Elliptic curve data - 159936.gl2

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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': '159936l', 'Clabel': '159936l2', 'Cnumber': 2, 'abc_quality': 1.0201210746994576, 'absD': 3451911414257383870464, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 1, 0, -6666809, -5994553209], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 159936, 'degree': 7077888, 'elladic_images': ['8.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8675219918952138742778936036', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 167, 'isogeny_degrees': [1, 2], 'jinv': [68003243639904448, 7163272192041], 'lmfdb_iso': '159936.gl', 'lmfdb_label': '159936.gl2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -34014, -2172456], 'min_quad_twist_disc': 56, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.1', '12.12.0-2.a.1.2', '24.24.0-24.a.1.8', '28.12.0.a.1', '56.24.0-28.a.1.1', '84.24.0.?', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.2198942836928860144221550264', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 53312], [7, 32, 3264], [17, 18, 9408]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2014197368076119123079851104', 'prec': 100}, 'szpiro_ratio': 4.90310174012427, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -2, 0, 0, 0, 1, 0, -4, 0, 2, 0, -2, 0, 1, 0, 4, 0], 'aplist': [0, 1, -2, 0, -4, 2, 1, 4, -4, 2, 8, 2, 2, 8, 0, -6, -4, 2, -8, -4, 6, 0, 4, -6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 159936, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '159936.gl', 'trace_hash': 1677610419313163895}
• 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': '0.0032307402650171455970113884028', 'prec': 110}, 'conductor': 159936, 'gens': [[8899, 799680, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.2198942836928860144221550264', 'prec': 100}], 'lmfdb_label': '159936.gl2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.094595127562272901856205198963', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.3100714520710852182318517888333729624', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[-1097, 0, 1], [2949, 0, 1]], 'xcoord_integral_points': [-1853, -1403, -1097, 2949, 8899]}
• lmfdb_label 159936.gl2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7152782
    {'degree': 4, 'field': [4, 0, 10, 0, 1], 'lmfdb_label': '159936.gl2', 'torsion': [2, 4]}
  • id: 7152781
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '159936.gl2', 'torsion': [2, 4]}
  • id: 7152783
    {'degree': 4, 'field': [121, 0, -20, 0, 1], 'lmfdb_label': '159936.gl2', 'torsion': [2, 4]}
  • id: 7152784
    {'degree': 8, 'field': [-28812, 0, -13720, 0, -588, 0, 0, 0, 1], 'lmfdb_label': '159936.gl2', 'torsion': [2, 6]}
  • id: 7152786
    {'degree': 16, 'field': [-149772167, 39891956, 462849472, 22341564, -38801504, 562632, -4070696, 361220, 93129, 1504, 3388, -3780, 1162, 84, -20, -8, 1], 'lmfdb_label': '159936.gl2', 'torsion': [2, 8]}
  • id: 7152788
    {'degree': 16, 'field': [36, 0, 0, 0, -192, 0, 1008, 0, 2932, 0, 2240, 0, 816, 0, 56, 0, 1], 'lmfdb_label': '159936.gl2', 'torsion': [2, 8]}
  • id: 7152785
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '159936.gl2', 'torsion': [4, 4]}
  • id: 7152787
    {'degree': 16, 'field': [10071928881, 0, 4148861472, 0, 1231924464, 0, 49143672, 0, 501102, 0, -10944, 0, 3360, 0, -24, 0, 1], 'lmfdb_label': '159936.gl2', 'torsion': [2, 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: 3955396
    {'conductor': 159936, 'conductor_valuation': 6, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '159936.gl2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3955397
    {'conductor': 159936, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '159936.gl2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 3955398
    {'conductor': 159936, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '159936.gl2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3955399
    {'conductor': 159936, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '159936.gl2', 'prime': 17, 'reduction_type': 1, '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: 2698452
    {'adelic_gens': [[45, 4, 8, 11], [95, 166, 0, 167], [1, 4, 0, 1], [1, 0, 4, 1], [3, 2, 110, 167], [81, 166, 2, 1], [165, 4, 164, 5]], 'adelic_image': '168.48.0.?', 'conductor': 159936, 'lmfdb_label': '159936.gl2', 'prime': 0}
  • id: 609247
    {'conductor': 159936, 'elladic_image': '8.12.0.1', 'lmfdb_label': '159936.gl2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 159936.gl does not appear in ec_padic