Elliptic curve isogeny class data - 21.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, 3, 1, 2, 4, -1, -2, 1, -2, -1, -6, -1, 4, 2], 'aplist': [-1, 1, -2, -1, 4, -2, -6, 4, 0, -2, 0, 6, 2, -4, 0, 6, 12, -2, 4, 0, -6, -16, -12, -14, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 21, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '21.a', 'trace_hash': 1161919666425559947}
• lmfdb_iso 21.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: 32
    {'Ciso': '21a', 'Clabel': '21a5', 'Cnumber': 5, 'abc_quality': 1.0508747826837916, 'absD': 147, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, 0, 0, -784, -8515], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 4, 'elladic_images': ['16.48.0.48'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854672', 'prec': 107}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [53297461115137, 147], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -784, -8515], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.n.1.6', '12.24.0-12.h.1.1', '16.48.0-16.e.2.5', '24.48.0-24.bl.1.1', '48.96.0-48.y.1.2', '56.48.0-56.bu.1.11', '112.96.0.?', '168.96.0.?', '336.192.1.?'], '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, 3], [3, 4, 7], [7, 8, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854672', 'prec': 107}, 'szpiro_ratio': 10.381565732764942, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 29
    {'Ciso': '21a', 'Clabel': '21a2', 'Cnumber': 2, 'abc_quality': 1.0814902740568197, 'absD': 21609, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 168, 'ainvs': [1, 0, 0, -49, -136], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 2, 'elladic_images': ['8.48.0.34'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020606', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [13027640977, 21609], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -49, -136], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.1', '8.48.0-8.e.1.1', '12.48.0-12.c.1.3', '24.96.0-24.j.2.5', '56.96.0-56.u.1.2', '168.192.1.?'], '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, 7], [7, 8, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020606', 'prec': 107}, 'szpiro_ratio': 7.649915427654956, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 30
    {'Ciso': '21a', 'Clabel': '21a3', 'Cnumber': 3, 'abc_quality': 1.0015974661127929, 'absD': 45927, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, 0, 0, -39, 90], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 2, 'elladic_images': ['8.48.0.159'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020606', 'prec': 107}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6570725617, 45927], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -39, 90], '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', '28.24.0-28.h.1.2', '48.96.0-48.bf.1.3', '56.96.0-56.bl.2.5', '336.192.1.?'], '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, 7], [3, 4, 7], [7, 8, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020606', 'prec': 107}, 'szpiro_ratio': 7.42510215304443, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [8]}
  • id: 33
    {'Ciso': '21a', 'Clabel': '21a6', 'Cnumber': 6, 'abc_quality': 1.042661241253942, 'absD': 17294403, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, 0, 0, -34, -217], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 4, 'elladic_images': ['8.48.0.177'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854672', 'prec': 107}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-4354703137, 17294403], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -34, -217], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '6.6.0.a.1', '8.48.0-8.bb.2.3', '12.24.0-12.g.1.1', '24.96.0-24.bj.1.1', '112.96.0.?', '336.192.1.?'], '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, 3], [3, 4, 7], [7, 8, 3]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854672', 'prec': 107}, 'szpiro_ratio': 7.967306624104166, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 28
    {'Ciso': '21a', 'Clabel': '21a1', 'Cnumber': 1, 'abc_quality': 1.1486166056524132, 'absD': 3969, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 168, 'ainvs': [1, 0, 0, -4, -1], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 1, 'elladic_images': ['8.48.0.24'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.61894179716900553865896626679', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [7189057, 3969], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -4, -1], '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.e.2.2', '24.96.0-24.w.2.6', '28.48.0-28.c.1.1', '56.96.0-56.i.1.1', '168.192.1.?'], '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, 7], [7, 8, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61894179716900553865896626679', 'prec': 107}, 'szpiro_ratio': 5.185729745687264, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
  • id: 31
    {'Ciso': '21a', 'Clabel': '21a4', 'Cnumber': 4, 'abc_quality': 0.9786808587681587, 'absD': 63, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, 0, 0, 1, 0], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 2, 'elladic_images': ['16.48.0.27'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.96551538744897819336758232752', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [103823, 63], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a6', 'lmfdb_number': 6, 'manin_constant': 2, 'min_quad_twist_ainvs': [1, 0, 0, 1, 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', '14.6.0.b.1', '16.48.0-16.e.1.2', '24.48.0-24.bz.1.3', '28.24.0-28.g.1.2', '48.96.0-48.bd.1.3', '56.48.0-56.bf.1.9', '112.96.0.?', '168.96.0.?', '336.192.1.?'], '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': [[2, 2, 7], [3, 4, 7], [7, 8, 3]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.96551538744897819336758232752', 'prec': 107}, 'szpiro_ratio': 3.793843875812311, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}