Elliptic curve data - 227136.hc2

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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': '227136ba', 'Clabel': '227136ba1', 'Cnumber': 1, 'abc_quality': 1.1348018921255314, 'absD': 54641830048743555072, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 2184, 'ainvs': [0, 1, 0, -952033, 36426911], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 227136, 'degree': 5031936, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4769847934033233277738104591', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 184, 'isogeny_degrees': [1, 3], 'jinv': [2640625, 1512], 'lmfdb_iso': '227136.hc', 'lmfdb_label': '227136.hc2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -88, -40], 'min_quad_twist_disc': -104, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '168.8.0.?', '312.8.0.?', '1092.8.0.?', '2184.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3549], [3, 4, 75712], [7, 8, 32448], [13, 50, 1344]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70019377532120858306327725772', 'prec': 107}, 'szpiro_ratio': 4.290226528244348, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 1, 0, 1, 0, -3, 0, 0, 0, 0, 0, 3, 0, -5, 0], 'aplist': [0, 1, 0, 1, -3, 0, 3, -5, -6, 3, -4, -4, 3, 8, 9, 9, 6, -5, -14, -6, 4, 1, 6, 9, -8], 'class_deg': 3, 'class_size': 2, 'conductor': 227136, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '227136.hc', 'trace_hash': 24868846596100332}
• 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': '0.0070553464574795324149146697293', 'prec': 110}, 'conductor': 227136, 'gens': [], 'heights': [], 'lmfdb_label': '227136.hc2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17029224408006790344205850153', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0435069289608148413047020183587064066', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 227136.hc2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9860524
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '227136.hc2', 'torsion': [3]}
  • id: 9860525
    {'degree': 3, 'field': [103, -43, -1, 1], 'lmfdb_label': '227136.hc2', 'torsion': [2]}
  • id: 9860527
    {'degree': 6, 'field': [-4992, 0, 1924, 0, -26, 0, 1], 'lmfdb_label': '227136.hc2', 'torsion': [3]}
  • id: 9860528
    {'degree': 6, 'field': [2250, 1360, 772, 136, 19, -2, 1], 'lmfdb_label': '227136.hc2', 'torsion': [6]}
  • id: 9860526
    {'degree': 6, 'field': [2800, -3920, 1166, 172, -73, -2, 1], 'lmfdb_label': '227136.hc2', 'torsion': [2, 2]}
  • id: 9860529
    {'degree': 12, 'field': [1348452, 5837454, -2741010, -10125558, 3759770, -1464802, -142778, 22502, 7580, -209, -25, -1, 1], 'lmfdb_label': '227136.hc2', 'torsion': [4]}
  • id: 9860531
    {'degree': 12, 'field': [13816089, 0, -6562836, 0, 1100439, 0, 56856, 0, 223, 0, -20, 0, 1], 'lmfdb_label': '227136.hc2', 'torsion': [2, 6]}
  • id: 9860530
    {'degree': 12, 'field': [24920064, 0, 9604608, 0, 3571984, 0, 40040, 0, -1248, 0, 26, 0, 1], 'lmfdb_label': '227136.hc2', 'torsion': [3, 3]}
  • id: 9860533
    {'degree': 18, 'field': [3977701272, -4401768744, -1102856583, 2417650434, -973570073, 226399530, -60951127, 33360176, -7626882, -1193540, 816330, -232260, 32754, -12656, 69, 266, -61, -6, 1], 'lmfdb_label': '227136.hc2', 'torsion': [6]}
  • id: 9860532
    {'degree': 18, 'field': [1043514345433, -278359772082, 279448482915, -49217058572, 20214458112, -1228190844, 13707578, 195133932, -60462246, 12629872, -2068752, -39492, 95204, -29244, 4170, -284, 9, -6, 1], 'lmfdb_label': '227136.hc2', 'torsion': [9]}
• 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: 5631834
    {'conductor': 227136, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '227136.hc2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5631835
    {'conductor': 227136, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '227136.hc2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 5631836
    {'conductor': 227136, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '227136.hc2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5631837
    {'conductor': 227136, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '227136.hc2', 'prime': 13, 'reduction_type': 0, '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: 3112764
    {'adelic_gens': [[4, 3, 9, 7], [2179, 6, 2178, 7], [1, 6, 0, 1], [545, 1170, 0, 2183], [1249, 1014, 2067, 859], [3, 4, 8, 11], [2094, 1105, 1963, 222], [167, 0, 0, 2183], [1091, 1170, 585, 1325], [1, 0, 6, 1]], 'adelic_image': '2184.16.0.?', 'conductor': 227136, 'lmfdb_label': '227136.hc2', 'prime': 0}
  • id: 829857
    {'conductor': 227136, 'elladic_image': '3.4.0.1', 'lmfdb_label': '227136.hc2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 227136.hc does not appear in ec_padic