Elliptic curve data - 510.b2

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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': '510b', 'Clabel': '510b1', 'Cnumber': 1, 'abc_quality': 0.9692928591029916, 'absD': 639221760, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2040, 'ainvs': [1, 0, 1, -723, -7634], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 510, 'degree': 336, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.49210480944797410664589422705', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [-41713327443241, 639221760], 'lmfdb_iso': '510.b', 'lmfdb_label': '510.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -723, -7634], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '30.6.0.a.1', '136.6.0.?', '2040.12.0.?'], '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': True, 'serre_invariants': [[2, 4, 15], [3, 4, 170], [5, 6, 102], [7, 2, 255], [17, 18, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49210480944797410664589422705', 'prec': 103}, 'szpiro_ratio': 5.034634193679831, '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, -1, 1, 1, 1, -1, -2, -1, 1, -1, 4, 1, 0, 2, 1, 1, 1, -1, 4, 1], 'aplist': [-1, 1, 1, -2, 4, 0, 1, 4, 4, 6, -8, -6, 8, 2, -8, 14, 6, 2, 2, -10, 4, 4, -16, 6, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 510, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '510.b', 'trace_hash': 252247044085173447}
• 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': '0.37373450292005060618310891134', 'prec': 103}, 'conductor': 510, 'gens': [], 'heights': [], 'lmfdb_label': '510.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.46000385520280639545017284822', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3800115656084191863505185446584144547', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[31, -16, 1]], 'xcoord_integral_points': [31]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [1, 0], '5': [1, 0], '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '510.b2'}
• ec_torsion_growth •

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

  
  
  • id: 22847
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '510.b2', 'torsion': [2, 2]}
  • id: 22848
    {'degree': 4, 'field': [-25, 6, -5, -2, 1], 'lmfdb_label': '510.b2', 'torsion': [4]}
  • id: 22851
    {'degree': 8, 'field': [-48, 0, -52, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '510.b2', 'torsion': [6]}
  • id: 22850
    {'degree': 8, 'field': [225, 0, 2070, 0, 31, 0, 2, 0, 1], 'lmfdb_label': '510.b2', 'torsion': [2, 4]}
  • id: 22849
    {'degree': 8, 'field': [256, 0, 149, 0, 51, 0, -1, 0, 1], 'lmfdb_label': '510.b2', 'torsion': [2, 4]}
  • id: 22852
    {'degree': 16, 'field': [-82500, 56394000, -34354200, -44761200, 23640160, -296520, -1836572, 1476520, -133395, -169440, 46648, -7584, 1810, -280, 60, -8, 1], 'lmfdb_label': '510.b2', 'torsion': [8]}
  • id: 22853
    {'degree': 16, 'field': [1440, -24570, 162765, -260490, 91200, 45000, -12299, -1448, -915, 1130, -457, 48, 83, -70, 30, -8, 1], 'lmfdb_label': '510.b2', '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: 5642
    {'conductor': 510, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '510.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5643
    {'conductor': 510, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '510.b2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 5644
    {'conductor': 510, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '510.b2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5645
    {'conductor': 510, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '510.b2', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1668081
    {'adelic_gens': [[1, 2, 2, 5], [257, 1786, 1784, 255], [1, 4, 0, 1], [1021, 4, 2, 9], [241, 4, 482, 9], [682, 1, 679, 0], [1, 0, 4, 1], [2037, 4, 2036, 5], [3, 4, 8, 11], [1634, 1, 1223, 0]], 'adelic_image': '2040.12.0.?', 'conductor': 510, 'lmfdb_label': '510.b2', 'prime': 0}
  • id: 2272
    {'conductor': 510, 'elladic_image': '2.3.0.1', 'lmfdb_label': '510.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 510.b does not appear in ec_padic