Elliptic curve isogeny class data - 136710.dd

Formats: - HTML - YAML - JSON - 2026-09-22T07:09:29.843398

• 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, 0, 1, 1, 0, 0, -1, 0, -1, 4, 0, -6, 0, 0, 1, 2, 0, -4, 1], 'aplist': [-1, 0, 1, 0, 4, -6, 2, -4, 8, -6, 1, -2, 10, -4, 0, 10, -12, 2, -4, 0, -2, 0, 4, -14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 136710, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '136710.dd', 'trace_hash': 789638758597802335}
• lmfdb_iso 136710.dd 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: 889477
    {'Ciso': '136710du', 'Clabel': '136710du6', 'Cnumber': 6, 'abc_quality': 1.0294895610311774, 'absD': 4945274536860, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 52080, 'ainvs': [1, -1, 0, -135616329, -607843627007], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 136710, 'degree': 12582912, 'elladic_images': ['16.24.0.13'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9040868610765545327458723025', 'prec': 97}, 'faltings_index': 5, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [3216206300355197383681, 57660], 'lmfdb_iso': '136710.dd', 'lmfdb_label': '136710.dd1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -307520, -65664060], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.e.2', '60.12.0.h.1', '84.12.0.?', '120.24.0.?', '140.12.0.?', '168.24.0.?', '240.48.0.?', '248.24.0.?', '280.24.0.?', '336.48.0.?', '420.24.0.?', '496.48.0.?', '560.48.0.?', '840.48.0.?', '1680.96.0.?', '3720.48.0.?', '5208.48.0.?', '7440.96.1.?', '8680.48.0.?', '10416.96.0.?', '17360.96.0.?', '26040.96.0.?', '52080.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.9867598881646642089284949970', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 2205], [3, 8, 15190], [5, 6, 27342], [7, 26, 2790], [31, 32, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3818256422148430344955733123', 'prec': 97}, 'szpiro_ratio': 5.732438576803842, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 889475
    {'Ciso': '136710du', 'Clabel': '136710du4', 'Cnumber': 4, 'abc_quality': 1.0007838605326649, 'absD': 285144529795347600, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 26040, 'ainvs': [1, -1, 0, -8476029, -9495947147], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 136710, 'degree': 6291456, 'elladic_images': ['8.24.0.18'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5575132707965818780372562418', 'prec': 97}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 1, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4], 'jinv': [785209010066844481, 3324675600], 'lmfdb_iso': '136710.dd', 'lmfdb_label': '136710.dd2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -19220, -1027200], 'min_quad_twist_disc': 21, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.1', '60.24.0.c.1', '84.24.0.?', '120.48.0.?', '140.24.0.?', '168.48.0.?', '248.48.0.?', '280.48.0.?', '420.48.0.?', '840.96.0.?', '3720.96.1.?', '5208.96.0.?', '8680.96.0.?', '26040.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.9933799440823321044642474985', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 441], [3, 8, 15190], [5, 6, 27342], [7, 26, 2790], [31, 32, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0352520519348703797869572516', 'prec': 97}, 'szpiro_ratio': 5.029070372294241, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 889476
    {'Ciso': '136710du', 'Clabel': '136710du5', 'Cnumber': 5, 'abc_quality': 1.0019471514445586, 'absD': 4388949355018820181660, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 52080, 'ainvs': [1, -1, 0, -8343729, -9806825687], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 136710, 'degree': 12582912, 'elladic_images': ['8.24.0.90'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9040868610765545327458723025', 'prec': 97}, 'faltings_index': 4, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-749011598724977281, 51173462246460], 'lmfdb_iso': '136710.dd', 'lmfdb_label': '136710.dd3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -18920, -1060740], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '30.6.0.a.1', '60.12.0.g.1', '84.12.0.?', '120.48.0.?', '140.12.0.?', '168.48.0.?', '280.48.0.?', '420.24.0.?', '496.48.0.?', '840.96.0.?', '7440.96.1.?', '10416.96.0.?', '17360.96.0.?', '52080.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.9867598881646642089284949970', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 2205], [3, 8, 15190], [5, 6, 27342], [7, 26, 2790], [31, 32, 4410]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3818256422148430344955733123', 'prec': 97}, 'szpiro_ratio': 5.034516083486645, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 889474
    {'Ciso': '136710du', 'Clabel': '136710du3', 'Cnumber': 3, 'abc_quality': 0.9852559430448156, 'absD': 109025356976943750000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 52080, 'ainvs': [1, -1, 0, -1631709, 625898965], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 136710, 'degree': 6291456, 'elladic_images': ['8.24.0.88'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5575132707965818780372562418', 'prec': 97}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [5601911201812801, 1271193750000], 'lmfdb_iso': '136710.dd', 'lmfdb_label': '136710.dd4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3700, 67232], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '84.12.0.?', '124.12.0.?', '168.48.0.?', '240.48.0.?', '248.48.0.?', '560.48.0.?', '1680.96.0.?', '2604.24.0.?', '5208.96.0.?', '7440.96.1.?', '17360.96.0.?', '52080.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.99834498602058302611606187463', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 13671], [3, 8, 15190], [5, 6, 27342], [7, 26, 2790], [31, 32, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0352520519348703797869572516', 'prec': 97}, 'szpiro_ratio': 4.611092854556974, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 889473
    {'Ciso': '136710du', 'Clabel': '136710du2', 'Cnumber': 2, 'abc_quality': 0.9623179151422657, 'absD': 1068179299961760000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 26040, 'ainvs': [1, -1, 0, -538029, -143395547], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 136710, 'degree': 3145728, 'elladic_images': ['8.24.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2109396805166092233286401811', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4], 'jinv': [200828550012481, 12454560000], 'lmfdb_iso': '136710.dd', 'lmfdb_label': '136710.dd5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1220, -15600], 'min_quad_twist_disc': 21, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.2', '84.24.0.?', '120.48.0.?', '124.24.0.?', '168.48.0.?', '248.48.0.?', '280.48.0.?', '840.96.0.?', '2604.48.0.?', '3720.96.1.?', '5208.96.0.?', '8680.96.0.?', '26040.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9966899720411660522321237493', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 441], [3, 8, 15190], [5, 6, 27342], [7, 26, 2790], [31, 32, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.68867846165489772507834119092', 'prec': 97}, 'szpiro_ratio': 4.3296351093232825, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 889472
    {'Ciso': '136710du', 'Clabel': '136710du1', 'Cnumber': 1, 'abc_quality': 0.9618201087930732, 'absD': 39204860328345600, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 52080, 'ainvs': [1, -1, 0, 26451, -9387995], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 136710, 'degree': 1572864, 'elladic_images': ['16.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8643660902366365686200241203', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [23862997439, 457113600], 'lmfdb_iso': '136710.dd', 'lmfdb_label': '136710.dd6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 60, -1008], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.e.1', '62.6.0.b.1', '84.12.0.?', '120.24.0.?', '124.12.0.?', '168.24.0.?', '240.48.0.?', '248.24.0.?', '280.24.0.?', '336.48.0.?', '496.48.0.?', '560.48.0.?', '840.48.0.?', '1680.96.0.?', '2604.24.0.?', '3720.48.0.?', '5208.48.0.?', '7440.96.1.?', '8680.48.0.?', '10416.96.0.?', '17360.96.0.?', '26040.96.0.?', '52080.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.9933799440823321044642474985', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 13671], [3, 8, 15190], [5, 6, 27342], [7, 26, 2790], [31, 32, 4410]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.34210487137492507036972513012', 'prec': 97}, 'szpiro_ratio': 3.8587094626914578, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}