Elliptic curve data - 398544.w2

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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': '398544w', 'Clabel': '398544w1', 'Cnumber': 1, 'abc_quality': 1.0472106764374878, 'absD': 1324911815479256832, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [0, -1, 0, -1049908, 418108288], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 398544, 'degree': 5870592, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2949669477401339238019881075', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2], 'jinv': [-10627137250000, 110008287], 'lmfdb_iso': '398544.w', 'lmfdb_label': '398544.w2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2908, 61876], 'min_quad_twist_disc': 76, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.b.1', '46.6.0.a.1', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 8303], [3, 4, 132848], [7, 2, 132848], [19, 182, 1104], [23, 24, 17328]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.36064933778361682085265297725', 'prec': 103}, 'szpiro_ratio': 4.127305707899595, '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, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 8, 0, 0, 0], 'aplist': [0, -1, 0, 2, 0, -2, 8, 0, -1, -2, -4, -6, -10, -6, 0, -12, 4, -10, -6, 0, 2, -6, 0, 12, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 398544, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '398544.w', 'trace_hash': 543430034907005318}
• 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': '0.010153529545379949438756823462', 'prec': 107}, 'conductor': 398544, 'gens': [], 'heights': [], 'lmfdb_label': '398544.w2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27247917051889006932788256434', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.54495834103778013865576512867258964850', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-1184, 0, 1]], 'xcoord_integral_points': [-1184]}
• lmfdb_label 398544.w2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16441564
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '398544.w2', 'torsion': [2, 2]}
  • id: 16441565
    {'degree': 4, 'field': [-554, -114, -49, 0, 1], 'lmfdb_label': '398544.w2', 'torsion': [4]}
  • id: 16441568
    {'degree': 8, 'field': [-2178726, 4922940, 2619422, 151416, 3840, -2642, -48, 0, 1], 'lmfdb_label': '398544.w2', 'torsion': [6]}
  • id: 16441566
    {'degree': 8, 'field': [82944, 0, 1260, 0, 900, 0, 59, 0, 1], 'lmfdb_label': '398544.w2', 'torsion': [2, 4]}
  • id: 16441567
    {'degree': 8, 'field': [121104, 0, -21276, 0, 1264, 0, -31, 0, 1], 'lmfdb_label': '398544.w2', 'torsion': [2, 4]}
  • id: 16441569
    {'degree': 16, 'field': [38912644, 0, 118805104, 0, 16594276, 0, 6245188, 0, 481837, 0, -95540, 0, 4582, 0, -104, 0, 1], 'lmfdb_label': '398544.w2', 'torsion': [8]}
  • id: 16441570
    {'degree': 16, 'field': [204421263216108, -254091064934688, 137499469306264, -31702756835320, 3041085626968, -211078965384, 27208863192, 1378617432, -195785580, -5141748, -252804, -28632, 11574, -1032, 34, -4, 1], 'lmfdb_label': '398544.w2', 'torsion': [2, 6]}
• 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: 9858844
    {'conductor': 398544, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '398544.w2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9858845
    {'conductor': 398544, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '398544.w2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9858846
    {'conductor': 398544, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '398544.w2', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9858847
    {'conductor': 398544, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '398544.w2', 'prime': 23, '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: 4136222
    {'adelic_gens': [[1, 0, 4, 1], [185, 4, 94, 9], [3, 4, 8, 11], [1, 2, 2, 5], [194, 1, 179, 0], [1, 4, 0, 1], [273, 4, 272, 5], [73, 208, 68, 207]], 'adelic_image': '276.12.0.?', 'conductor': 398544, 'lmfdb_label': '398544.w2', 'prime': 0}
  • id: 1355734
    {'conductor': 398544, 'elladic_image': '2.3.0.1', 'lmfdb_label': '398544.w2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 398544.w does not appear in ec_padic