Elliptic curve isogeny class data - 31680.cx

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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, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, 0, 1, 0, -1, 2, -2, 4, 0, -2, 0, 2, -2, 12, -8, 6, -12, -6, -4, 0, -6, -16, 4, -10, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 31680, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '31680.cx', 'trace_hash': 1607573037386529976}
• ec_padic •

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

  
  
  • id: 1540918
    {'lmfdb_iso': '31680.cx', 'p': 13, 'prec': 20, 'unit': 517930220648515513186, 'val': 1}
  • id: 1540920
    {'lmfdb_iso': '31680.cx', 'p': 17, 'prec': 20, 'unit': 201920224322069215794794, 'val': 1}
  • id: 1540921
    {'lmfdb_iso': '31680.cx', 'p': 19, 'prec': 20, 'unit': 966114309493923858323594, 'val': 1}
  • id: 1540917
    {'lmfdb_iso': '31680.cx', 'p': 29, 'prec': 20, 'unit': 111285946085483741647399983, 'val': 2}
  • id: 1540914
    {'lmfdb_iso': '31680.cx', 'p': 37, 'prec': 20, 'unit': 251480802180883214611376686161, 'val': 1}
  • id: 1540915
    {'lmfdb_iso': '31680.cx', 'p': 41, 'prec': 20, 'unit': 4107926523186834816948122664478, 'val': 1}
  • id: 1540916
    {'lmfdb_iso': '31680.cx', 'p': 43, 'prec': 20, 'unit': 2849994899524134310109664592073, 'val': 1}
  • id: 1540926
    {'lmfdb_iso': '31680.cx', 'p': 47, 'prec': 20, 'unit': 40189033218364457032201875209437, 'val': 1}
  • id: 1540922
    {'lmfdb_iso': '31680.cx', 'p': 53, 'prec': 20, 'unit': 54716571617063965696871926523393, 'val': 1}
  • id: 1540923
    {'lmfdb_iso': '31680.cx', 'p': 59, 'prec': 20, 'unit': 159862775653037138073263408784841, 'val': 1}
  • id: 1540927
    {'lmfdb_iso': '31680.cx', 'p': 61, 'prec': 20, 'unit': 1760488750040134835399709987654668, 'val': 1}
  • id: 1540913
    {'lmfdb_iso': '31680.cx', 'p': 67, 'prec': 20, 'unit': 2506879964272804411347551496813749, 'val': 1}
  • id: 1540924
    {'lmfdb_iso': '31680.cx', 'p': 73, 'prec': 20, 'unit': 34965351383626917201426270487573843, 'val': 1}
  • id: 1540919
    {'lmfdb_iso': '31680.cx', 'p': 79, 'prec': 20, 'unit': 414807940767433538312721923281091795, 'val': 1}
  • id: 1540912
    {'lmfdb_iso': '31680.cx', 'p': 83, 'prec': 20, 'unit': 1787994871490477154967569890388998974, 'val': 1}
  • id: 1540925
    {'lmfdb_iso': '31680.cx', 'p': 89, 'prec': 20, 'unit': 4647374008297841719040540165034644981, 'val': 1}
  • id: 1540911
    {'lmfdb_iso': '31680.cx', 'p': 97, 'prec': 20, 'unit': 31418502007825820378319970858806984912, '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: 210691
    {'Ciso': '31680bd', 'Clabel': '31680bd6', 'Cnumber': 6, 'abc_quality': 1.0074430799323078, 'absD': 54195609600000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [0, 0, 0, -2237772, 1288414064], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 31680, 'degree': 393216, 'elladic_images': ['8.24.0.46'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2891155556563764425096654508', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 75, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6484907238722641, 283593750], 'lmfdb_iso': '31680.cx', 'lmfdb_label': '31680.cx1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3885, -93525], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.12', '24.48.0-24.bj.1.4', '80.48.0.?', '88.48.0.?', '240.96.0.?', '264.96.0.?', '880.96.0.?', '2640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1692769217042847706053433290', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.70008864048240363268619465015', 'prec': 103}, 'szpiro_ratio': 5.35310402360095, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
  • id: 210689
    {'Ciso': '31680bd', 'Clabel': '31680bd4', 'Cnumber': 4, 'abc_quality': 0.990076389601979, 'absD': 275841857617920, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [0, 0, 0, -676812, -214312336], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 31680, 'degree': 196608, 'elladic_images': ['16.24.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9425419653764037878010493900', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 75, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [179415687049201, 1443420], 'lmfdb_iso': '31680.cx', 'lmfdb_label': '31680.cx2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1175, 15405], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.8', '24.24.0-8.n.1.9', '40.24.0.cb.1', '48.48.0-48.h.1.19', '80.48.0.?', '88.24.0.?', '120.48.0.?', '176.48.0.?', '220.12.0.?', '240.96.0.?', '264.48.0.?', '440.48.0.?', '528.96.0.?', '880.96.0.?', '1320.96.0.?', '2640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.3542153736342781648427466323', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 495], [3, 8, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.35351505020243097797757858935', 'prec': 103}, 'szpiro_ratio': 5.006932567762989, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 210688
    {'Ciso': '31680bd', 'Clabel': '31680bd3', 'Cnumber': 3, 'abc_quality': 0.9688781293995236, 'absD': 62953620111360000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1320, 'ainvs': [0, 0, 0, -146892, 17995376], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 31680, 'degree': 196608, 'elladic_images': ['4.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9425419653764037878010493900', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 75, 'isogeny_degrees': [1, 2, 4], 'jinv': [1834216913521, 329422500], 'lmfdb_iso': '31680.cx', 'lmfdb_label': '31680.cx3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -255, -1323], 'min_quad_twist_disc': -24, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.2', '24.48.0-24.e.1.12', '40.48.0-40.i.1.30', '88.48.0.?', '120.96.0.?', '264.96.0.?', '440.96.0.?', '1320.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3385538434085695412106866581', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.35351505020243097797757858935', 'prec': 103}, 'szpiro_ratio': 4.564696459564392, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 210687
    {'Ciso': '31680bd', 'Clabel': '31680bd2', 'Cnumber': 2, 'abc_quality': 0.9379136566213516, 'absD': 749200107110400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1320, 'ainvs': [0, 0, 0, -43212, -3196816], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 31680, 'degree': 98304, 'elladic_images': ['8.24.0.24'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5959683750964311330924333293', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 75, 'isogeny_degrees': [1, 2, 4], 'jinv': [46694890801, 3920400], 'lmfdb_iso': '31680.cx', 'lmfdb_label': '31680.cx4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -75, 225], 'min_quad_twist_disc': -24, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0-4.b.1.5', '24.48.0-24.l.1.9', '40.48.0-40.i.2.15', '88.48.0.?', '120.96.0.?', '220.24.0.?', '264.96.0.?', '440.96.0.?', '1320.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.6771076868171390824213733162', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0069414599224583232689625286521', 'prec': 110}, 'szpiro_ratio': 4.2104957438125306, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 210686
    {'Ciso': '31680bd', 'Clabel': '31680bd1', 'Cnumber': 1, 'abc_quality': 0.921271538093497, 'absD': 24216569118720, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [0, 0, 0, 2868, -229264], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 31680, 'degree': 49152, 'elladic_images': ['16.24.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2493947848164584783838172686', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 75, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13651919, 126720], 'lmfdb_iso': '31680.cx', 'lmfdb_label': '31680.cx5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 5, 17], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.8', '24.24.0-8.n.1.9', '40.24.0-8.n.1.3', '48.48.0-48.h.1.19', '80.48.0.?', '88.24.0.?', '110.6.0.?', '120.48.0.?', '176.48.0.?', '220.12.0.?', '240.96.0.?', '264.48.0.?', '440.48.0.?', '528.96.0.?', '880.96.0.?', '1320.96.0.?', '2640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.3542153736342781648427466323', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 495], [3, 8, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33963213035751433143965353205', 'prec': 107}, 'szpiro_ratio': 3.6868454232102246, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 210690
    {'Ciso': '31680bd', 'Clabel': '31680bd5', 'Cnumber': 5, 'abc_quality': 1.0027749166866642, 'absD': 6144693013669478400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [0, 0, 0, 285108, 103876976], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 31680, 'degree': 393216, 'elladic_images': ['8.24.0.56'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2891155556563764425096654508', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 75, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13411719834479, 32153832150], 'lmfdb_iso': '31680.cx', 'lmfdb_label': '31680.cx6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 495, -7473], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.n.1.10', '24.48.0-24.bn.1.2', '40.48.0-40.cb.2.14', '120.96.0.?', '176.48.0.?', '528.96.0.?', '880.96.0.?', '2640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.6771076868171390824213733162', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.70008864048240363268619465015', 'prec': 103}, 'szpiro_ratio': 4.867165447764522, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}