Elliptic curve data - 528.a2

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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': '528f', 'Clabel': '528f4', 'Cnumber': 4, 'abc_quality': 1.0638684203296611, 'absD': 1912314440982528, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 1320, 'ainvs': [0, -1, 0, -160880, 24979776], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 528, 'degree': 4800, 'elladic_images': ['8.6.0.5', '5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7875740372364656222411238363', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 10, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [-112427521449300721, 466873642818], 'lmfdb_iso': '528.a', 'lmfdb_label': '528.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -10055, -390309], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '5B.4.2'], 'modm_images': ['2.3.0.a.1', '5.12.0.a.2', '8.6.0.a.1', '10.36.0.a.1', '20.72.0-10.a.1.10', '40.144.1-40.c.2.15', '132.6.0.?', '264.12.0.?', '660.144.1.?', '1320.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1], [3, 4, 176], [5, 2, 48], [11, 12, 48]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0944268566765203128238917148', 'prec': 100}, 'szpiro_ratio': 7.590567977744762, '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, -4, 0, 2, 0, 1, 0, -1, 0, 4, 0, 4, 0, -2, 0, 0, 0], 'aplist': [0, -1, -4, 2, -1, 4, -2, 0, 6, 10, 8, -2, 2, -4, 2, 4, 0, -8, 12, -2, -6, -10, -4, 10, -2], 'class_deg': 10, 'class_size': 4, 'conductor': 528, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '528.a', 'trace_hash': 2023697010879541442}
• 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': '0.028011277711934999063742484036', 'prec': 107}, 'conductor': 528, 'gens': [], 'heights': [], 'lmfdb_label': '528.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.47013980264314379478391436484', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.94027960528628758956782872967824368222', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-463, 0, 1]], 'xcoord_integral_points': [-463]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [2, 0], '11': [0, 0]}, 'iwp0': 7, 'lmfdb_label': '528.a2'}
• ec_torsion_growth •

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

  
  
  • id: 23873
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [2, 2]}
  • id: 23874
    {'degree': 4, 'field': [4, -2, -4, -1, 1], 'lmfdb_label': '528.a2', 'torsion': [4]}
  • id: 23875
    {'degree': 4, 'field': [5, 0, -5, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [10]}
  • id: 23878
    {'degree': 8, 'field': [-192, 0, 100, 0, 48, 0, 0, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [6]}
  • id: 23877
    {'degree': 8, 'field': [1, 0, -12, 0, 40, 0, -12, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [2, 4]}
  • id: 23879
    {'degree': 8, 'field': [1, 0, 12, 0, 19, 0, 8, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [2, 10]}
  • id: 23876
    {'degree': 8, 'field': [256, 128, 16, 32, 42, -8, 1, -2, 1], 'lmfdb_label': '528.a2', 'torsion': [2, 4]}
  • id: 23880
    {'degree': 10, 'field': [144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [10]}
  • id: 23881
    {'degree': 16, 'field': [-4688, 1072, 5424, 7784, -612, -6024, 4240, 7736, 1356, -2492, -860, 234, 159, 10, -12, -4, 1], 'lmfdb_label': '528.a2', 'torsion': [8]}
  • id: 23883
    {'degree': 16, 'field': [1681, -82, -5690, 7722, -9796, 3744, 8984, -13546, 2541, 5672, -1864, -1122, 364, 106, -30, -4, 1], 'lmfdb_label': '528.a2', 'torsion': [20]}
  • id: 23882
    {'degree': 16, 'field': [47089, 0, -18896, 0, 41260, 0, 26364, 0, 4434, 0, -96, 0, -104, 0, 4, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [2, 6]}
  • id: 23884
    {'degree': 20, 'field': [648, 0, 0, 0, 0, -2160, 0, 0, 0, 0, 2124, 0, 0, 0, 0, -36, 0, 0, 0, 0, 1], 'lmfdb_label': '528.a2', 'torsion': [2, 10]}
• 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: 5960
    {'conductor': 528, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '528.a2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5961
    {'conductor': 528, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '528.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5962
    {'conductor': 528, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '528.a2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1668166
    {'adelic_gens': [[881, 6, 0, 1], [1301, 20, 1300, 21], [1201, 6, 0, 1], [11, 16, 1080, 971], [654, 1315, 935, 1274], [1057, 20, 0, 1], [1, 10, 10, 101], [1, 0, 20, 1], [6, 13, 575, 1136], [1, 20, 0, 1]], 'adelic_image': '1320.288.5.?', 'conductor': 528, 'lmfdb_label': '528.a2', 'prime': 0}
  • id: 2349
    {'conductor': 528, 'elladic_image': '8.6.0.5', 'lmfdb_label': '528.a2', 'modell_image': '2B', 'prime': 2}
  • id: 2350
    {'conductor': 528, 'elladic_image': '5.12.0.2', 'lmfdb_label': '528.a2', 'modell_image': '5B.4.2', 'prime': 5}
• lmfdb_iso 528.a does not appear in ec_padic