Elliptic curve isogeny class data - 30.a

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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, -1, -1, -4, -1, 1, 1, 0, 1, 2, 4, -1, 1, 6, -1, -4, -1], 'aplist': [-1, 1, -1, -4, 0, 2, 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': 30, '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': '30.a', 'trace_hash': 148452494971348580}
• lmfdb_iso 30.a 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: 55
    {'Ciso': '30a', 'Clabel': '30a7', 'Cnumber': 7, 'abc_quality': 1.0818126452233845, 'absD': 81000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -5334, -150368], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 24, 'elladic_images': ['8.12.0.7', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232156', 'prec': 103}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [16778985534208729, 81000], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5334, -150368], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '8.12.0-4.c.1.3', '12.48.0-12.g.1.10', '20.12.0-4.c.1.1', '24.192.1-24.dj.3.8', '40.24.0-40.v.1.4', '60.96.0-60.c.3.12', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 5], [3, 4, 1], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232156', 'prec': 103}, 'szpiro_ratio': 10.984044571686695, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 56
    {'Ciso': '30a', 'Clabel': '30a8', 'Cnumber': 8, 'abc_quality': 1.1359972360691755, 'absD': 5859375000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -454, -544], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 24, 'elladic_images': ['8.12.0.8', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232156', 'prec': 103}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [10316097499609, 5859375000], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -454, -544], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '8.12.0-4.c.1.4', '12.96.0-12.c.3.3', '24.192.1-24.da.1.4', '40.24.0-40.bb.1.14', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 3], [3, 4, 1], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232156', 'prec': 103}, 'szpiro_ratio': 8.810052252997776, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 54
    {'Ciso': '30a', 'Clabel': '30a6', 'Cnumber': 6, 'abc_quality': 1.0522127879225598, 'absD': 9000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -334, -2368], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 12, 'elladic_images': ['8.12.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626083', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4102915888729, 9000000], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -334, -2368], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs', '3B.1.2'], 'modm_images': ['2.6.0.a.1', '3.8.0-3.a.1.1', '6.48.0-6.a.1.2', '8.12.0-2.a.1.1', '12.96.0-12.a.1.15', '20.12.0-2.a.1.1', '24.192.1-24.cp.2.4', '40.24.0-40.a.1.3', '60.192.1-60.h.3.4', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 1], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626083', 'prec': 103}, 'szpiro_ratio': 8.538969007156295, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 53
    {'Ciso': '30a', 'Clabel': '30a5', 'Cnumber': 5, 'abc_quality': 1.0501740895315954, 'absD': 33750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -289, 1862], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 8, 'elladic_images': ['8.12.0.8', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703102', 'prec': 107}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [2656166199049, 33750], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -289, 1862], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '8.12.0-4.c.1.4', '12.96.0-12.c.4.5', '24.192.1-24.da.3.4', '40.24.0-40.bb.1.14', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 3], [3, 4, 10], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703102', 'prec': 107}, 'szpiro_ratio': 8.411127526667551, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
  • id: 52
    {'Ciso': '30a', 'Clabel': '30a4', 'Cnumber': 4, 'abc_quality': 1.0339287621454463, 'absD': 5314410, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -69, -194], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 8, 'elladic_images': ['8.12.0.7', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703102', 'prec': 107}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [35578826569, 5314410], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -69, -194], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '8.12.0-4.c.1.3', '12.48.0-12.g.1.12', '20.12.0-4.c.1.1', '24.192.1-24.dj.4.8', '40.24.0-40.v.1.4', '60.96.0-60.c.4.16', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 5], [3, 4, 10], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703102', 'prec': 107}, 'szpiro_ratio': 7.143077514276536, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
  • id: 50
    {'Ciso': '30a', 'Clabel': '30a2', 'Cnumber': 2, 'abc_quality': 1.0045688963827404, 'absD': 72900, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -19, 26], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 4, 'elladic_images': ['8.12.0.1', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.33171374939767582011699635763', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [702595369, 72900], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -19, 26], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs', '3B.1.1'], 'modm_images': ['2.6.0.a.1', '3.8.0-3.a.1.2', '6.48.0-6.a.1.1', '8.12.0-2.a.1.1', '12.96.0-12.a.2.13', '20.12.0-2.a.1.1', '24.192.1-24.cp.4.4', '40.24.0-40.a.1.3', '60.192.1-60.h.1.6', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 10, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 10], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33171374939767582011699635763', 'prec': 107}, 'szpiro_ratio': 5.989153060145781, 'torsion': 12, 'torsion_primes': [2, 3], 'torsion_structure': [2, 6]}
  • id: 51
    {'Ciso': '30a', 'Clabel': '30a3', 'Cnumber': 3, 'abc_quality': 1.0491971880149842, 'absD': 1536000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -14, -64], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 6, 'elladic_images': ['8.12.0.12', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.12898119534359362912798979990', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-273359449, 1536000], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -14, -64], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '8.12.0-4.c.1.2', '12.96.0-12.c.1.6', '20.12.0-4.c.1.2', '24.192.1-24.dh.4.2', '30.48.0-30.b.1.3', '40.24.0-40.bb.1.9', '60.192.1-60.n.2.4', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 15], [3, 4, 1], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12898119534359362912798979990', 'prec': 107}, 'szpiro_ratio': 6.408754108329178, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 49
    {'Ciso': '30a', 'Clabel': '30a1', 'Cnumber': 1, 'abc_quality': 0.9968917246282063, 'absD': 2160, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, 1, 2], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 2, 'elladic_images': ['8.12.0.12', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.67828733967764847482561241836', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [357911, 2160], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 1, 2], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '8.12.0-4.c.1.2', '12.96.0-12.c.2.7', '20.12.0-4.c.1.2', '24.192.1-24.dh.3.2', '30.48.0-30.b.1.4', '40.24.0-40.bb.1.9', '60.192.1-60.n.4.4', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 15], [3, 4, 10], [5, 6, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.67828733967764847482561241836', 'prec': 107}, 'szpiro_ratio': 4.419554787227392, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}