Elliptic curve isogeny class data - 232050.bf

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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, 0, 1, 1, -1, 1, 0, -4, -1, -1, -1, 0, 1, -1, -1, 4, 0], 'aplist': [-1, -1, 0, 1, -4, -1, -1, 4, -8, -2, 0, -6, 10, 4, 0, 10, -4, -2, -4, 8, -10, -16, 12, 10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 232050, 'isogeny_matrix': [[1, 2, 16, 4, 4, 8, 16, 8], [2, 1, 8, 2, 2, 4, 8, 4], [16, 8, 1, 16, 4, 2, 4, 8], [4, 2, 16, 1, 4, 8, 16, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 2, 8, 2, 1, 2, 4], [16, 8, 4, 16, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '232050.bf', 'trace_hash': 414055393845505124}
• lmfdb_iso 232050.bf 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: 1479590
    {'Ciso': '232050bf', 'Clabel': '232050bf8', 'Cnumber': 8, 'abc_quality': 1.0263816719000685, 'absD': 219883332845398136929218750, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 742560, 'ainvs': [1, 1, 0, -56463198500, -5164143505383750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 603979776, 'elladic_images': ['16.48.0.122'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.6240778196099909640286341041', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 16, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1274090022584975661628188489514561, 14072533302105480763470], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -2258527940, -41313148043070], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '16.48.0.v.2', '20.12.0-4.c.1.1', '24.48.0-8.bb.2.7', '40.48.0-8.bb.2.3', '48.96.0-16.v.2.12', '80.96.0.?', '120.96.0.?', '240.192.1.?', '2912.96.0.?', '3536.96.0.?', '3808.96.1.?', '8736.192.2.?', '10608.192.2.?', '11424.192.1.?', '14560.192.2.?', '17680.192.2.?', '19040.192.1.?', '43680.384.5.?', '49504.192.1.?', '53040.384.5.?', '57120.384.5.?', '148512.384.5.?', '247520.384.5.?', '742560.768.13.?'], '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': False, 'serre_invariants': [[2, 4, 75], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.8193588633929407767282544375', 'prec': 100}, 'szpiro_ratio': 6.951533516919843, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 1479588
    {'Ciso': '232050bf', 'Clabel': '232050bf6', 'Cnumber': 6, 'abc_quality': 1.0085585396011327, 'absD': 16151454407859546898139062500, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 371280, 'ainvs': [1, 1, 0, -3531764750, -80555676600000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 301989888, 'elladic_images': ['8.48.0.144'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.2775042293300183093200180434', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [311802066473807207098058600161, 1033693082103011001480900], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -141270590, -644445412800], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.l.1', '20.24.0-4.b.1.1', '24.96.0-8.l.1.3', '40.96.0-8.l.1.1', '120.192.1.?', '1456.96.0.?', '1904.96.1.?', '3536.96.0.?', '4368.192.2.?', '5712.192.1.?', '7280.192.2.?', '9520.192.1.?', '10608.192.2.?', '17680.192.2.?', '21840.384.5.?', '24752.192.1.?', '28560.384.5.?', '53040.384.5.?', '74256.384.5.?', '123760.384.5.?', '371280.768.13.?'], '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': False, 'serre_invariants': [[2, 4, 25], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.4727852731129681220196383768', 'prec': 100}, 'szpiro_ratio': 6.278480451444418, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 1479585
    {'Ciso': '232050bf', 'Clabel': '232050bf3', 'Cnumber': 3, 'abc_quality': 1.0084010450121792, 'absD': 62141075134277343750000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 742560, 'ainvs': [1, 1, 0, -3475384250, 78857749126500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 150994944, 'elladic_images': ['16.48.0.96'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9309306390500456546114019827', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [297106512928238351998640242081, 3977028808593750000], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -139015370, 630861993012], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '16.48.0.v.1', '20.12.0-4.c.1.2', '40.48.0-8.bb.1.7', '80.96.0.?', '96.96.0.?', '476.12.0.?', '480.192.1.?', '952.48.0.?', '1904.96.1.?', '2380.24.0.?', '2912.96.0.?', '4368.96.2.?', '4760.96.0.?', '7072.96.0.?', '8736.192.2.?', '9520.192.1.?', '10608.96.2.?', '11424.192.1.?', '14560.192.2.?', '21216.192.2.?', '21840.192.2.?', '35360.192.2.?', '43680.384.5.?', '49504.192.1.?', '53040.192.2.?', '57120.384.5.?', '74256.192.5.?', '106080.384.5.?', '148512.384.5.?', '247520.384.5.?', '371280.384.5.?', '742560.768.13.?'], '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': False, 'serre_invariants': [[2, 4, 2975], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.1262116828329954673110223161', 'prec': 100}, 'szpiro_ratio': 6.274572801041045, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 1479589
    {'Ciso': '232050bf', 'Clabel': '232050bf7', 'Cnumber': 7, 'abc_quality': 1.0260946324567908, 'absD': 9255563984155063854687604218750, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 742560, 'ainvs': [1, 1, 0, -2010131000, -150427576766250], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 603979776, 'elladic_images': ['16.48.0.122'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.6240778196099909640286341041', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-57487943130312093140621093761, 592356094985924086700006670], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -80405240, -1203420614130], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '16.48.0.v.2', '20.12.0-4.c.1.1', '24.48.0-8.bb.2.8', '40.48.0-8.bb.2.3', '48.96.0-16.v.2.10', '80.96.0.?', '120.96.0.?', '240.192.1.?', '1456.96.0.?', '3808.96.1.?', '4368.192.2.?', '7072.96.0.?', '7280.192.2.?', '11424.192.1.?', '19040.192.1.?', '21216.192.2.?', '21840.384.5.?', '35360.192.2.?', '49504.192.1.?', '57120.384.5.?', '106080.384.5.?', '148512.384.5.?', '247520.384.5.?', '742560.768.13.?'], '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': False, 'serre_invariants': [[2, 4, 75], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.8193588633929407767282544375', 'prec': 100}, 'szpiro_ratio': 6.379117921091511, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 1479586
    {'Ciso': '232050bf', 'Clabel': '232050bf4', 'Cnumber': 4, 'abc_quality': 1.063140702220356, 'absD': 2070330637022695362656250000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 371280, 'ainvs': [1, 1, 0, -318652250, -31864237500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 150994944, 'elladic_images': ['8.48.0.45'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9309306390500456546114019827', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4], 'jinv': [229010110533436633465952161, 132501160769452503210000], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -12746090, -254913900], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0.b.1', '8.48.0.c.1', '20.48.0-4.b.1.1', '24.96.0-8.c.1.7', '40.96.0-8.c.1.1', '120.192.1.?', '952.96.1.?', '1456.96.0.?', '2856.192.1.?', '3536.96.0.?', '4368.192.2.?', '4760.192.1.?', '7280.192.2.?', '10608.192.2.?', '14280.384.5.?', '17680.192.2.?', '21840.384.5.?', '24752.192.1.?', '53040.384.5.?', '74256.384.5.?', '123760.384.5.?', '371280.768.13.?'], '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': False, 'serre_invariants': [[2, 4, 25], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.1262116828329954673110223161', 'prec': 100}, 'szpiro_ratio': 5.694382662547741, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 1479584
    {'Ciso': '232050bf', 'Clabel': '232050bf2', 'Cnumber': 2, 'abc_quality': 0.9864606854599206, 'absD': 4146268247001562500000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 371280, 'ainvs': [1, 1, 0, -217402250, 1229812012500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 75497472, 'elladic_images': ['8.48.0.98'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5843570487700729999027859220', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [72727020009972527154752161, 265361167808100000000], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -8696090, 9838496100], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.l.2', '20.24.0-4.b.1.3', '40.96.0-8.l.2.2', '48.96.0-8.l.2.5', '240.192.1.?', '476.24.0.?', '952.96.1.?', '1456.96.0.?', '2380.48.0.?', '3536.96.0.?', '4368.192.2.?', '4760.192.1.?', '5712.192.1.?', '7280.192.2.?', '10608.192.2.?', '17680.192.2.?', '21840.384.5.?', '24752.192.1.?', '28560.384.5.?', '53040.384.5.?', '74256.384.5.?', '123760.384.5.?', '371280.768.13.?'], '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': False, 'serre_invariants': [[2, 4, 25], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.7796380925530228126024062554', 'prec': 100}, 'szpiro_ratio': 5.601539257430565, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 1479583
    {'Ciso': '232050bf', 'Clabel': '232050bf1', 'Cnumber': 1, 'abc_quality': 0.9819893668946688, 'absD': 554056067859840000000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 742560, 'ainvs': [1, 1, 0, -7450250, 36654796500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 37748736, 'elladic_images': ['16.48.0.96'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2377834584901003451941698612', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-2926956820564562516641, 35459588343029760000], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -298010, 293238372], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '16.48.0.v.1', '20.12.0-4.c.1.2', '40.48.0-8.bb.1.7', '80.96.0.?', '96.96.0.?', '238.6.0.?', '476.12.0.?', '480.192.1.?', '952.48.0.?', '1456.96.0.?', '1904.96.1.?', '2380.24.0.?', '3536.96.0.?', '4760.96.0.?', '7280.192.2.?', '8736.192.2.?', '9520.192.1.?', '11424.192.1.?', '17680.192.2.?', '21216.192.2.?', '24752.192.1.?', '43680.384.5.?', '57120.384.5.?', '106080.384.5.?', '123760.384.5.?', '148512.384.5.?', '742560.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2975], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4330645022730501578937901946', 'prec': 100}, 'szpiro_ratio': 5.032327307193162, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 1479587
    {'Ciso': '232050bf', 'Clabel': '232050bf5', 'Cnumber': 5, 'abc_quality': 1.070974036311186, 'absD': 132510439724667324305639062500, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 742560, 'ainvs': [1, 1, 0, 1274460250, -253306875000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 232050, 'degree': 301989888, 'elladic_images': ['16.48.0.60'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.2775042293300183093200180434', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [14651516183052242700771495839, 8480668142378708755560900], 'lmfdb_iso': '232050.bf', 'lmfdb_label': '232050.bf8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 50978410, -2026455000], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0.q.1', '16.48.0.j.1', '20.24.0-4.d.1.1', '24.48.0-8.q.1.2', '40.48.0-8.q.1.2', '48.96.0-16.j.1.10', '80.96.0.?', '120.96.0.?', '240.192.1.?', '952.48.0.?', '1428.24.0.?', '1904.96.1.?', '2856.96.0.?', '2912.96.0.?', '4760.96.0.?', '5712.192.1.?', '7072.96.0.?', '7140.48.0.?', '8736.192.2.?', '9520.192.1.?', '14280.192.1.?', '14560.192.2.?', '21216.192.2.?', '28560.384.5.?', '35360.192.2.?', '43680.384.5.?', '49504.192.1.?', '106080.384.5.?', '148512.384.5.?', '247520.384.5.?', '742560.768.13.?'], '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': False, 'serre_invariants': [[2, 4, 25], [3, 4, 77350], [5, 18, 9282], [7, 8, 33150], [13, 14, 17850], [17, 18, 13650]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.4727852731129681220196383768', 'prec': 100}, 'szpiro_ratio': 6.030977659429754, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}