Elliptic curve isogeny class data - 121680.e

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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, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, -1, -4, 0, 0, -6, -4, 0, 6, 8, -2, -6, 4, 0, 6, 0, -10, -4, 0, -2, -8, -12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 121680, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '121680.e', 'trace_hash': 1750704086879226857}
• ec_padic •

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

  
  
  • id: 6361699
    {'lmfdb_iso': '121680.e', 'p': 7, 'prec': 20, 'unit': 3655126417512847, 'val': 1}
  • id: 6361704
    {'lmfdb_iso': '121680.e', 'p': 17, 'prec': 20, 'unit': 157486403324793425271999, 'val': 1}
  • id: 6361695
    {'lmfdb_iso': '121680.e', 'p': 19, 'prec': 20, 'unit': 1465719948403277590253664, 'val': 1}
  • id: 6361702
    {'lmfdb_iso': '121680.e', 'p': 29, 'prec': 20, 'unit': 1210003974022209909380232618, 'val': 1}
  • id: 6361710
    {'lmfdb_iso': '121680.e', 'p': 31, 'prec': 20, 'unit': 519916441349091585730491626, 'val': 1}
  • id: 6361698
    {'lmfdb_iso': '121680.e', 'p': 37, 'prec': 20, 'unit': 320824555419521225653657006687, 'val': 1}
  • id: 6361700
    {'lmfdb_iso': '121680.e', 'p': 41, 'prec': 20, 'unit': 1006818582697798013754455184026, 'val': 1}
  • id: 6361701
    {'lmfdb_iso': '121680.e', 'p': 43, 'prec': 20, 'unit': 154738038948532199300645832436, 'val': 1}
  • id: 6361706
    {'lmfdb_iso': '121680.e', 'p': 53, 'prec': 20, 'unit': 434237483939887250325972754640005, 'val': 1}
  • id: 6361709
    {'lmfdb_iso': '121680.e', 'p': 61, 'prec': 20, 'unit': 6444350278983481418665141482497898, 'val': 1}
  • id: 6361697
    {'lmfdb_iso': '121680.e', 'p': 67, 'prec': 20, 'unit': 22832319830563244966439552818854775, 'val': 1}
  • id: 6361707
    {'lmfdb_iso': '121680.e', 'p': 73, 'prec': 20, 'unit': 20544479874469637442433102095691288, 'val': 1}
  • id: 6361703
    {'lmfdb_iso': '121680.e', 'p': 79, 'prec': 20, 'unit': 195501196714420863351160941671496151, 'val': 1}
  • id: 6361705
    {'lmfdb_iso': '121680.e', 'p': 83, 'prec': 20, 'unit': 796565802152685252515251970240006901, 'val': 1}
  • id: 6361708
    {'lmfdb_iso': '121680.e', 'p': 89, 'prec': 20, 'unit': 2976206864814925705708995924057961043, 'val': 1}
  • id: 6361696
    {'lmfdb_iso': '121680.e', 'p': 97, 'prec': 20, 'unit': 43208109913718632311793379341079283355, '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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  
  • id: 794498
    {'Ciso': '121680dz', 'Clabel': '121680dz7', 'Cnumber': 7, 'abc_quality': 1.0818126452233845, 'absD': 1167434730049536000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -129796563, -569171178862], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 10616832, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0890939888411202034308407823', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [16778985534208729, 81000], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5334, -150368], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.96.1.dj.3', '40.12.0.v.1', '60.48.0.c.3', '104.12.0.?', '120.192.5.?', '156.48.0.?', '312.192.1.?', '520.24.0.?', '780.96.0.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.993925787616846496861917737', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232160', 'prec': 103}, 'szpiro_ratio': 5.778219606288636, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 794499
    {'Ciso': '121680dz', 'Clabel': '121680dz8', 'Cnumber': 8, 'abc_quality': 1.1359972360691755, 'absD': 84449850264000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -11036883, -1920823918], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 10616832, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0890939888411202034308407823', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [10316097499609, 5859375000], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -454, -544], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.3', '24.96.1.da.1', '40.12.0.bb.1', '52.12.0-4.c.1.2', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '1560.384.5.?'], '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': '2.7484814469042116242154794343', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232160', 'prec': 103}, 'szpiro_ratio': 5.146732518992022, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 794497
    {'Ciso': '121680dz', 'Clabel': '121680dz6', 'Cnumber': 6, 'abc_quality': 1.0522127879225598, 'absD': 129714970005504000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -8116563, -8883450862], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 5308416, 'elladic_images': ['2.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7425203985611475487222247215', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4102915888729, 9000000], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -334, -2368], 'min_quad_twist_disc': 156, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '12.48.0.a.1', '24.96.1.cp.2', '40.12.0.a.1', '52.12.0-2.a.1.1', '60.96.1.h.3', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '780.192.1.?', '1560.384.5.?'], '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': '5.4969628938084232484309588685', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626080', 'prec': 103}, 'szpiro_ratio': 5.067990028570259, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 794496
    {'Ciso': '121680dz', 'Clabel': '121680dz5', 'Cnumber': 5, 'abc_quality': 1.0501740895315954, 'absD': 486431137520640000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -7021443, 7161152258], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 3538944, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5397878445070653577332181638', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [2656166199049, 33750], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -289, 1862], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.4', '24.96.1.da.3', '40.12.0.bb.1', '52.12.0-4.c.1.2', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.91616048230140387473849314475', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703097', 'prec': 107}, 'szpiro_ratio': 5.03085547043244, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 794495
    {'Ciso': '121680dz', 'Clabel': '121680dz4', 'Cnumber': 4, 'abc_quality': 1.0339287621454463, 'absD': 76595392638550056960, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -1667523, -713879998], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 3538944, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5397878445070653577332181638', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [35578826569, 5314410], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -69, -194], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.96.1.dj.4', '40.12.0.v.1', '60.48.0.c.4', '104.12.0.?', '120.192.5.?', '156.48.0.?', '312.192.1.?', '520.24.0.?', '780.96.0.?', '1560.384.5.?'], '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': '3.6646419292056154989539725790', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703097', 'prec': 107}, 'szpiro_ratio': 4.662520586271418, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 794493
    {'Ciso': '121680dz', 'Clabel': '121680dz2', 'Cnumber': 2, 'abc_quality': 1.0045688963827404, 'absD': 1050691257044582400, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -450723, 105513122], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 1769472, 'elladic_images': ['2.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1932142542270927030246021031', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [702595369, 72900], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -19, 26], 'min_quad_twist_disc': 156, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '12.48.0.a.2', '24.96.1.cp.4', '40.12.0.a.1', '52.12.0-2.a.1.1', '60.96.1.h.1', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '780.192.1.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 13, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8323209646028077494769862895', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33171374939767582011699635760', 'prec': 107}, 'szpiro_ratio': 4.32733614875748, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 794494
    {'Ciso': '121680dz', 'Clabel': '121680dz3', 'Cnumber': 3, 'abc_quality': 1.0491971880149842, 'absD': 22138021547606016000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -329043, -237746158], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 2654208, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3959468082811748940136086608', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-273359449, 1536000], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -14, -64], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.1', '24.96.1.dh.4', '30.24.0.b.1', '40.12.0.bb.1', '52.12.0-4.c.1.1', '60.96.1.n.2', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '780.192.1.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.993925787616846496861917737', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12898119534359362912798979990', 'prec': 107}, 'szpiro_ratio': 4.449219120222503, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 794492
    {'Ciso': '121680dz', 'Clabel': '121680dz1', 'Cnumber': 1, 'abc_quality': 0.9968917246282063, 'absD': 31131592801320960, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 0, 0, 35997, 8071778], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 121680, 'degree': 884736, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8466406639471200483159860423', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [357911, 2160], 'lmfdb_iso': '121680.e', 'lmfdb_label': '121680.e8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 1, 2], 'min_quad_twist_disc': 156, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.2', '24.96.1.dh.3', '30.24.0.b.1', '40.12.0.bb.1', '52.12.0-4.c.1.1', '60.96.1.n.4', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '780.192.1.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.6646419292056154989539725790', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.67828733967764847482561241840', 'prec': 107}, 'szpiro_ratio': 3.8714094957190808, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}