Elliptic curve isogeny class data - 68770.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, -2, 1, -1, 2, 4, -1, 1, 1, 6, -2, 1, -4, 2, 1, 6, -1, -2, -1], 'aplist': [-1, -2, -1, 4, 6, 1, 6, -2, 0, -6, 2, -2, -6, -2, -12, -6, 6, -2, 4, -6, -10, 4, 0, 6, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 68770, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '68770.a', 'trace_hash': 936824825511992903}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 3517548
    {'lmfdb_iso': '68770.a', 'p': 7, 'prec': 20, 'unit': 9906418052844311, 'val': 1}
  • id: 3517553
    {'lmfdb_iso': '68770.a', 'p': 11, 'prec': 20, 'unit': 27215500856999879674, 'val': 1}
  • id: 3517554
    {'lmfdb_iso': '68770.a', 'p': 17, 'prec': 20, 'unit': 38107715732508141337733, 'val': 1}
  • id: 3517555
    {'lmfdb_iso': '68770.a', 'p': 19, 'prec': 20, 'unit': 1544923764021003006017009, 'val': 1}
  • id: 3517551
    {'lmfdb_iso': '68770.a', 'p': 29, 'prec': 20, 'unit': 4634394006321049659192971518, 'val': 1}
  • id: 3517563
    {'lmfdb_iso': '68770.a', 'p': 31, 'prec': 20, 'unit': 4333262045090900310072779676, 'val': 1}
  • id: 3517547
    {'lmfdb_iso': '68770.a', 'p': 37, 'prec': 20, 'unit': 313050183373646987888482742478, 'val': 1}
  • id: 3517549
    {'lmfdb_iso': '68770.a', 'p': 41, 'prec': 20, 'unit': 3021646996786735963506284768249, 'val': 1}
  • id: 3517550
    {'lmfdb_iso': '68770.a', 'p': 43, 'prec': 20, 'unit': 3925270738950235572775619405324, 'val': 1}
  • id: 3517561
    {'lmfdb_iso': '68770.a', 'p': 47, 'prec': 20, 'unit': 16286516719188375258111888417153, 'val': 1}
  • id: 3517556
    {'lmfdb_iso': '68770.a', 'p': 53, 'prec': 20, 'unit': 8959111719481933483436736614215, 'val': 1}
  • id: 3517557
    {'lmfdb_iso': '68770.a', 'p': 59, 'prec': 20, 'unit': 52320900252309456178820271752011, 'val': 2}
  • id: 3517562
    {'lmfdb_iso': '68770.a', 'p': 61, 'prec': 20, 'unit': 7644868022112154176701345223818170, 'val': 1}
  • id: 3517546
    {'lmfdb_iso': '68770.a', 'p': 67, 'prec': 20, 'unit': 41160218568776484037838203542107337, 'val': 1}
  • id: 3517560
    {'lmfdb_iso': '68770.a', 'p': 71, 'prec': 20, 'unit': 85796669661303794954528006850795622, 'val': 1}
  • id: 3517558
    {'lmfdb_iso': '68770.a', 'p': 73, 'prec': 20, 'unit': 202085453852703097274211839683302328, 'val': 1}
  • id: 3517552
    {'lmfdb_iso': '68770.a', 'p': 79, 'prec': 20, 'unit': 245240245217429751896471114986930682, 'val': 1}
  • id: 3517559
    {'lmfdb_iso': '68770.a', 'p': 89, 'prec': 20, 'unit': 3855239851556335064638006732424439988, 'val': 1}
  • id: 3517545
    {'lmfdb_iso': '68770.a', 'p': 97, 'prec': 20, 'unit': 5092042963563678737218598077866487884, 'val': 1}
• 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: 454592
    {'Ciso': '68770d', 'Clabel': '68770d3', 'Cnumber': 3, 'abc_quality': 0.9543225417743602, 'absD': 6660809689763840, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 35880, 'ainvs': [1, 0, 1, -109779, 13428782], 'analytic_rank': 1, 'bad_primes': [2, 5, 13, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 68770, 'degree': 855360, 'elladic_images': ['4.6.0.3', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7981965104422384309932128606', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [988345570681, 44994560], 'lmfdb_iso': '68770.a', 'lmfdb_label': '68770.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -208, -1122], 'min_quad_twist_disc': -23, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.b.1', '6.12.0.a.1', '12.24.0.f.1', '24.48.0.br.2', '69.8.0-3.a.1.1', '130.6.0.?', '138.24.0.?', '184.12.0.?', '260.24.0.?', '276.48.0.?', '390.24.0.?', '552.96.0.?', '780.96.3.?', '1560.192.9.?', '8970.48.0.?', '11960.48.0.?', '17940.192.3.?', '35880.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.1993283701203162428103910315', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 34385], [3, 2, 2645], [5, 6, 13754], [13, 14, 5290], [23, 266, 130]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.23044940247766358558983644470', 'prec': 103}, 'szpiro_ratio': 4.168619486407582, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 454590
    {'Ciso': '68770d', 'Clabel': '68770d1', 'Cnumber': 1, 'abc_quality': 0.906187683689355, 'absD': 3848933114000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 35880, 'ainvs': [1, 0, 1, -17204, -864798], 'analytic_rank': 1, 'bad_primes': [2, 5, 13, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 68770, 'degree': 285120, 'elladic_images': ['4.6.0.3', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2488903661081835852955902421', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [3803721481, 26000], 'lmfdb_iso': '68770.a', 'lmfdb_label': '68770.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -33, 68], 'min_quad_twist_disc': -23, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.b.1', '6.12.0.a.1', '12.24.0.f.1', '24.48.0.br.1', '69.8.0-3.a.1.2', '130.6.0.?', '138.24.0.?', '184.12.0.?', '260.24.0.?', '276.48.0.?', '390.24.0.?', '552.96.0.?', '780.96.3.?', '1560.192.9.?', '8970.48.0.?', '11960.48.0.?', '17940.192.3.?', '35880.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.5979851103609487284311730946', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 34385], [3, 2, 13754], [5, 6, 13754], [13, 14, 5290], [23, 266, 130]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.31885674185639126010778617380', 'prec': 107}, 'szpiro_ratio': 3.6694462532387893, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 454591
    {'Ciso': '68770d', 'Clabel': '68770d2', 'Cnumber': 2, 'abc_quality': 0.9774623648888189, 'absD': 1563629077562500, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 35880, 'ainvs': [1, 0, 1, -6624, -1914334], 'analytic_rank': 1, 'bad_primes': [2, 5, 13, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 68770, 'degree': 570240, 'elladic_images': ['4.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5954639563881562400042063029', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-217081801, 10562500], 'lmfdb_iso': '68770.a', 'lmfdb_label': '68770.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -13, 156], 'min_quad_twist_disc': -23, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.a.1', '6.12.0.a.1', '12.48.0.b.1', '69.8.0-3.a.1.2', '92.12.0.?', '138.24.0.?', '260.12.0.?', '276.96.0.?', '520.24.0.?', '780.96.3.?', '1560.192.9.?', '5980.24.0.?', '11960.48.0.?', '17940.192.3.?', '35880.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7989925551804743642155865473', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 529], [3, 2, 13754], [5, 6, 13754], [13, 14, 5290], [23, 266, 130]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.027716848423581394600829886996', 'prec': 107}, 'szpiro_ratio': 3.811306908558756, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 454593
    {'Ciso': '68770d', 'Clabel': '68770d4', 'Cnumber': 4, 'abc_quality': 1.0187728994158647, 'absD': 1143265538157121600, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 35880, 'ainvs': [1, 0, 1, 59501, 51144366], 'analytic_rank': 1, 'bad_primes': [2, 5, 13, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 68770, 'degree': 1710720, 'elladic_images': ['4.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1447701007222110857018289213', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [157376536199, 7722894400], 'lmfdb_iso': '68770.a', 'lmfdb_label': '68770.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 112, -4194], 'min_quad_twist_disc': -23, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.a.1', '6.12.0.a.1', '12.48.0.b.2', '69.8.0-3.a.1.1', '92.12.0.?', '138.24.0.?', '260.12.0.?', '276.96.0.?', '520.24.0.?', '780.96.3.?', '1560.192.9.?', '5980.24.0.?', '11960.48.0.?', '17940.192.3.?', '35880.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5996641850601581214051955158', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 529], [3, 2, 2645], [5, 6, 13754], [13, 14, 5290], [23, 266, 130]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.57702299275763624029845250540', 'prec': 103}, 'szpiro_ratio': 4.401236856166604, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}