Elliptic curve data - 224576.j2

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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': '224576bf', 'Clabel': '224576bf2', 'Cnumber': 2, 'abc_quality': 0.8742214421492837, 'absD': 707896954535936, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 7656, 'ainvs': [0, -1, 0, 17263, 930481], 'analytic_rank': 0, 'bad_primes': [2, 11, 29], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 224576, 'degree': 1036800, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5355077480028211338449901572', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 9, 'isogeny_degrees': [1, 3], 'jinv': [19600688, 24389], 'lmfdb_iso': '224576.j', 'lmfdb_label': '224576.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 36, -76], 'min_quad_twist_disc': -88, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '116.2.0.?', '264.8.0.?', '348.8.0.?', '7656.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 3509], [3, 2, 7744], [11, 62, 1856], [29, 30, 7744]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.47211159904963366583941910682', 'prec': 107}, 'szpiro_ratio': 3.3292072190875177, '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, -3, 0, 4, 0, -2, 0, 0, 0, 5, 0, 3, 0, 6, 0, -4, 0], 'aplist': [0, -1, -3, 4, 0, 5, 6, -4, -6, -1, 5, -8, 0, -1, -3, -3, -6, 2, -8, 6, 16, -11, 6, -12, 8], 'class_deg': 3, 'class_size': 2, 'conductor': 224576, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '224576.j', 'trace_hash': 1203019161551243517}
• 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': '0.046374038287489540190440786984', 'prec': 107}, 'conductor': 224576, 'gens': [], 'heights': [], 'lmfdb_label': '224576.j2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34079880283054010462547083611', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3631952113221604185018833444590452850', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 224576.j2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9766731
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '224576.j2', 'torsion': [3]}
  • id: 9766732
    {'degree': 3, 'field': [-2, 0, -1, 1], 'lmfdb_label': '224576.j2', 'torsion': [2]}
  • id: 9766735
    {'degree': 6, 'field': [-71874, 0, 1089, 0, 66, 0, 1], 'lmfdb_label': '224576.j2', 'torsion': [6]}
  • id: 9766733
    {'degree': 6, 'field': [16, -8, 22, 10, -1, -2, 1], 'lmfdb_label': '224576.j2', 'torsion': [2, 2]}
  • id: 9766734
    {'degree': 6, 'field': [2662, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '224576.j2', 'torsion': [3]}
  • id: 9766736
    {'degree': 12, 'field': [-3054421, -3975308, -1814510, -7488, 347997, 147516, 25500, 1892, 47, -56, -38, -4, 1], 'lmfdb_label': '224576.j2', 'torsion': [4]}
  • id: 9766737
    {'degree': 12, 'field': [7091569, -15978, -39909, 106430, -39840, -16098, 5465, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '224576.j2', 'torsion': [3, 3]}
  • id: 9766738
    {'degree': 12, 'field': [5820469264, -1007054400, -27536488, 16579432, -8837970, 990348, 16598, -1872, 7615, -408, 138, -4, 1], 'lmfdb_label': '224576.j2', 'torsion': [2, 6]}
  • id: 9766739
    {'degree': 18, 'field': [-50477397451839, -80016363835650, 83861767266075, -5758193603538, -5197787652267, 9263436534, 34491118126, 2964096438, -2265885420, -217986968, 70137105, 913848, -868549, 14094, 19563, -58, -120, 0, 1], 'lmfdb_label': '224576.j2', 'torsion': [9]}
  • id: 9766740
    {'degree': 18, 'field': [10706185664, 0, 0, -670229696, 0, 0, 43677904, 0, 0, 914048, 0, 0, 15970, 0, 0, -12, 0, 0, 1], 'lmfdb_label': '224576.j2', 'torsion': [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: 5571964
    {'conductor': 224576, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '224576.j2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5571965
    {'conductor': 224576, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '224576.j2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5571966
    {'conductor': 224576, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '224576.j2', 'prime': 29, '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: 3097781
    {'adelic_gens': [[4, 3, 9, 7], [7651, 6, 7650, 7], [1187, 1386, 429, 4157], [4871, 0, 0, 7655], [3827, 0, 0, 7655], [2441, 1386, 2442, 1385], [3970, 3333, 3905, 1385], [1, 6, 0, 1], [3, 4, 8, 11], [5743, 6270, 5049, 3499], [1, 0, 6, 1]], 'adelic_image': '7656.16.0.?', 'conductor': 224576, 'lmfdb_label': '224576.j2', 'prime': 0}
  • id: 822301
    {'conductor': 224576, 'elladic_image': '3.4.0.1', 'lmfdb_label': '224576.j2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 224576.j does not appear in ec_padic