Elliptic curve isogeny class data - 110670.cm

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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, 1, 1, 1, 1, -4, 1, -2, 1, 1, 1, 1, 1, 4, 1], 'aplist': [1, 1, 1, 1, -4, -2, 1, 4, 8, -2, -1, 6, 10, -4, 0, 6, 12, -2, 4, -8, 10, 0, -12, -6, -14], 'class_deg': 16, 'class_size': 8, 'conductor': 110670, 'isogeny_matrix': [[1, 16, 2, 4, 8, 16, 4, 8], [16, 1, 8, 4, 2, 4, 16, 8], [2, 8, 1, 2, 4, 8, 2, 4], [4, 4, 2, 1, 2, 4, 4, 2], [8, 2, 4, 2, 1, 2, 8, 4], [16, 4, 8, 4, 2, 1, 16, 8], [4, 16, 2, 4, 8, 16, 1, 8], [8, 8, 4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '110670.cm', 'trace_hash': 2030220627107999368}
• lmfdb_iso 110670.cm 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: 725233
    {'Ciso': '110670cp', 'Clabel': '110670cp8', 'Cnumber': 8, 'abc_quality': 1.039784151271963, 'absD': 2359330710565906457438184052500, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 354144, 'ainvs': [1, 0, 0, -258731208280, -50654853221670100], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 788529152, 'elladic_images': ['16.96.0.149'], 'faltings_height': {'__RealLiteral__': 0, 'data': '5.1080513193284656759127979465', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 16, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1915447099311696788795300773853656437121, 2359330710565906457438184052500], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -258731208280, -50654853221670100], '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', '16.96.0-16.v.2.5', '42.6.0.a.1', '84.24.0.?', '168.96.0.?', '336.192.1.?', '1488.192.2.?', '1632.192.2.?', '3472.192.2.?', '3808.192.2.?', '10416.384.5.?', '11424.384.5.?', '16864.192.1.?', '50592.384.5.?', '118048.384.5.?', '354144.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 21], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 16, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '5.1080513193284656759127979465', 'prec': 100}, 'szpiro_ratio': 7.787874152908431, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 725229
    {'Ciso': '110670cp', 'Clabel': '110670cp4', 'Cnumber': 4, 'abc_quality': 1.0302181844877023, 'absD': 226978257155929261920000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 354144, 'ainvs': [1, 0, 0, -36426360100, 2675908664482832], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 197132288, 'elladic_images': ['16.96.0.95'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.4149041387685203664955658251', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [5345287166085790635663218704920974401, 226978257155929261920000], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -36426360100, 2675908664482832], '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', '16.96.0-16.v.1.2', '672.192.1.?', '816.192.2.?', '1488.192.2.?', '2108.24.0.?', '3808.192.2.?', '4216.96.0.?', '6944.192.2.?', '8432.192.1.?', '11424.384.5.?', '20832.384.5.?', '25296.384.5.?', '118048.384.5.?', '354144.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 527], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '4.4149041387685203664955658251', 'prec': 100}, 'szpiro_ratio': 7.28147368227307, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [8]}
  • id: 725231
    {'Ciso': '110670cp', 'Clabel': '110670cp6', 'Cnumber': 6, 'abc_quality': 1.0263485391766844, 'absD': 16398477508430925116750756250000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 177072, 'ainvs': [1, 0, 0, -16306945780, -777467273017600], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 394264576, 'elladic_images': ['8.96.0.60'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.7614777290484930212041818858', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [479558500651862026155270257138637121, 16398477508430925116750756250000], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -16306945780, -777467273017600], '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.l.1.1', '84.48.0.?', '168.192.1.?', '816.192.2.?', '1488.192.2.?', '1904.192.2.?', '3472.192.2.?', '5712.384.5.?', '8432.192.1.?', '10416.384.5.?', '25296.384.5.?', '59024.384.5.?', '177072.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '4.7614777290484930212041818858', 'prec': 100}, 'szpiro_ratio': 7.073875895013549, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 725228
    {'Ciso': '110670cp', 'Clabel': '110670cp3', 'Cnumber': 3, 'abc_quality': 1.0208830799951816, 'absD': 585975791707934414062500000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 177072, 'ainvs': [1, 0, 0, -2525695780, 32101233232400], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 197132288, 'elladic_images': ['8.96.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.4149041387685203664955658251', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4], 'jinv': [1781832302709884421209712638637121, 585975791707934414062500000000], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -2525695780, 32101233232400], '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.c.1.1', '168.192.1.?', '816.192.2.?', '1488.192.2.?', '1904.192.2.?', '3472.192.2.?', '4216.192.1.?', '5712.384.5.?', '10416.384.5.?', '25296.384.5.?', '59024.384.5.?', '88536.384.5.?', '177072.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '4.4149041387685203664955658251', 'prec': 100}, 'szpiro_ratio': 6.592123247008471, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
  • id: 725227
    {'Ciso': '110670cp', 'Clabel': '110670cp2', 'Cnumber': 2, 'abc_quality': 1.014562548669828, 'absD': 268915325631261926400000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 177072, 'ainvs': [1, 0, 0, -2276760100, 41806588162832], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 98566144, 'elladic_images': ['8.96.0.40'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.0683305484885477117869497643', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1305195379419707692723460338574401, 268915325631261926400000000], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -2276760100, 41806588162832], '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.l.2.2', '336.192.1.?', '816.192.2.?', '1488.192.2.?', '1904.192.2.?', '2108.48.0.?', '3472.192.2.?', '4216.192.1.?', '5712.384.5.?', '10416.384.5.?', '25296.384.5.?', '59024.384.5.?', '177072.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 14, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '4.0683305484885477117869497643', 'prec': 100}, 'szpiro_ratio': 6.56532100698919, 'torsion': 16, 'torsion_primes': [2], 'torsion_structure': [2, 8]}
  • id: 725226
    {'Ciso': '110670cp', 'Clabel': '110670cp1', 'Cnumber': 1, 'abc_quality': 1.0003817703541293, 'absD': 146211902909299839467520000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 354144, 'ainvs': [1, 0, 0, -126851620, 800523760400], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 49283072, 'elladic_images': ['16.96.0.95'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7217569582085750570783337036', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-225741686871429146260559062081, 146211902909299839467520000], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -126851620, 800523760400], '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', '16.96.0-16.v.1.2', '672.192.1.?', '1054.6.0.?', '1632.192.2.?', '1904.192.2.?', '2108.24.0.?', '2976.192.2.?', '3472.192.2.?', '4216.96.0.?', '8432.192.1.?', '11424.384.5.?', '20832.384.5.?', '50592.384.5.?', '59024.384.5.?', '354144.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 527], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.7217569582085750570783337036', 'prec': 100}, 'szpiro_ratio': 5.884141834621277, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [8]}
  • id: 725232
    {'Ciso': '110670cp', 'Clabel': '110670cp7', 'Cnumber': 7, 'abc_quality': 1.0544306075265952, 'absD': 3189643093950949672061474484052500, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 354144, 'ainvs': [1, 0, 0, 5617316720, -2712410599365100], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 788529152, 'elladic_images': ['16.96.0.149'], 'faltings_height': {'__RealLiteral__': 0, 'data': '5.1080513193284656759127979465', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [19602454118850102896203267379162879, 3189643093950949672061474484052500], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 5617316720, -2712410599365100], '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', '16.96.0-16.v.2.5', '84.24.0.?', '168.96.0.?', '336.192.1.?', '816.192.2.?', '1904.192.2.?', '2976.192.2.?', '5712.384.5.?', '6944.192.2.?', '16864.192.1.?', '20832.384.5.?', '50592.384.5.?', '118048.384.5.?', '354144.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 21], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 64, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '5.1080513193284656759127979465', 'prec': 100}, 'szpiro_ratio': 7.283806630099089, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 725230
    {'Ciso': '110670cp', 'Clabel': '110670cp5', 'Cnumber': 5, 'abc_quality': 1.0304080502994275, 'absD': 45626792684197425842285156250000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 354144, 'ainvs': [1, 0, 0, 7272583340, 220528019677472], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17, 31], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 110670, 'degree': 394264576, 'elladic_images': ['16.96.0.25'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.7614777290484930212041818858', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [42539250356844378683161410804461759, 45626792684197425842285156250000], 'lmfdb_iso': '110670.cm', 'lmfdb_label': '110670.cm8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 7272583340, 220528019677472], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '8.48.0-8.q.1.2', '16.96.0-16.j.1.2', '168.96.0.?', '336.192.1.?', '1632.192.2.?', '2976.192.2.?', '3808.192.2.?', '4216.96.0.?', '6944.192.2.?', '8432.192.1.?', '11424.384.5.?', '20832.384.5.?', '50592.384.5.?', '88536.192.1.?', '118048.384.5.?', '177072.384.5.?', '354144.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 36890], [5, 6, 22134], [7, 8, 15810], [17, 18, 6510], [31, 32, 3570]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '4.7614777290484930212041818858', 'prec': 100}, 'szpiro_ratio': 6.865302238601516, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}