Elliptic curve isogeny class data - 42.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, 1, -1, 1, -2, -1, -1, 1, 1, -2, -4, -1, 6, -1, 2, 1, 2, 1, -4, -2], 'aplist': [1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10, -6, -4, 0, 6, 4, 6, 4, 8, 10, 0, -4, -6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 42, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '42.a', 'trace_hash': 1611795495172191507}
• lmfdb_iso 42.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
  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[]

  
  
  • id: 96
    {'Ciso': '42a', 'Clabel': '42a4', 'Cnumber': 4, 'abc_quality': 1.0572692378622217, 'absD': 252, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 112, 'ainvs': [1, 1, 1, -1344, 18405], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 16, 'elladic_images': ['16.96.0.103'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105447', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [268498407453697, 252], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1344, 18405], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.bb.2.4', '16.96.0-16.z.2.3', '28.24.0-28.h.1.2', '56.96.0-56.bl.1.5', '112.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 7], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105447', 'prec': 103}, 'szpiro_ratio': 8.888925317547928, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
  • id: 97
    {'Ciso': '42a', 'Clabel': '42a5', 'Cnumber': 5, 'abc_quality': 1.0530860389430399, 'absD': 933897762, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 112, 'ainvs': [1, 1, 1, -914, -10915], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 32, 'elladic_images': ['8.96.0.164'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.53567478369769316355008711520', 'prec': 103}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [84448510979617, 933897762], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -914, -10915], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.96.0-8.p.1.4', '112.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.53567478369769316355008711520', 'prec': 103}, 'szpiro_ratio': 8.57945361735277, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 95
    {'Ciso': '42a', 'Clabel': '42a3', 'Cnumber': 3, 'abc_quality': 1.0649865394830864, 'absD': 63011844, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 56, 'ainvs': [1, 1, 1, -104, 101], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 16, 'elladic_images': ['8.96.0.50'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105447', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [124475734657, 63011844], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -104, 101], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.1', '8.96.0-8.f.1.1', '56.192.1-56.bp.2.4'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105447', 'prec': 103}, 'szpiro_ratio': 6.835108300244897, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 94
    {'Ciso': '42a', 'Clabel': '42a2', 'Cnumber': 2, 'abc_quality': 1.0169154011150379, 'absD': 63504, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 56, 'ainvs': [1, 1, 1, -84, 261], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 8, 'elladic_images': ['8.96.0.37'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.15747239686225214586714500626', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [65597103937, 63504], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -84, 261], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.96.0-8.i.1.2', '28.48.0-28.c.1.1', '56.192.1-56.by.1.7'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15747239686225214586714500626', 'prec': 107}, 'szpiro_ratio': 6.663723637526653, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
  • id: 93
    {'Ciso': '42a', 'Clabel': '42a1', 'Cnumber': 1, 'abc_quality': 0.9822408596528094, 'absD': 16128, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 112, 'ainvs': [1, 1, 1, -4, 5], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 4, 'elladic_images': ['16.96.0.98'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.50404598714222480057576106699', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-7189057, 16128], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -4, 5], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.bb.1.1', '14.6.0.b.1', '16.96.0-16.z.1.2', '28.24.0-28.g.1.2', '56.96.0-56.bh.2.1', '112.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 7], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50404598714222480057576106699', 'prec': 107}, 'szpiro_ratio': 4.647955287455925, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [8]}
  • id: 98
    {'Ciso': '42a', 'Clabel': '42a6', 'Cnumber': 6, 'abc_quality': 1.083141850233532, 'absD': 4218578658, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 112, 'ainvs': [1, 1, 1, 386, 1277], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 32, 'elladic_images': ['16.96.0.137'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.53567478369769316355008711520', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6359387729183, 4218578658], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 386, 1277], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.48.0-8.k.1.6', '16.96.0-16.e.1.6', '56.96.0-56.bc.1.4', '112.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.53567478369769316355008711520', 'prec': 103}, 'szpiro_ratio': 7.887522502106543, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}