Elliptic curve isogeny class data - 163800.cd

Formats: - HTML - YAML - JSON - 2026-04-19T21:53:33.303599

• 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, 0, 0, -1, 0, 0, 0, 4, 0, -1, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, 0, -1, 4, -1, -6, 4, 0, -6, 0, -6, 6, -4, 0, -2, -4, -2, -4, 0, 6, 8, 12, -10, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 163800, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '163800.cd', 'trace_hash': 2196944659661749459}
• lmfdb_iso 163800.cd 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  
  • id: 1060096
    {'Ciso': '163800bu', 'Clabel': '163800bu5', 'Cnumber': 5, 'abc_quality': 1.0362567238567626, 'absD': 1547556192000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 21840, 'ainvs': [0, 0, 0, -636854475, 6185978707750], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 163800, 'degree': 18874368, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3053138272797103050978193461', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 55, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1224522642327678150914, 66339], 'lmfdb_iso': '163800.cd', 'lmfdb_label': '163800.cd1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2830464, -1831939092], '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', '48.24.0.g.1', '60.12.0-4.c.1.1', '80.24.0.?', '112.24.0.?', '120.24.0.?', '168.24.0.?', '208.24.0.?', '240.48.0.?', '280.24.0.?', '312.24.0.?', '336.48.0.?', '520.24.0.?', '560.48.0.?', '624.48.0.?', '728.24.0.?', '840.48.0.?', '1040.48.0.?', '1456.48.0.?', '1560.48.0.?', '1680.96.0.?', '2184.48.0.?', '3120.96.0.?', '3640.48.0.?', '4368.96.1.?', '7280.96.0.?', '10920.96.0.?', '21840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.5427393376686025978651106518', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 20475], [3, 6, 18200], [5, 14, 6552], [7, 8, 23400], [13, 14, 12600]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3159038112153220718006876164', 'prec': 100}, 'szpiro_ratio': 6.032595072984771, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 1060094
    {'Ciso': '163800bu', 'Clabel': '163800bu3', 'Cnumber': 3, 'abc_quality': 1.0073457381943538, 'absD': 51331665110544000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 10920, 'ainvs': [0, 0, 0, -39803475, 96655558750], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 163800, 'degree': 9437184, 'elladic_images': ['4.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9587402369997376503892032853', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 1, 'iso_nlabel': 55, 'isogeny_degrees': [1, 2, 4], 'jinv': [597914615076708388, 4400862921], 'lmfdb_iso': '163800.cd', 'lmfdb_label': '163800.cd2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -176904, -28579716], 'min_quad_twist_disc': -15, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '24.24.0.m.1', '40.24.0-4.b.1.5', '56.24.0.h.2', '60.24.0-4.b.1.1', '104.24.0.?', '120.48.0.?', '168.48.0.?', '280.48.0.?', '312.48.0.?', '520.48.0.?', '728.48.0.?', '840.96.0.?', '1560.96.0.?', '2184.96.1.?', '3640.96.0.?', '10920.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7713696688343012989325553259', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 6, 18200], [5, 14, 6552], [7, 8, 23400], [13, 14, 12600]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0270924859820115262101742323', 'prec': 100}, 'szpiro_ratio': 5.339817898941311, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 1060097
    {'Ciso': '163800bu', 'Clabel': '163800bu6', 'Cnumber': 6, 'abc_quality': 1.0089455216720034, 'absD': 599554976659617888000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 21840, 'ainvs': [0, 0, 0, -38984475, 100823449750], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 163800, 'degree': 18874368, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3053138272797103050978193461', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 55, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-280880296871140514, 25701087819771], 'lmfdb_iso': '163800.cd', 'lmfdb_label': '163800.cd3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -173264, -29815860], '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', '48.24.0.g.1', '56.24.0.bu.2', '60.12.0-4.c.1.1', '80.24.0.?', '104.24.0.?', '120.24.0.?', '240.48.0.?', '336.48.0.?', '560.48.0.?', '624.48.0.?', '728.48.0.?', '840.48.0.?', '1040.48.0.?', '1560.48.0.?', '1680.96.0.?', '3120.96.0.?', '4368.96.1.?', '7280.96.0.?', '10920.96.0.?', '21840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.5427393376686025978651106518', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 20475], [3, 6, 18200], [5, 14, 6552], [7, 8, 23400], [13, 14, 12600]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3159038112153220718006876164', 'prec': 100}, 'szpiro_ratio': 5.346849295909306, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 1060095
    {'Ciso': '163800bu', 'Clabel': '163800bu4', 'Cnumber': 4, 'abc_quality': 0.991751601068022, 'absD': 12587925780651312000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 21840, 'ainvs': [0, 0, 0, -8492475, -7848652250], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 163800, 'degree': 9437184, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9587402369997376503892032853', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 55, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [5807363790481348, 1079211743883], 'lmfdb_iso': '163800.cd', 'lmfdb_label': '163800.cd4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -37744, 2338108], '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', '12.12.0.h.1', '20.12.0-4.c.1.1', '24.24.0.bl.1', '40.24.0-8.n.1.10', '56.24.0.bu.1', '60.24.0-12.h.1.1', '120.48.0.?', '168.48.0.?', '208.24.0.?', '280.48.0.?', '624.48.0.?', '840.96.0.?', '1040.48.0.?', '1456.48.0.?', '3120.96.0.?', '4368.96.1.?', '7280.96.0.?', '21840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7713696688343012989325553259', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 6, 18200], [5, 14, 6552], [7, 8, 23400], [13, 14, 12600]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0270924859820115262101742323', 'prec': 100}, 'szpiro_ratio': 4.953830369919252, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 1060093
    {'Ciso': '163800bu', 'Clabel': '163800bu2', 'Cnumber': 2, 'abc_quality': 0.9686459833518319, 'absD': 145774183395204000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 10920, 'ainvs': [0, 0, 0, -2538975, 1444761250], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 163800, 'degree': 4718592, 'elladic_images': ['4.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6121666467197649956805872246', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 55, 'isogeny_degrees': [1, 2, 4], 'jinv': [620742479063632, 49991146569], 'lmfdb_iso': '163800.cd', 'lmfdb_label': '163800.cd5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -11284, -424316], 'min_quad_twist_disc': -15, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '12.24.0.c.1', '20.24.0-4.b.1.2', '56.24.0.h.1', '60.48.0-12.c.1.2', '104.24.0.?', '168.48.0.?', '280.48.0.?', '312.48.0.?', '520.48.0.?', '728.48.0.?', '840.96.0.?', '1560.96.0.?', '2184.96.1.?', '3640.96.0.?', '10920.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3856848344171506494662776630', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 6, 18200], [5, 14, 6552], [7, 8, 23400], [13, 14, 12600]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.79604342579536308973776352522', 'prec': 103}, 'szpiro_ratio': 4.652136304636393, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 1060092
    {'Ciso': '163800bu', 'Clabel': '163800bu1', 'Cnumber': 1, 'abc_quality': 1.0143277708927247, 'absD': 4794047424006750000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 21840, 'ainvs': [0, 0, 0, 162150, 102302125], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 163800, 'degree': 2359296, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2655930564397923409719711639', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 55, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [2587063175168, 26304786963], 'lmfdb_iso': '163800.cd', 'lmfdb_label': '163800.cd6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 721, -30552], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '8.12.0.n.1', '12.12.0.g.1', '20.12.0-4.c.1.2', '24.24.0.bh.1', '40.24.0-8.n.1.12', '60.24.0-12.g.1.2', '104.24.0.?', '112.24.0.?', '120.48.0.?', '312.48.0.?', '336.48.0.?', '520.48.0.?', '560.48.0.?', '1456.48.0.?', '1560.96.0.?', '1680.96.0.?', '4368.96.1.?', '7280.96.0.?', '21840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7713696688343012989325553259', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 6, 18200], [5, 14, 6552], [7, 8, 23400], [13, 14, 12600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.68051889570203887150155817167', 'prec': 103}, 'szpiro_ratio': 4.198595870023427, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}