Elliptic curve data - 270504.c1

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• 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[]

  
  {'Ciso': '270504c', 'Clabel': '270504c2', 'Cnumber': 2, 'abc_quality': 0.9036561668018798, 'absD': 42690564989459712, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 0, 0, -156927, -21764590], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 270504, 'degree': 3538944, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9274456151471850830489505288', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2], 'jinv': [94875856, 9477], 'lmfdb_iso': '270504.c', 'lmfdb_label': '270504.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -60, 144], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '26.6.0.b.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 33813], [3, 6, 30056], [13, 14, 20808], [17, 146, 936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50056532158827467571826081290', 'prec': 107}, 'szpiro_ratio': 3.7978934218295244, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, -4, 0, 4, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, 0, -4, 4, -2, -1, 0, 4, 4, -6, -8, 10, -4, -4, 6, -6, 6, 6, 0, 10, 2, 0, 10, -8, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 270504, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '270504.c', 'trace_hash': 391461650184262000}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.021175906481971082752217194206', 'prec': 107}, 'conductor': 270504, 'gens': [], 'heights': [], 'lmfdb_label': '270504.c1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24141276572859815912851500393', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9313021258287852730281200314180015727', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-170, 0, 1]], 'xcoord_integral_points': [-170]}
• lmfdb_label 270504.c1 does not appear in ec_iwasawa
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 11557416
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '270504.c1', 'torsion': [2, 2]}
  • id: 11557417
    {'degree': 4, 'field': [3757, 0, 119, 0, 1], 'lmfdb_label': '270504.c1', 'torsion': [4]}
  • id: 11557420
    {'degree': 8, 'field': [-18708, 16728, 3468, -1944, 312, 204, -16, -2, 1], 'lmfdb_label': '270504.c1', 'torsion': [6]}
  • id: 11557418
    {'degree': 8, 'field': [-5847, 11958, -3746, -608, 20, -38, -19, -2, 1], 'lmfdb_label': '270504.c1', 'torsion': [2, 4]}
  • id: 11557419
    {'degree': 8, 'field': [751689, 0, -14739, 0, 1156, 0, 17, 0, 1], 'lmfdb_label': '270504.c1', 'torsion': [2, 4]}
  • id: 11557422
    {'degree': 16, 'field': [287234704, 0, -11829792, 0, -24863504, 0, -3323456, 0, 108744, 0, 23416, 0, 1000, 0, -60, 0, 1], 'lmfdb_label': '270504.c1', 'torsion': [2, 6]}
  • id: 11557421
    {'degree': 16, 'field': [572628841, -444108164, -130446652, 392348508, -132552964, -132430444, 120559156, -26832012, -5623298, 3070836, -94244, -114284, 11948, 1116, -148, -4, 1], 'lmfdb_label': '270504.c1', 'torsion': [8]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 6702930
    {'conductor': 270504, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '270504.c1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6702931
    {'conductor': 270504, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '270504.c1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6702932
    {'conductor': 270504, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '270504.c1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6702933
    {'conductor': 270504, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '270504.c1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3374159
    {'adelic_gens': [[1, 2, 2, 5], [53, 4, 106, 9], [134, 1, 11, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 270504, 'lmfdb_label': '270504.c1', 'prime': 0}
  • id: 966970
    {'conductor': 270504, 'elladic_image': '2.3.0.1', 'lmfdb_label': '270504.c1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 270504.c does not appear in ec_padic