Elliptic curve isogeny class data - 4950.bg

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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, 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, -6, 0, 0, 1, 2, 0, -4, 0], 'aplist': [1, 0, 0, 0, -1, -6, 2, -4, 0, 10, 0, -6, -2, -4, -8, -10, 4, -2, 4, 8, -2, -8, -12, 6, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 4950, 'isogeny_matrix': [[1, 8, 2, 4, 4, 8], [8, 1, 4, 8, 2, 4], [2, 4, 1, 2, 2, 4], [4, 8, 2, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '4950.bg', 'trace_hash': 824979498769070353}
• ec_padic •

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

  
  
  • id: 181721
    {'lmfdb_iso': '4950.bg', 'p': 13, 'prec': 20, 'unit': 287633208733399436405, 'val': 1}
  • id: 181723
    {'lmfdb_iso': '4950.bg', 'p': 17, 'prec': 20, 'unit': 127869434646829541346642, 'val': 1}
  • id: 181724
    {'lmfdb_iso': '4950.bg', 'p': 19, 'prec': 20, 'unit': 1789608698582677107407404, 'val': 1}
  • id: 181720
    {'lmfdb_iso': '4950.bg', 'p': 29, 'prec': 20, 'unit': 946768773948852611133720648, 'val': 1}
  • id: 181716
    {'lmfdb_iso': '4950.bg', 'p': 37, 'prec': 20, 'unit': 197769909711389287123315708616, 'val': 1}
  • id: 181718
    {'lmfdb_iso': '4950.bg', 'p': 41, 'prec': 20, 'unit': 3722174886715258545857149557350, 'val': 1}
  • id: 181719
    {'lmfdb_iso': '4950.bg', 'p': 43, 'prec': 20, 'unit': 5439148562012763230789903586618, 'val': 1}
  • id: 181729
    {'lmfdb_iso': '4950.bg', 'p': 47, 'prec': 20, 'unit': 22730015351476821565853501522460, 'val': 1}
  • id: 181725
    {'lmfdb_iso': '4950.bg', 'p': 53, 'prec': 20, 'unit': 165778898425750711274975245906564, 'val': 1}
  • id: 181726
    {'lmfdb_iso': '4950.bg', 'p': 59, 'prec': 20, 'unit': 2519564891318059544678457178283570, 'val': 1}
  • id: 181730
    {'lmfdb_iso': '4950.bg', 'p': 61, 'prec': 20, 'unit': 294883084308570075344585564560192, 'val': 1}
  • id: 181715
    {'lmfdb_iso': '4950.bg', 'p': 67, 'prec': 20, 'unit': 25258315681971499793894601549102139, 'val': 1}
  • id: 181717
    {'lmfdb_iso': '4950.bg', 'p': 71, 'prec': 20, 'unit': 65563841479534352696716968245950748, 'val': 1}
  • id: 181727
    {'lmfdb_iso': '4950.bg', 'p': 73, 'prec': 20, 'unit': 245220373159421044369838772853487355, 'val': 1}
  • id: 181722
    {'lmfdb_iso': '4950.bg', 'p': 79, 'prec': 20, 'unit': 1132317970793008354419662658817909857, 'val': 1}
  • id: 181714
    {'lmfdb_iso': '4950.bg', 'p': 83, 'prec': 20, 'unit': 986330207955417594218911752553866628, 'val': 1}
  • id: 181728
    {'lmfdb_iso': '4950.bg', 'p': 89, 'prec': 20, 'unit': 3696030805101484303898684167234808938, 'val': 1}
  • id: 181713
    {'lmfdb_iso': '4950.bg', 'p': 97, 'prec': 20, 'unit': 48762158880650397204023965601003084010, '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: 30770
    {'Ciso': '4950be', 'Clabel': '4950be5', 'Cnumber': 5, 'abc_quality': 1.047398607062714, 'absD': 142720971679687500, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [1, -1, 1, -38494130, 91935940997], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4950, 'degree': 294912, 'elladic_images': ['16.24.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8157847241240352837965587579', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [553808571467029327441, 12529687500], 'lmfdb_iso': '4950.bg', 'lmfdb_label': '4950.bg1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -171085, -27308713], 'min_quad_twist_disc': -15, '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.by.1', '40.24.0-8.n.1.3', '44.12.0.h.1', '48.48.0-24.by.1.13', '60.12.0-4.c.1.1', '80.48.0.?', '88.24.0.?', '120.48.0.?', '176.48.0.?', '240.96.0.?', '264.48.0.?', '440.48.0.?', '528.96.0.?', '660.24.0.?', '880.96.0.?', '1320.96.0.?', '2640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.7593974945483251408726544835', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2475], [3, 6, 550], [5, 18, 198], [11, 12, 450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4617596235729302507985564728', 'prec': 100}, 'szpiro_ratio': 7.524459510729422, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 30768
    {'Ciso': '4950be', 'Clabel': '4950be3', 'Cnumber': 3, 'abc_quality': 1.0750149448569075, 'absD': 5274032318403750000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [1, -1, 1, -2660630, -1666093003], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4950, 'degree': 147456, 'elladic_images': ['8.24.0.56'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4692111338440626290879426972', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [182864522286982801, 463015182960], 'lmfdb_iso': '4950.bg', 'lmfdb_label': '4950.bg2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -11825, 488927], 'min_quad_twist_disc': -15, '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.by.2.6', '40.48.0-40.cb.2.14', '60.24.0-60.h.1.1', '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': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8796987472741625704363272418', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 225], [3, 6, 550], [5, 18, 198], [11, 12, 450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1151860332929575960899404121', 'prec': 100}, 'szpiro_ratio': 6.582212631848521, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 30769
    {'Ciso': '4950be', 'Clabel': '4950be4', 'Cnumber': 4, 'abc_quality': 1.0201673387474062, 'absD': 7324668620156250000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1320, 'ainvs': [1, -1, 1, -2408630, 1433506997], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4950, 'degree': 147456, 'elladic_images': ['8.24.0.24'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4692111338440626290879426972', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4], 'jinv': [135670761487282321, 643043610000], 'lmfdb_iso': '4950.bg', 'lmfdb_label': '4950.bg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -10705, -429025], 'min_quad_twist_disc': -15, '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.h.1.3', '40.48.0-40.i.2.15', '44.24.0.c.1', '60.24.0-4.b.1.1', '88.48.0.?', '120.96.0.?', '264.96.0.?', '440.96.0.?', '660.48.0.?', '1320.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8796987472741625704363272418', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 225], [3, 6, 550], [5, 18, 198], [11, 12, 450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1151860332929575960899404121', 'prec': 100}, 'szpiro_ratio': 6.54712276806025, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 30771
    {'Ciso': '4950be', 'Clabel': '4950be6', 'Cnumber': 6, 'abc_quality': 1.0568860237866882, 'absD': 3538753832876779687500, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [1, -1, 1, -1171130, 2903656997], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4950, 'degree': 294912, 'elladic_images': ['16.24.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8157847241240352837965587579', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-15595206456730321, 310672490129100], 'lmfdb_iso': '4950.bg', 'lmfdb_label': '4950.bg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5205, -862425], 'min_quad_twist_disc': -15, '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', '22.6.0.a.1', '24.24.0-8.n.1.7', '40.24.0.cb.1', '44.12.0.g.1', '48.48.0-48.f.1.1', '60.12.0-4.c.1.1', '80.48.0.?', '88.24.0.?', '120.48.0.?', '176.48.0.?', '240.96.0.?', '264.48.0.?', '440.48.0.?', '528.96.0.?', '660.24.0.?', '880.96.0.?', '1320.96.0.?', '2640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.7593974945483251408726544835', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2475], [3, 6, 550], [5, 18, 198], [11, 12, 450]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4617596235729302507985564728', 'prec': 100}, 'szpiro_ratio': 6.71217334167415, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 30767
    {'Ciso': '4950be', 'Clabel': '4950be2', 'Cnumber': 2, 'abc_quality': 1.0644140254035126, 'absD': 778082768100000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1320, 'ainvs': [1, -1, 1, -230630, -3973003], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4950, 'degree': 73728, 'elladic_images': ['4.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1226375435640899743793266365', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4], 'jinv': [119102750067601, 68309049600], 'lmfdb_iso': '4950.bg', 'lmfdb_label': '4950.bg5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1025, 767], 'min_quad_twist_disc': -15, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.2', '24.48.0-24.h.2.32', '40.48.0-40.i.1.30', '60.48.0-60.c.1.8', '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': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4398493736370812852181636209', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 225], [3, 6, 550], [5, 18, 198], [11, 12, 450]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.76861244301298494138132435142', 'prec': 103}, 'szpiro_ratio': 5.719818006491653, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 30766
    {'Ciso': '4950be', 'Clabel': '4950be1', 'Cnumber': 1, 'abc_quality': 1.0470620627792697, 'absD': 12194012160000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2640, 'ainvs': [1, -1, 1, 57370, -517003], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4950, 'degree': 36864, 'elladic_images': ['8.24.0.46'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7760639532841173196707105757', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1833318007919, 1070530560], 'lmfdb_iso': '4950.bg', 'lmfdb_label': '4950.bg6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 255, 255], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.12', '30.6.0.a.1', '48.48.0-48.f.2.18', '60.24.0-60.g.1.3', '80.48.0.?', '120.48.0.?', '176.48.0.?', '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': 19, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.71992468681854064260908181044', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 225], [3, 6, 550], [5, 18, 198], [11, 12, 450]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.42203885273301228667270829063', 'prec': 103}, 'szpiro_ratio': 5.229188050800356, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}