Elliptic curve isogeny class data - 27.a

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• 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, -2, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 4, 0, 0, -7, 0], 'aplist': [0, 0, 0, -1, 0, 5, 0, -7, 0, 0, -4, 11, 0, 8, 0, 0, 0, -1, 5, 0, -7, 17, 0, 0, -19], 'class_deg': 27, 'class_size': 4, 'conductor': 27, 'isogeny_matrix': [[1, 27, 3, 9], [27, 1, 9, 3], [3, 9, 1, 3], [9, 3, 3, 1]], 'lmfdb_iso': '27.a', 'trace_hash': 903291523394155081}
• lmfdb_iso 27.a does not appear in ec_padic
• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  
  • id: 46
    {'Ciso': '27a', 'Clabel': '27a2', 'Cnumber': 2, 'abc_quality': 1.23864473399791, 'absD': 177147, 'ainvs': [0, 0, 1, -270, -1708], 'analytic_rank': 0, 'bad_primes': [3], 'class_deg': 27, 'class_size': 4, 'cm': -27, 'conductor': 27, 'degree': 3, 'elladic_images': ['27.648.13.34'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.052147932407099199254187350298', 'prec': 107}, 'faltings_index': 3, 'faltings_ratio': 9, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9, 27], 'jinv': [-12288000, 1], 'lmfdb_iso': '27.a', 'lmfdb_label': '27.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -30, 63], 'min_quad_twist_disc': -3, 'modell_images': ['3B.1.2'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 4, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95491333220533468452478745021', 'prec': 107}, 'szpiro_ratio': 8.619664953039187, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
  • id: 48
    {'Ciso': '27a', 'Clabel': '27a4', 'Cnumber': 4, 'abc_quality': 1.23864473399791, 'absD': 243, 'ainvs': [0, 0, 1, -30, 63], 'analytic_rank': 0, 'bad_primes': [3], 'class_deg': 27, 'class_size': 4, 'cm': -27, 'conductor': 27, 'degree': 9, 'elladic_images': ['27.648.13.25'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.49715821192695564644343526816', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 3, 'intrinsic_torsion': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9, 27], 'jinv': [-12288000, 1], 'lmfdb_iso': '27.a', 'lmfdb_label': '27.a2', 'lmfdb_number': 2, 'manin_constant': 3, 'min_quad_twist_ainvs': [0, 0, 1, -30, 63], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 8, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95491333220533468452478745021', 'prec': 107}, 'szpiro_ratio': 6.619664953039187, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
  • id: 45
    {'Ciso': '27a', 'Clabel': '27a1', 'Cnumber': 1, 'absD': 19683, 'ainvs': [0, 0, 1, 0, -7], 'analytic_rank': 0, 'bad_primes': [3], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 27, 'degree': 1, 'elladic_images': ['27.1944.55.37'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.49715821192695564644343526816', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '27.a', 'lmfdb_label': '27.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': -3, 'modell_images': ['3Cs.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 2, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 5.261859507142915, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
  • id: 47
    {'Ciso': '27a', 'Clabel': '27a3', 'Cnumber': 3, 'absD': 27, 'ainvs': [0, 0, 1, 0, 0], 'analytic_rank': 0, 'bad_primes': [3], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 27, 'degree': 3, 'elladic_images': ['27.1944.55.31'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-1.0464643562610104921410578866', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '27.a', 'lmfdb_label': '27.a4', 'lmfdb_number': 4, 'manin_constant': 3, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': 1, 'modell_images': ['3Cs.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 2, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691958', 'prec': 103}, 'szpiro_ratio': 3.261859507142915, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}