Elliptic curve data - 156816.bf1

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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': '156816cw', 'Clabel': '156816cw1', 'Cnumber': 1, 'abc_quality': 0.7594669708787151, 'absD': 2151353746105344, 'adelic_genus': 0, 'adelic_index': 4, 'adelic_level': 44, 'ainvs': [0, 0, 0, -43923, -4187326], 'analytic_rank': 2, 'bad_primes': [2, 3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 156816, 'degree': 684288, 'elladic_images': ['4.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6617656928067901820381673352', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1], 'jinv': [-4356, 1], 'lmfdb_iso': '156816.bf', 'lmfdb_label': '156816.bf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -363, -3146], 'min_quad_twist_disc': 44, 'modell_images': [], 'modm_images': ['4.2.0.a.1', '44.4.0-4.a.1.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': True, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '36.871617886464920756544720079', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9801], [3, 8, 1936], [11, 32, 1296]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2803071145478429263262274933', 'prec': 103}, 'szpiro_ratio': 3.6795889556361985, '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, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3, 0, -2, 0], 'aplist': [0, 0, -1, -2, 0, 6, -3, -2, -6, 6, -6, -6, 5, -8, -6, 3, -14, 5, 0, -14, -11, -4, -6, -9, -13], 'class_deg': 1, 'class_size': 1, 'conductor': 156816, 'isogeny_matrix': [[1]], 'lmfdb_iso': '156816.bf', 'trace_hash': 1086576962305791561}
• 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': '0.036025387324256178108055428134', 'prec': 107}, 'conductor': 156816, 'gens': [[587, 13126, 1], [947, 28346, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.8751705733871296472422409065', 'prec': 100}, {'__RealLiteral__': 0, 'data': '6.2841009710920969734906802726', 'prec': 100}], 'lmfdb_label': '156816.bf1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.16290422994607153166393434709', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.013085037320730920332399268144617923', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [587, 947]}
• lmfdb_label 156816.bf1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7027254
    {'degree': 3, 'field': [-22, 33, 0, 1], 'lmfdb_label': '156816.bf1', 'torsion': [2]}
  • id: 7027255
    {'degree': 6, 'field': [484, 0, 1089, 0, -66, 0, 1], 'lmfdb_label': '156816.bf1', 'torsion': [2, 2]}
  • id: 7027256
    {'degree': 8, 'field': [859, 674, 718, -40, -80, -70, -20, -4, 1], 'lmfdb_label': '156816.bf1', 'torsion': [3]}
  • id: 7027257
    {'degree': 12, 'field': [6428, -9969, 2649, 279, 1449, -465, -201, -75, 39, 9, 3, -3, 1], 'lmfdb_label': '156816.bf1', 'torsion': [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: 3879146
    {'conductor': 156816, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '156816.bf1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3879147
    {'conductor': 156816, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '156816.bf1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3879148
    {'conductor': 156816, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '156816.bf1', 'prime': 11, '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: 2679245
    {'adelic_gens': [[1, 2, 2, 5], [43, 11, 0, 21], [41, 4, 40, 5], [2, 3, 39, 37], [31, 0, 0, 43], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '44.4.0.?', 'conductor': 156816, 'lmfdb_label': '156816.bf1', 'prime': 0}
  • id: 598771
    {'conductor': 156816, 'elladic_image': '4.2.0.1', 'lmfdb_label': '156816.bf1', 'modell_image': '2G', 'prime': 2}
• lmfdb_iso 156816.bf does not appear in ec_padic