Elliptic curve isogeny class data - 1728.o

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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, 0, 0, 1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -7, 0], 'aplist': [0, 0, 0, 1, 0, -5, 0, -7, 0, 0, 4, -11, 0, 8, 0, 0, 0, 1, 5, 0, -7, -17, 0, 0, -19], 'class_deg': 27, 'class_size': 4, 'conductor': 1728, 'isogeny_matrix': [[1, 27, 9, 3], [27, 1, 3, 9], [9, 3, 1, 3], [3, 9, 3, 1]], 'lmfdb_iso': '1728.o', 'trace_hash': 1415855867502297635}
• ec_padic •

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

  
  
  • id: 47970
    {'lmfdb_iso': '1728.o', 'p': 7, 'prec': 20, 'unit': 64466393800564870, 'val': 0}
  • id: 47973
    {'lmfdb_iso': '1728.o', 'p': 13, 'prec': 20, 'unit': 238153760673429703495, 'val': 1}
  • id: 47975
    {'lmfdb_iso': '1728.o', 'p': 19, 'prec': 20, 'unit': 94004648432768508193260, 'val': 2}
  • id: 47977
    {'lmfdb_iso': '1728.o', 'p': 31, 'prec': 20, 'unit': 12619005292858312548951081581, 'val': 1}
  • id: 47969
    {'lmfdb_iso': '1728.o', 'p': 37, 'prec': 20, 'unit': 517362074490160783924396477122, 'val': 1}
  • id: 47972
    {'lmfdb_iso': '1728.o', 'p': 43, 'prec': 20, 'unit': 3087603812699019464049631429247, 'val': 1}
  • id: 47976
    {'lmfdb_iso': '1728.o', 'p': 61, 'prec': 20, 'unit': 151259172822003095902853785112513908, 'val': 0}
  • id: 47968
    {'lmfdb_iso': '1728.o', 'p': 67, 'prec': 20, 'unit': 44232311809664014036836424880869767, 'val': 1}
  • id: 47971
    {'lmfdb_iso': '1728.o', 'p': 73, 'prec': 20, 'unit': 9906620409695149067343618220492485, 'val': 1}
  • id: 47974
    {'lmfdb_iso': '1728.o', 'p': 79, 'prec': 20, 'unit': 520945465242566161265436488804170554, 'val': 1}
  • id: 47967
    {'lmfdb_iso': '1728.o', 'p': 97, 'prec': 20, 'unit': 36055190393614427169637265108839436338, '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
  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: 9652
    {'Ciso': '1728v', 'Clabel': '1728v4', 'Cnumber': 4, 'abc_quality': 1.23864473399791, 'absD': 11337408, 'ainvs': [0, 0, 0, -1080, 13662], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 27, 'class_size': 4, 'cm': -27, 'conductor': 1728, 'degree': 432, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.39872152268707185396280341103', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 9, 'intrinsic_torsion': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 3, 9, 27], 'jinv': [-12288000, 1], 'lmfdb_iso': '1728.o', 'lmfdb_label': '1728.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -30, 63], 'min_quad_twist_disc': 24, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3495768356801180454777611856', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 4, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95491333220533468452478745021', 'prec': 107}, 'szpiro_ratio': 4.36876137928833, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
  • id: 9650
    {'Ciso': '1728v', 'Clabel': '1728v2', 'Cnumber': 2, 'abc_quality': 1.23864473399791, 'absD': 15552, 'ainvs': [0, 0, 0, -120, -506], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 27, 'class_size': 4, 'cm': -27, 'conductor': 1728, 'degree': 144, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.15058462164698299173481920743', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 3, 9, 27], 'jinv': [-12288000, 1], 'lmfdb_iso': '1728.o', 'lmfdb_label': '1728.o2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -30, 63], 'min_quad_twist_disc': -8, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.0487305070403541364332835569', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 8, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95491333220533468452478745021', 'prec': 107}, 'szpiro_ratio': 3.4845331618928492, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
  • id: 9649
    {'Ciso': '1728v', 'Clabel': '1728v1', 'Cnumber': 1, 'absD': 1728, 'ainvs': [0, 0, 0, 0, -2], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 1728, 'degree': 48, 'elladic_images': ['27.972.55.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.69989076598103783743244182590', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '1728.o', 'lmfdb_label': '1728.o3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': -8, 'modell_images': ['3Cs'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3495768356801180454777611856', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 2, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 2.0, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
  • id: 9651
    {'Ciso': '1728v', 'Clabel': '1728v3', 'Cnumber': 3, 'absD': 1259712, 'ainvs': [0, 0, 0, 0, 54], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 1728, 'degree': 144, 'elladic_images': ['27.972.55.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.15058462164698299173481920743', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '1728.o', 'lmfdb_label': '1728.o4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': 24, 'modell_images': ['3Cs'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.44985894522670601515925372855', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 2, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 2.8842282173954805, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}