Elliptic curve data - 2535.k3

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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': '2535f', 'Clabel': '2535f8', 'Cnumber': 8, 'abc_quality': 1.0142537292135114, 'absD': 28723991546630859375, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 6240, 'ainvs': [1, 0, 1, -1340174, -650564653], 'analytic_rank': 0, 'bad_primes': [3, 5, 13], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 2535, 'degree': 64512, 'elladic_images': ['16.48.0.111'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4718917465254022550009405943', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-55150149867714721, 5950927734375], 'lmfdb_iso': '2535.k', 'lmfdb_label': '2535.k3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -7930, -296725], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.7', '12.12.0-4.c.1.1', '16.48.0-16.g.1.9', '24.48.0-24.bz.2.2', '48.96.0-48.bv.2.6', '52.12.0-4.c.1.1', '78.6.0.?', '104.48.0.?', '156.24.0.?', '160.96.0.?', '208.192.2.?', '312.96.0.?', '480.192.1.?', '624.384.5.?', '2080.384.5.?', '6240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 507], [3, 4, 845], [5, 6, 507], [13, 98, 15]], 'sha': 16, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1894170677946338869741968735', 'prec': 100}, 'szpiro_ratio': 6.903528618579306, '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, 1, 1, -1, -1, 1, 0, -3, 1, -1, -4, -1, 0, 0, -1, -1, 2, 1, 4, 1], 'aplist': [1, 1, -1, 0, -4, 0, 2, 4, 8, -2, 8, -6, 6, -4, 8, 6, 12, -2, 4, 0, 6, 16, 4, -10, -18], 'class_deg': 16, 'class_size': 8, 'conductor': 2535, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '2535.k', 'trace_hash': 1708021107077896659}
• 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': '0.0071275801429632126469515791613', 'prec': 110}, 'conductor': 2535, 'gens': [], 'heights': [], 'lmfdb_label': '2535.k3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.069733589851184516007111422466', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2314748752379045122275655189106007756', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[5399, -5403, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 4], '3': [1, 0], '5': [0, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '2535.k3'}
• ec_torsion_growth •

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

  
  
  • id: 131185
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [4]}
  • id: 131184
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 2]}
  • id: 131186
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [4]}
  • id: 131187
    {'degree': 4, 'field': [16, 0, 5, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 4]}
  • id: 131189
    {'degree': 4, 'field': [49, 0, -12, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [8]}
  • id: 131188
    {'degree': 4, 'field': [49, 0, 38, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [8]}
  • id: 131195
    {'degree': 8, 'field': [-387, 225, -288, 125, -59, -7, 7, -4, 1], 'lmfdb_label': '2535.k3', 'torsion': [6]}
  • id: 131192
    {'degree': 8, 'field': [166, 228, 6, 48, 95, -12, 18, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 8]}
  • id: 131191
    {'degree': 8, 'field': [900, 0, -1512, 0, -24, 0, -12, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [8]}
  • id: 131190
    {'degree': 8, 'field': [1521, 0, 0, 0, -39, 0, 0, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 4]}
  • id: 131193
    {'degree': 8, 'field': [20449, 0, -4056, 0, 156, 0, 0, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [16]}
  • id: 131194
    {'degree': 8, 'field': [1656369, 0, -109512, 0, 1404, 0, 0, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [16]}
  • id: 131200
    {'degree': 16, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1071, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [16]}
  • id: 131196
    {'degree': 16, 'field': [256, -768, 1152, -1152, 112, 576, 360, 132, -87, 66, 90, 72, 7, -36, 18, -6, 1], 'lmfdb_label': '2535.k3', 'torsion': [4, 4]}
  • id: 131198
    {'degree': 16, 'field': [1521, 0, 0, 0, 0, 0, 0, 0, -39, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 8]}
  • id: 131204
    {'degree': 16, 'field': [11449, 0, 91061, 0, 58600, 0, 124337, 0, 24145, 0, 2207, 0, 235, 0, 26, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [12]}
  • id: 131202
    {'degree': 16, 'field': [70425, -20610, -31704, 45321, -24585, -19965, 45771, 21369, 2932, 5729, 937, 155, 373, -73, 37, -4, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 6]}
  • id: 131199
    {'degree': 16, 'field': [123201, 0, 0, 0, 0, 0, 0, 0, -41769, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [16]}
  • id: 131203
    {'degree': 16, 'field': [1734021, 932364, -890649, 45486, -334926, 348822, -80699, -15896, -13791, 11264, -1969, 204, -307, 98, 6, -8, 1], 'lmfdb_label': '2535.k3', 'torsion': [12]}
  • id: 131197
    {'degree': 16, 'field': [2436721, 0, -791068, 0, 339406, 0, -81220, 0, 3307, 0, -100, 0, 106, 0, 8, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 8]}
  • id: 131201
    {'degree': 16, 'field': [397683364, 0, 84997536, 0, 13841100, 0, 632736, 0, 4901, 0, 4056, 0, 312, 0, 0, 0, 1], 'lmfdb_label': '2535.k3', 'torsion': [2, 16]}
• 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: 43898
    {'conductor': 2535, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2535.k3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 43899
    {'conductor': 2535, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '2535.k3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 43900
    {'conductor': 2535, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '2535.k3', 'prime': 13, '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: 1680508
    {'adelic_gens': [[1, 0, 32, 1], [1951, 32, 406, 513], [2497, 32, 2512, 513], [23, 18, 3678, 4235], [6209, 32, 6208, 33], [2341, 32, 2356, 513], [5, 28, 68, 381], [30, 31, 4009, 6084], [1, 32, 0, 1], [4298, 6237, 3955, 212]], 'adelic_image': '6240.768.13.?', 'conductor': 2535, 'lmfdb_label': '2535.k3', 'prime': 0}
  • id: 12659
    {'conductor': 2535, 'elladic_image': '16.48.0.111', 'lmfdb_label': '2535.k3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 2535.k does not appear in ec_padic