Elliptic curve data - 272832.bb2

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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': '272832bb', 'Clabel': '272832bb1', 'Cnumber': 1, 'abc_quality': 0.8907255200292924, 'absD': 1540723774464, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 812, 'ainvs': [0, -1, 0, -17509, -883931], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 29], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 272832, 'degree': 589824, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2142725266694922716358954858', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2], 'jinv': [4927700992, 12789], 'lmfdb_iso': '272832.bb', 'lmfdb_label': '272832.bb2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -89, 354], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.b.1', '58.6.0.a.1', '812.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33630519832478547209780765380', 'prec': 107}, 'szpiro_ratio': 3.2696605695187664, '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, 2, 0, -2, 0, 2, 0, -8, 0, 4, 0], 'aplist': [0, -1, -2, 0, 2, -2, -8, 4, 4, -1, -4, 2, 12, 2, 0, 6, -4, -8, 16, 12, 4, -10, 12, 0, 12], 'class_deg': 2, 'class_size': 2, 'conductor': 272832, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '272832.bb', 'trace_hash': 2163587662841947810}
• 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': '0.088165014704447845665669523189', 'prec': 107}, 'conductor': 272832, 'gens': [], 'heights': [], 'lmfdb_label': '272832.bb2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41509728381419707569160077945', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6603891352567883027664031177936119778', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-79, 0, 1]], 'xcoord_integral_points': [-79]}
• lmfdb_label 272832.bb2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11643564
    {'degree': 2, 'field': [-7, -1, 1], 'lmfdb_label': '272832.bb2', 'torsion': [2, 2]}
  • id: 11643565
    {'degree': 4, 'field': [29, 0, 12, 0, 1], 'lmfdb_label': '272832.bb2', 'torsion': [4]}
  • id: 11643568
    {'degree': 8, 'field': [-2352, 0, 3808, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '272832.bb2', 'torsion': [6]}
  • id: 11643566
    {'degree': 8, 'field': [1, 0, 884, 0, 395, 0, 44, 0, 1], 'lmfdb_label': '272832.bb2', 'torsion': [2, 4]}
  • id: 11643567
    {'degree': 8, 'field': [8357881, 0, -111468, 0, -8182, 0, -12, 0, 1], 'lmfdb_label': '272832.bb2', 'torsion': [2, 4]}
  • id: 11643569
    {'degree': 16, 'field': [3337929, 0, 0, 0, -3712464, 0, 745416, 0, 1262458, 0, 145792, 0, 6656, 0, 136, 0, 1], 'lmfdb_label': '272832.bb2', 'torsion': [8]}
  • id: 11643570
    {'degree': 16, 'field': [375672857, -27156584, 12969796, 40514096, -49395598, 31587528, -4947824, -4687480, 1058219, 65288, -3360, -4312, -70, 336, -28, -8, 1], 'lmfdb_label': '272832.bb2', '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: 6758080
    {'conductor': 272832, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '272832.bb2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6758081
    {'conductor': 272832, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '272832.bb2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6758082
    {'conductor': 272832, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '272832.bb2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6758083
    {'conductor': 272832, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '272832.bb2', 'prime': 29, '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: 3387618
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [758, 1, 27, 0], [1, 0, 4, 1], [465, 4, 118, 9], [3, 4, 8, 11], [613, 204, 608, 203], [809, 4, 808, 5]], 'adelic_image': '812.12.0.?', 'conductor': 272832, 'lmfdb_label': '272832.bb2', 'prime': 0}
  • id: 973718
    {'conductor': 272832, 'elladic_image': '2.3.0.1', 'lmfdb_label': '272832.bb2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 272832.bb does not appear in ec_padic