Elliptic curve data - 270480.z1

Formats: - HTML - YAML - JSON - 2025-11-05T20:48:52.645609

• 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': '270480z', 'Clabel': '270480z1', 'Cnumber': 1, 'abc_quality': 0.90192877869967, 'absD': 54128714285520, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 9660, 'ainvs': [0, -1, 0, -10061, -156624], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 270480, 'degree': 645120, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3289449168242062061925151077', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [174456832, 83835], 'lmfdb_iso': '270480.z', 'lmfdb_label': '270480.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -205, -398], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '84.6.0.?', '1380.6.0.?', '1610.6.0.?', '9660.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 805], [3, 4, 90160], [5, 6, 54096], [7, 20, 5520], [23, 24, 11760]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.36153675515392720910891015703', 'prec': 107}, 'szpiro_ratio': 3.139040143394595, '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, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 2, 0, 4, 0], 'aplist': [0, -1, -1, 0, 0, -2, 2, 4, 1, -6, -8, -6, -10, 8, -12, 6, -10, 2, 4, 8, -2, 10, 14, -10, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 270480, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '270480.z', 'trace_hash': 451270549091048035}
• 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': '0.070095979970924770548332753679', 'prec': 107}, 'conductor': 270480, 'gens': [], 'heights': [], 'lmfdb_label': '270480.z1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.50001578736998075925720330162', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.50001578736998075925720330162118001760', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-16, 0, 1]], 'xcoord_integral_points': [-16]}
• lmfdb_label 270480.z1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11552921
    {'degree': 2, 'field': [-201, -1, 1], 'lmfdb_label': '270480.z1', 'torsion': [2, 2]}
  • id: 11552922
    {'degree': 4, 'field': [5821, -298, -100, -2, 1], 'lmfdb_label': '270480.z1', 'torsion': [4]}
  • id: 11552925
    {'degree': 8, 'field': [-1323, 0, 196, 0, 126, 0, 0, 0, 1], 'lmfdb_label': '270480.z1', 'torsion': [6]}
  • id: 11552923
    {'degree': 8, 'field': [670761, 0, 574182, 0, -1197, 0, 42, 0, 1], 'lmfdb_label': '270480.z1', 'torsion': [2, 4]}
  • id: 11552924
    {'degree': 8, 'field': [688747536, 0, -26395632, 0, 186444, 0, -648, 0, 1], 'lmfdb_label': '270480.z1', 'torsion': [2, 4]}
  • id: 11552927
    {'degree': 16, 'field': [-132315455, 432743200, -295133016, -186682340, 180159526, -98045208, 39625596, 2876724, -2575125, -30384, 14052, 996, 1534, 40, -24, -8, 1], 'lmfdb_label': '270480.z1', 'torsion': [2, 6]}
  • id: 11552926
    {'degree': 16, 'field': [37511942400, 0, -4781555712, 0, 1613233152, 0, 20051712, 0, -1870560, 0, -34560, 0, 6144, 0, -144, 0, 1], 'lmfdb_label': '270480.z1', '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: 6700473
    {'conductor': 270480, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '270480.z1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6700474
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '270480.z1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6700475
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '270480.z1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6700476
    {'conductor': 270480, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '270480.z1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6700477
    {'conductor': 270480, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '270480.z1', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 3374052
    {'adelic_gens': [[1, 2, 2, 5], [3782, 1, 2939, 0], [3221, 4, 6442, 9], [1, 4, 0, 1], [1934, 1, 3863, 0], [1, 0, 4, 1], [1384, 1, 6899, 0], [3, 4, 8, 11], [9657, 4, 9656, 5], [7249, 2416, 7244, 2415]], 'adelic_image': '9660.12.0.?', 'conductor': 270480, 'lmfdb_label': '270480.z1', 'prime': 0}
  • id: 966896
    {'conductor': 270480, 'elladic_image': '2.3.0.1', 'lmfdb_label': '270480.z1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 270480.z does not appear in ec_padic