Elliptic curve data - 15.a4

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '15a', 'Clabel': '15a7', 'Cnumber': 7, 'abc_quality': 1.030187200332639, 'absD': 15, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, -80, 242], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 4, 'elladic_images': ['32.96.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.40227757208284378744359649716', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [56667352321, 15], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a4', 'lmfdb_number': 4, 'manin_constant': 2, 'min_quad_twist_ainvs': [1, 1, 1, -80, 242], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.2', '16.48.0-16.g.1.2', '24.48.0-24.by.2.3', '32.96.0-32.e.1.2', '40.48.0-40.cb.2.7', '48.96.0-48.bs.1.1', '60.24.0-60.h.1.3', '80.192.2.?', '96.192.1.?', '120.96.0.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40227757208284378744359649716', 'prec': 107}, 'szpiro_ratio': 9.143281049575778, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, 3, 1, -1, -4, 1, -2, 0, -1, -1, 2, -1, 4, -1], 'aplist': [-1, -1, 1, 0, -4, -2, 2, 4, 0, -2, 0, -10, 10, 4, 8, -10, -4, -2, 12, -8, 10, 0, 12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 15, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '15.a', 'trace_hash': 750292609497685491}
• 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': '2.2357017126175291017667427821', 'prec': 100}, 'conductor': 15, 'gens': [], 'heights': [], 'lmfdb_label': '15.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '5.6024121693304080927207233472', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.35015076058315050579504520920239987269', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [[5, -2, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '3': [0, 0], '5': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '15.a4'}
• ec_torsion_growth •

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

  
  
  • id: 224
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [2, 4]}
  • id: 226
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [8]}
  • id: 225
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '15.a4', 'torsion': [8]}
  • id: 228
    {'degree': 4, 'field': [1, 4, -4, -1, 1], 'lmfdb_label': '15.a4', 'torsion': [16]}
  • id: 227
    {'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '15.a4', 'torsion': [2, 8]}
  • id: 229
    {'degree': 4, 'field': [5, 0, -5, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [16]}
  • id: 235
    {'degree': 8, 'field': [-1, 4, -4, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '15.a4', 'torsion': [12]}
  • id: 233
    {'degree': 8, 'field': [1, 0, -8, 0, 14, 0, -7, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [2, 16]}
  • id: 234
    {'degree': 8, 'field': [45, 0, -90, 0, 60, 0, -15, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [32]}
  • id: 230
    {'degree': 8, 'field': [196, 0, 184, 0, -24, 0, 4, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [4, 4]}
  • id: 232
    {'degree': 8, 'field': [225, 0, -180, 0, 63, 0, -12, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [16]}
  • id: 231
    {'degree': 8, 'field': [3600, 0, 0, 0, 105, 0, 0, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [2, 8]}
  • id: 239
    {'degree': 16, 'field': [1, 36, 60, -350, -655, 1068, 1908, -1770, -2280, 1840, 1038, -1002, -30, 170, -30, -4, 1], 'lmfdb_label': '15.a4', 'torsion': [2, 32]}
  • id: 242
    {'degree': 16, 'field': [9, 0, -207, 0, -72, 0, -111, 0, -75, 0, -21, 0, 7, 0, -2, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [24]}
  • id: 241
    {'degree': 16, 'field': [9, 0, -63, 0, 135, 0, -146, 0, 125, 0, -89, 0, 43, 0, -10, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [24]}
  • id: 237
    {'degree': 16, 'field': [81, 0, 0, 0, 81, 0, 0, 0, 72, 0, 0, 0, 9, 0, 0, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [2, 16]}
  • id: 240
    {'degree': 16, 'field': [5625, 0, -19125, 0, 11025, 0, -225, 0, -675, 0, 0, 0, 10, 0, 5, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [2, 12]}
  • id: 238
    {'degree': 16, 'field': [50625, 0, -67500, 0, 39375, 0, -14100, 0, 3905, 0, -940, 0, 175, 0, -20, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [32]}
  • id: 236
    {'degree': 16, 'field': [58081, 0, -52252, 0, 39118, 0, -12484, 0, 235, 0, -4, 0, 58, 0, 8, 0, 1], 'lmfdb_label': '15.a4', 'torsion': [4, 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: 27
    {'conductor': 15, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15.a4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 28
    {'conductor': 15, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15.a4', 'prime': 5, '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: 1665900
    {'adelic_gens': [[214, 3, 365, 268], [1, 0, 32, 1], [1, 32, 0, 1], [5, 28, 68, 381], [449, 32, 448, 33], [183, 2, 154, 463], [23, 18, 318, 395], [30, 31, 169, 324], [242, 19, 15, 398]], 'adelic_image': '480.768.13.?', 'conductor': 15, 'lmfdb_label': '15.a4', 'prime': 0}
  • id: 18
    {'conductor': 15, 'elladic_image': '32.96.0.5', 'lmfdb_label': '15.a4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 15.a does not appear in ec_padic