240
    {'conductor': 187425, 'elladic_image': '2.3.0.1', 'lmfdb_label': '187425.bc1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 187425.bc does not appear in ec_padic