Elliptic curve data - 1520.b1

Formats: - HTML - YAML - JSON - 2023-01-27T07:43:38.410275

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1520i', 'Clabel': '1520i1', 'Cnumber': 1, 'absD': 6516050000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 760, 'ainvs': [0, 1, 0, -921, -10346], 'analytic_rank': 1, 'bad_primes': [2, 5, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1520, 'degree': 960, 'elladic_images': ['4.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.62837344719942831334375604364', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [5405726654464, 407253125], 'lmfdb_iso': '1520.b', 'lmfdb_label': '1520.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -921, 10346], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.1688769544000068094200299101', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.39732438701277987687134533649', 'prec': 103}, '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, -2, 0, 1, 0, 0, 0, 6, 0, 2, 0, 2, 0, 1, 0], 'aplist': [0, -2, -1, -2, 0, 6, 2, 1, 2, -2, -4, -10, -10, -6, 6, 6, 4, 2, 2, -12, -6, -8, 2, 2, -18], 'class_deg': 2, 'class_size': 2, 'conductor': 1520, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1520.b', 'trace_hash': 339103750695775740}
• 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': '0.28457828554320329714104802057', 'prec': 103}, 'conductor': 1520, 'gens': [[62, 418, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1688769544000068094200299101', 'prec': 100}], 'lmfdb_label': '1520.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.87068173419410979797942301164', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8884015479106371258984507535861225271', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-14, 0, 1]], 'xcoord_integral_points': [-14, 62]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1520.b1'}
• ec_torsion_growth •

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

  
  
  • id: 75449
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '1520.b1', 'torsion': [2, 2]}
  • id: 75450
    {'degree': 4, 'field': [2, 0, 0, -2, 1], 'lmfdb_label': '1520.b1', 'torsion': [4]}
  • id: 75453
    {'degree': 8, 'field': [-1728, 0, 1044, 0, -144, 0, 0, 0, 1], 'lmfdb_label': '1520.b1', 'torsion': [6]}
  • id: 75451
    {'degree': 8, 'field': [-4, 16, -16, -8, 14, 4, -4, -2, 1], 'lmfdb_label': '1520.b1', 'torsion': [2, 4]}
  • id: 75452
    {'degree': 8, 'field': [1, -2, 2, 2, -2, 2, 2, -2, 1], 'lmfdb_label': '1520.b1', 'torsion': [2, 4]}
  • id: 75454
    {'degree': 16, 'field': [1, -6, 18, -36, 47, -30, -18, 72, -95, 72, -18, -30, 47, -36, 18, -6, 1], 'lmfdb_label': '1520.b1', 'torsion': [4, 4]}
  • id: 75456
    {'degree': 16, 'field': [56169, 0, 32904, 0, -6740, 0, -12048, 0, -3330, 0, -88, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '1520.b1', 'torsion': [2, 6]}
  • id: 75455
    {'degree': 16, 'field': [280900, 0, -168000, 0, 845160, 0, -146880, 0, 8136, 0, -3184, 0, 436, 0, -16, 0, 1], 'lmfdb_label': '1520.b1', '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: 23403
    {'conductor': 1520, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '1520.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 23404
    {'conductor': 1520, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '1520.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 23405
    {'conductor': 1520, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1520.b1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1673994
    {'adelic_gens': [[1, 0, 8, 1], [753, 8, 752, 9], [1, 8, 0, 1], [1, 4, 4, 17], [381, 8, 0, 1], [3, 8, 28, 75], [183, 754, 6, 5], [616, 3, 5, 2], [5, 8, 48, 77], [401, 8, 84, 33]], 'adelic_image': '760.48.0.?', 'conductor': 1520, 'lmfdb_label': '1520.b1', 'prime': 0}
  • id: 7260
    {'conductor': 1520, 'elladic_image': '4.6.0.3', 'lmfdb_label': '1520.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 40296
    {'lmfdb_iso': '1520.b', 'p': 7, 'prec': 20, 'unit': 7513573613607076, 'val': 1}
  • id: 40300
    {'lmfdb_iso': '1520.b', 'p': 13, 'prec': 20, 'unit': 136320962409874045298, 'val': 1}
  • id: 40302
    {'lmfdb_iso': '1520.b', 'p': 17, 'prec': 20, 'unit': 86999915225273998065789, 'val': 1}
  • id: 40307
    {'lmfdb_iso': '1520.b', 'p': 23, 'prec': 20, 'unit': 68436854090306598399265885, 'val': 1}
  • id: 40299
    {'lmfdb_iso': '1520.b', 'p': 29, 'prec': 20, 'unit': 5269587742058786822450375883, 'val': 1}
  • id: 40312
    {'lmfdb_iso': '1520.b', 'p': 31, 'prec': 20, 'unit': 3100671042253233564362206974, 'val': 1}
  • id: 40295
    {'lmfdb_iso': '1520.b', 'p': 37, 'prec': 20, 'unit': 271644318641232352689836076238, 'val': 1}
  • id: 40297
    {'lmfdb_iso': '1520.b', 'p': 41, 'prec': 20, 'unit': 616580751670236710955175491208, 'val': 1}
  • id: 40298
    {'lmfdb_iso': '1520.b', 'p': 43, 'prec': 20, 'unit': 9669088923411583770292463911712, 'val': 1}
  • id: 40310
    {'lmfdb_iso': '1520.b', 'p': 47, 'prec': 20, 'unit': 27286715444188609515985884812509, 'val': 1}
  • id: 40304
    {'lmfdb_iso': '1520.b', 'p': 53, 'prec': 20, 'unit': 413250389833941859393596331418906, 'val': 1}
  • id: 40305
    {'lmfdb_iso': '1520.b', 'p': 59, 'prec': 20, 'unit': 2693428606873948197144622970259895, 'val': 1}
  • id: 40311
    {'lmfdb_iso': '1520.b', 'p': 61, 'prec': 20, 'unit': 1671961326964971344987939847166193, 'val': 1}
  • id: 40294
    {'lmfdb_iso': '1520.b', 'p': 67, 'prec': 20, 'unit': 46841739422158298566945651262529363, 'val': 1}
  • id: 40309
    {'lmfdb_iso': '1520.b', 'p': 71, 'prec': 20, 'unit': 139523393408289155845202693498216992, 'val': 1}
  • id: 40306
    {'lmfdb_iso': '1520.b', 'p': 73, 'prec': 20, 'unit': 73232970328651790251313944335240855, 'val': 1}
  • id: 40301
    {'lmfdb_iso': '1520.b', 'p': 79, 'prec': 20, 'unit': 940907412944140855495586256384758860, 'val': 1}
  • id: 40303
    {'lmfdb_iso': '1520.b', 'p': 83, 'prec': 20, 'unit': 2052664972079869191655599590965258129, 'val': 1}
  • id: 40308
    {'lmfdb_iso': '1520.b', 'p': 89, 'prec': 20, 'unit': 4834621450722713279255487148025499198, 'val': 1}
  • id: 40293
    {'lmfdb_iso': '1520.b', 'p': 97, 'prec': 20, 'unit': 34432199415114778413147164558135879054, 'val': 1}