Elliptic curve data - 520.b2

Formats: - HTML - YAML - JSON - 2025-01-26T15:38:56.116687

• 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': '520b', 'Clabel': '520b2', 'Cnumber': 2, 'abc_quality': 1.0943056888733467, 'absD': 4326400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [0, -1, 0, 0, -100], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 520, 'degree': 64, 'elladic_images': ['4.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.047762304261233957529395433250', 'prec': 110}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [-4, 4225], 'lmfdb_iso': '520.b', 'lmfdb_label': '520.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 0, -100], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.a.1.1', '260.24.0.?', '520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1], [5, 6, 104], [13, 14, 40]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.62538495472785504871042220113', 'prec': 107}, 'szpiro_ratio': 3.6353676327945914, '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, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0], 'aplist': [0, 2, 1, 0, 2, 1, 2, 2, 2, -6, 2, -6, 2, 6, -8, -2, 6, -14, 0, 10, -2, -4, 12, -6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 520, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '520.b', 'trace_hash': 1186478678348536011}
• 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': '1.1002358968805863477264740580', 'prec': 100}, 'conductor': 520, 'gens': [], 'heights': [], 'lmfdb_label': '520.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1253540262307849498608073576', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2507080524615698997216147152920679497', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[5, 0, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '5': [1, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '520.b2'}
• ec_torsion_growth •

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

  
  
  • id: 23336
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '520.b2', 'torsion': [2, 2]}
  • id: 23337
    {'degree': 4, 'field': [-4, 0, -7, 0, 1], 'lmfdb_label': '520.b2', 'torsion': [4]}
  • id: 23338
    {'degree': 4, 'field': [5, -2, -3, 0, 1], 'lmfdb_label': '520.b2', 'torsion': [2, 4]}
  • id: 23340
    {'degree': 8, 'field': [-48, 0, 112, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '520.b2', 'torsion': [6]}
  • id: 23339
    {'degree': 8, 'field': [196, -84, 18, -62, 29, -2, 8, -4, 1], 'lmfdb_label': '520.b2', 'torsion': [4, 4]}
  • id: 23342
    {'degree': 16, 'field': [1, 0, -8, 0, 12, 0, 8, 0, 234, 0, 8, 0, 12, 0, -8, 0, 1], 'lmfdb_label': '520.b2', 'torsion': [2, 8]}
  • id: 23343
    {'degree': 16, 'field': [9, 0, 0, 0, 232, 0, 0, 0, 30, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '520.b2', 'torsion': [2, 6]}
  • id: 23341
    {'degree': 16, 'field': [10000, 0, 164000, 0, 226100, 0, -43560, 0, -11059, 0, 636, 0, 311, 0, -44, 0, 1], 'lmfdb_label': '520.b2', 'torsion': [8]}
• 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: 5793
    {'conductor': 520, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '520.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5794
    {'conductor': 520, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '520.b2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5795
    {'conductor': 520, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '520.b2', 'prime': 13, '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: 1668126
    {'adelic_gens': [[513, 8, 512, 9], [3, 8, 10, 27], [1, 0, 8, 1], [1, 8, 0, 1], [5, 8, 48, 77], [261, 8, 0, 1], [417, 6, 0, 1], [391, 8, 327, 17], [41, 6, 0, 1]], 'adelic_image': '520.48.0.?', 'conductor': 520, 'lmfdb_label': '520.b2', 'prime': 0}
  • id: 2314
    {'conductor': 520, 'elladic_image': '4.12.0.12', 'lmfdb_label': '520.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 520.b does not appear in ec_padic