Elliptic curve data - 397488.gg2

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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': '397488gg', 'Clabel': '397488gg2', 'Cnumber': 2, 'abc_quality': 0.9475546814672546, 'absD': 224666643746944372506624, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1092, 'ainvs': [0, 1, 0, -18088464, 18881529876], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 397488, 'degree': 37158912, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1826466763501536243091952097', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 162, 'isogeny_degrees': [1, 2], 'jinv': [281397674377, 96589584], 'lmfdb_iso': '397488.gg', 'lmfdb_label': '397488.gg2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -137, 380], 'min_quad_twist_disc': 364, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '12.24.0-12.b.1.3', '364.24.0.?', '1092.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 8281], [3, 4, 132496], [7, 32, 8112], [13, 98, 2352]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.23406974253178329431254299573', 'prec': 103}, 'szpiro_ratio': 4.789136813714766, '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, 0, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, 1, -2, 0, -4, 0, 2, 4, 4, -2, 0, 2, 2, -4, 12, 6, 0, 10, 4, -8, -6, -8, -8, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 397488, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '397488.gg', 'trace_hash': 1501947480604541864}
• 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': '0.0017202367492772988682270483622', 'prec': 110}, 'conductor': 397488, 'gens': [], 'heights': [], 'lmfdb_label': '397488.gg2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.091439614521112732275721150010', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1945507485067055746173076002364392696', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[1122, 0, 1], [3579, 0, 1]], 'xcoord_integral_points': [-4702, 1122, 3579]}
• lmfdb_label 397488.gg2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16400741
    {'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 4]}
  • id: 16400742
    {'degree': 4, 'field': [529, 0, -45, 0, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 4]}
  • id: 16400743
    {'degree': 4, 'field': [8281, 0, 91, 0, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 4]}
  • id: 16400746
    {'degree': 8, 'field': [-223587, 0, -42952, 0, -1638, 0, 0, 0, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 6]}
  • id: 16400745
    {'degree': 8, 'field': [6561, 0, -2916, 0, -3882, 0, -36, 0, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 8]}
  • id: 16400744
    {'degree': 8, 'field': [279841, 0, 23805, 0, 1496, 0, 45, 0, 1], 'lmfdb_label': '397488.gg2', 'torsion': [4, 4]}
  • id: 16400747
    {'degree': 16, 'field': [256, 0, 0, 0, 3168, 0, 0, 0, 4009, 0, 0, 0, 198, 0, 0, 0, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 8]}
  • id: 16400748
    {'degree': 16, 'field': [100116, -198936, 550476, -798408, 808950, -735960, 577962, -330060, 203059, -62104, 32218, -5908, 2413, -256, 82, -4, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 8]}
  • id: 16400749
    {'degree': 16, 'field': [589824, 0, -8334336, 0, -4622336, 0, -1041792, 0, 7680, 0, 10852, 0, -192, 0, 0, 0, 1], 'lmfdb_label': '397488.gg2', 'torsion': [2, 12]}
• 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: 9832317
    {'conductor': 397488, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '397488.gg2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9832318
    {'conductor': 397488, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '397488.gg2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 9832319
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '397488.gg2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9832320
    {'conductor': 397488, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '397488.gg2', '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: 4129777
    {'adelic_gens': [[1, 0, 4, 1], [501, 1090, 758, 1], [365, 4, 730, 9], [545, 1090, 0, 1091], [1, 4, 0, 1], [621, 1090, 314, 1], [1089, 4, 1088, 5]], 'adelic_image': '1092.48.0.?', 'conductor': 397488, 'lmfdb_label': '397488.gg2', 'prime': 0}
  • id: 1352351
    {'conductor': 397488, 'elladic_image': '4.12.0.1', 'lmfdb_label': '397488.gg2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 397488.gg does not appear in ec_padic