Elliptic curve data - 397488.bz1

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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': '397488bz', 'Clabel': '397488bz1', 'Cnumber': 1, 'abc_quality': 0.6777937141616772, 'absD': 140292197136, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1092, 'ainvs': [0, -1, 0, -1486, -12221], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 397488, 'degree': 338688, 'elladic_images': ['2.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.83789300896619503436426513983', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 51, 'isogeny_degrees': [1], 'jinv': [23296, 9], 'lmfdb_iso': '397488.bz', 'lmfdb_label': '397488.bz1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -30, -27], 'min_quad_twist_disc': 28, 'modell_images': ['2Cn'], 'modm_images': ['2.2.0.a.1', '156.4.0.?', '182.6.0.?', '1092.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 8281], [3, 4, 132496], [7, 26, 8112], [13, 38, 2352]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1179210435009183948539619699', 'prec': 103}, 'szpiro_ratio': 2.600326808693904, '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, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -7, 0, 4, 0], 'aplist': [0, -1, -1, 0, 0, 0, -7, 4, 3, 5, -5, 5, -1, 1, 11, 9, -9, 10, -4, 5, -3, 15, 4, 11, 5], 'class_deg': 1, 'class_size': 1, 'conductor': 397488, 'isogeny_matrix': [[1]], 'lmfdb_iso': '397488.bz', 'trace_hash': 355663224695816633}
• 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': '0.18716100974060585625383058089', 'prec': 103}, 'conductor': 397488, 'gens': [], 'heights': [], 'lmfdb_label': '397488.bz1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.79451239031423540555402132871', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5890247806284708111080426574138593967', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 397488.bz1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16399608
    {'degree': 3, 'field': [-27, -30, -1, 1], 'lmfdb_label': '397488.bz1', 'torsion': [2, 2]}
  • id: 16399609
    {'degree': 8, 'field': [-61347, 0, 68536, 0, 858, 0, 0, 0, 1], 'lmfdb_label': '397488.bz1', 'torsion': [3]}
  • id: 16399610
    {'degree': 12, 'field': [-325053, 1114110, -384882, -138614, 29759, 15930, -3798, -568, 72, 40, 16, -6, 1], 'lmfdb_label': '397488.bz1', 'torsion': [2, 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: 9831653
    {'conductor': 397488, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '397488.bz1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 9831654
    {'conductor': 397488, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '397488.bz1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9831655
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '397488.bz1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9831656
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '397488.bz1', 'prime': 13, 'reduction_type': 0, '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: 4129605
    {'adelic_gens': [[1, 0, 4, 1], [1, 2, 2, 5], [1, 4, 0, 1], [543, 1088, 538, 1081], [3, 4, 736, 11], [464, 1091, 621, 1091], [925, 3, 925, 4], [3, 2, 1084, 1087], [1089, 4, 1088, 5]], 'adelic_image': '1092.12.0.?', 'conductor': 397488, 'lmfdb_label': '397488.bz1', 'prime': 0}
  • id: 1352227
    {'conductor': 397488, 'elladic_image': '2.2.0.1', 'lmfdb_label': '397488.bz1', 'modell_image': '2Cn', 'prime': 2}
• lmfdb_iso 397488.bz does not appear in ec_padic