Elliptic curve data - 5200.bc2

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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': '5200bj', 'Clabel': '5200bj1', 'Cnumber': 1, 'abc_quality': 0.945239209920167, 'absD': 5452595200000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 156, 'ainvs': [0, -1, 0, -52208, 5822912], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 5200, 'degree': 43200, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7309455674217890382454625332', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 28, 'isogeny_degrees': [1, 3], 'jinv': [-9836106385, 3407872], 'lmfdb_iso': '5200.bc', 'lmfdb_label': '5200.bc2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -130, -780], 'min_quad_twist_disc': -20, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '12.8.0-3.a.1.1', '52.2.0.a.1', '78.8.0.?', '156.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 325], [5, 14, 208], [13, 14, 400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.035160221427556520905609143741', 'prec': 110}, 'szpiro_ratio': 5.220853248774041, '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, 2, 0, 0, 0, -5, 0, 1, 0, 3, 0, 1, 0, 0, 0, 3, 0, 4, 0], 'aplist': [0, 2, 0, -5, 3, 1, 3, 4, -6, 9, -5, 2, 0, -2, 9, -9, 9, -1, -5, 0, 14, 16, 15, -6, 8], 'class_deg': 3, 'class_size': 2, 'conductor': 5200, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '5200.bc', 'trace_hash': 2240015882112967206}
• 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': '0.031370380267436231848995926586', 'prec': 107}, 'conductor': 5200, 'gens': [], 'heights': [], 'lmfdb_label': '5200.bc2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.40423734416991492255595548196', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4254240650194895353357328917563963747', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [0, 0], '11': [0, 0], '13': [1, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '5200.bc2'}
• ec_torsion_growth •

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

  
  
  • id: 272525
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '5200.bc2', 'torsion': [3]}
  • id: 272526
    {'degree': 3, 'field': [-13, -3, -1, 1], 'lmfdb_label': '5200.bc2', 'torsion': [2]}
  • id: 272528
    {'degree': 6, 'field': [-3888, 0, 217, 0, -1, 0, 1], 'lmfdb_label': '5200.bc2', 'torsion': [3]}
  • id: 272529
    {'degree': 6, 'field': [32, -8, 1, -6, 2, -2, 1], 'lmfdb_label': '5200.bc2', 'torsion': [6]}
  • id: 272527
    {'degree': 6, 'field': [36, 48, 41, 22, 6, -2, 1], 'lmfdb_label': '5200.bc2', 'torsion': [2, 2]}
  • id: 272530
    {'degree': 12, 'field': [-8, 48, -46, -210, 633, -744, 424, -78, -29, 4, 12, -6, 1], 'lmfdb_label': '5200.bc2', 'torsion': [4]}
  • id: 272532
    {'degree': 12, 'field': [36, 168, 392, 232, 85, 54, 74, 4, -5, 12, 2, -2, 1], 'lmfdb_label': '5200.bc2', 'torsion': [2, 6]}
  • id: 272531
    {'degree': 12, 'field': [20736, 0, -73152, 0, 264256, 0, 22132, 0, 1341, 0, 43, 0, 1], 'lmfdb_label': '5200.bc2', 'torsion': [3, 3]}
  • id: 272534
    {'degree': 18, 'field': [-1016172, 0, -183780, 0, -284907, 0, -28763, 0, 11556, 0, 1758, 0, -1150, 0, 108, 0, -3, 0, 1], 'lmfdb_label': '5200.bc2', 'torsion': [6]}
  • id: 272533
    {'degree': 18, 'field': [16384, 0, 68160, 0, -27756, 0, 26893, 0, 1053, 0, -1038, 0, 569, 0, -78, 0, 9, 0, 1], 'lmfdb_label': '5200.bc2', '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: 101508
    {'conductor': 5200, 'conductor_valuation': 4, 'discriminant_valuation': 30, 'j_denominator_valuation': 18, 'kodaira_symbol': -26, 'lmfdb_label': '5200.bc2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 101509
    {'conductor': 5200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '5200.bc2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 101510
    {'conductor': 5200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5200.bc2', 'prime': 13, '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: 1697964
    {'adelic_gens': [[153, 154, 146, 149], [1, 0, 6, 1], [4, 3, 9, 7], [77, 150, 75, 137], [66, 97, 13, 27], [3, 4, 8, 11], [145, 6, 123, 19], [151, 6, 150, 7], [1, 6, 0, 1]], 'adelic_image': '156.16.0.?', 'conductor': 5200, 'lmfdb_label': '5200.bc2', 'prime': 0}
  • id: 25874
    {'conductor': 5200, 'elladic_image': '3.4.0.1', 'lmfdb_label': '5200.bc2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 5200.bc does not appear in ec_padic