Elliptic curve isogeny class data - 15.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, 1, 1, 0, 3, 1, -1, -4, 1, -2, 0, -1, -1, 2, -1, 4, -1], 'aplist': [-1, -1, 1, 0, -4, -2, 2, 4, 0, -2, 0, -10, 10, 4, 8, -10, -4, -2, 12, -8, 10, 0, 12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 15, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '15.a', 'trace_hash': 750292609497685491}
• lmfdb_iso 15.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: 13
    {'Ciso': '15a', 'Clabel': '15a5', 'Cnumber': 5, 'abc_quality': 1.0735374703334082, 'absD': 405, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, -2160, -39540], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 4, 'elladic_images': ['16.96.0.148'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562429', 'prec': 103}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1114544804970241, 405], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -2160, -39540], '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.bb.2.3', '10.6.0.a.1', '16.96.0-16.x.2.4', '20.24.0-20.g.1.1', '40.96.0-40.bj.1.2', '80.192.1.?', '96.192.1.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 5], [3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562429', 'prec': 103}, 'szpiro_ratio': 12.794158120001653, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 10
    {'Ciso': '15a', 'Clabel': '15a2', 'Cnumber': 2, 'abc_quality': 1.038972011651739, 'absD': 164025, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 240, 'ainvs': [1, 1, 1, -135, -660], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 2, 'elladic_images': ['8.96.0.58'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436436', 'prec': 110}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [272223782641, 164025], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -135, -660], '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.k.1.1', '20.48.0-20.c.1.2', '40.192.1-40.cc.2.4', '48.192.1-48.e.2.2', '80.384.5.?', '240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436436', 'prec': 110}, 'szpiro_ratio': 9.72282208231094, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 14
    {'Ciso': '15a', 'Clabel': '15a6', 'Cnumber': 6, 'abc_quality': 1.0594919023465201, 'absD': 215233605, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, -110, -880], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 4, 'elladic_images': ['16.96.0.153'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562429', 'prec': 103}, 'faltings_index': 6, 'faltings_ratio': 16, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-147281603041, 215233605], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -110, -880], '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.ba.2.6', '16.96.0-16.u.2.3', '20.24.0-20.h.1.1', '40.96.0-40.bm.2.4', '80.384.5.?', '96.192.1.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 5], [3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562429', 'prec': 103}, 'szpiro_ratio': 9.961250033812139, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 15
    {'Ciso': '15a', 'Clabel': '15a7', 'Cnumber': 7, 'abc_quality': 1.030187200332639, 'absD': 15, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, -80, 242], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 4, 'elladic_images': ['32.96.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.40227757208284378744359649716', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [56667352321, 15], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a4', 'lmfdb_number': 4, 'manin_constant': 2, 'min_quad_twist_ainvs': [1, 1, 1, -80, 242], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.2', '16.48.0-16.g.1.2', '24.48.0-24.by.2.3', '32.96.0-32.e.1.2', '40.48.0-40.cb.2.7', '48.96.0-48.bs.1.1', '60.24.0-60.h.1.3', '80.192.2.?', '96.192.1.?', '120.96.0.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40227757208284378744359649716', 'prec': 107}, 'szpiro_ratio': 9.143281049575778, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
  • id: 9
    {'Ciso': '15a', 'Clabel': '15a1', 'Cnumber': 1, 'abc_quality': 1.0253374473912513, 'absD': 50625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 240, 'ainvs': [1, 1, 1, -10, -10], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 1, 'elladic_images': ['8.96.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.40227757208284378744359649716', 'prec': 107}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [111284641, 50625], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -10, -10], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.48.0-4.b.1.1', '8.96.0-8.b.2.9', '24.192.1-24.n.1.1', '40.192.1-40.s.1.5', '80.384.5.?', '120.384.5.?', '240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40227757208284378744359649716', 'prec': 107}, 'szpiro_ratio': 6.841675904965247, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
  • id: 11
    {'Ciso': '15a', 'Clabel': '15a3', 'Cnumber': 3, 'abc_quality': 0.9622954410890624, 'absD': 225, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 240, 'ainvs': [1, 1, 1, -5, 2], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 2, 'elladic_images': ['16.96.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.74885116236281644215221255789', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13997521, 225], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a6', 'lmfdb_number': 6, 'manin_constant': 2, 'min_quad_twist_ainvs': [1, 1, 1, -5, 2], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.48.0-8.i.1.10', '16.96.0-16.d.2.3', '24.96.0-24.bb.2.5', '40.96.0-40.bd.1.5', '48.192.1-48.n.1.7', '60.48.0-60.c.1.7', '80.384.5.?', '120.192.1.?', '240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74885116236281644215221255789', 'prec': 107}, 'szpiro_ratio': 6.076102575120219, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
  • id: 16
    {'Ciso': '15a', 'Clabel': '15a8', 'Cnumber': 8, 'abc_quality': 1.1980768440515948, 'absD': 15, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, 0, 0], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 4, 'elladic_images': ['32.96.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-1.0954247526427890968608286186', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-1, 15], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a7', 'lmfdb_number': 7, 'manin_constant': 4, 'min_quad_twist_ainvs': [1, 1, 1, 0, 0], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.2', '16.48.0-16.g.1.2', '24.48.0-24.bz.1.3', '30.6.0.a.1', '32.96.0-32.e.1.2', '40.48.0-40.cb.2.7', '48.96.0-48.bv.1.3', '60.24.0-60.g.1.3', '80.192.2.?', '96.192.1.?', '120.96.0.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0954247526427890968608286186', 'prec': 103}, 'szpiro_ratio': 3.7528140083343127, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
  • id: 12
    {'Ciso': '15a', 'Clabel': '15a4', 'Cnumber': 4, 'abc_quality': 1.0558519748642754, 'absD': 3515625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, 35, -28], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 2, 'elladic_images': ['8.96.0.99'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436435', 'prec': 110}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4733169839, 3515625], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 35, -28], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '8.96.0-8.n.2.5', '24.192.1-24.cv.2.2', '80.192.1.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [3, 4, 5], [5, 6, 3]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436435', 'prec': 110}, 'szpiro_ratio': 8.226531754162185, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [8]}