Elliptic curve data - 16731.a1

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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': '16731m', 'Clabel': '16731m3', 'Cnumber': 3, 'abc_quality': 1.0929566831983986, 'absD': 38706181371, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 21450, 'ainvs': [0, 0, 1, -11894727, 15789916444], 'analytic_rank': 1, 'bad_primes': [3, 11, 13], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 16731, 'degree': 324000, 'elladic_images': ['25.60.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3284899381634703363357317444', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 25, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '16731.a', 'lmfdb_label': '16731.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': -39, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '22.2.0.a.1', '25.60.0.a.2', '110.24.1.?', '195.24.0.?', '275.300.12.?', '550.600.37.?', '975.120.0.?', '4290.48.1.?', '10725.600.12.?', '21450.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.1862651030965394789503617031', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 6, 1859], [11, 12, 1521], [13, 86, 99]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540516', 'prec': 103}, 'szpiro_ratio': 6.219877101517268, '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, -2, 0, 2, 1, 0, 2, 0, 0, -2, 1, 0, 0, -4, 0, -4, 2, 0, 0, 2], 'aplist': [-2, 0, 1, 2, 1, 0, 2, 0, 1, 0, -7, -3, -8, -6, 8, 6, 5, 12, 7, -3, -4, -10, -6, 15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 16731, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '16731.a', 'trace_hash': 2063933016220174503}
• 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': '0.0094950955049023554754256754453', 'prec': 110}, 'conductor': 16731, 'gens': [[199121, -331, 10]], 'heights': [{'__RealLiteral__': 0, 'data': '3.1862651030965394789503617031', 'prec': 100}], 'lmfdb_label': '16731.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.46719522322108848816163524946', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9772156721655045738446176560900936056', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': 'a', '5': [3, 0], '7': [1, 0], '11': [2, 0], '13': 'a', '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '16731.a1'}
• ec_torsion_growth •

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

  
  
  • id: 857327
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '16731.a1', 'torsion': [2]}
  • id: 857328
    {'degree': 4, 'field': [451, 49, -49, -1, 1], 'lmfdb_label': '16731.a1', 'torsion': [5]}
  • id: 857329
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '16731.a1', 'torsion': [2, 2]}
  • id: 857330
    {'degree': 8, 'field': [-403, -520, -248, 52, 73, 23, -16, -1, 1], 'lmfdb_label': '16731.a1', 'torsion': [3]}
  • id: 857331
    {'degree': 10, 'field': [95160, -41145, 63190, -23090, 12995, -3179, 1305, -210, 60, -5, 1], 'lmfdb_label': '16731.a1', 'torsion': [5]}
  • id: 857332
    {'degree': 12, 'field': [-144887402, 20247920, 14228324, 4366164, 2460352, 169072, 59808, 9852, -2170, 74, 6, -2, 1], 'lmfdb_label': '16731.a1', 'torsion': [4]}
  • id: 857333
    {'degree': 12, 'field': [111518761, -15711752, -33388708, 2328873, 4019209, -128736, -252957, 1558, 8505, 53, -145, -1, 1], 'lmfdb_label': '16731.a1', 'torsion': [10]}
  • id: 857334
    {'degree': 20, 'field': [-190368299, -5875799490, 90691563710, 644271782165, 972043495665, 135507893973, -482887616315, -156501267540, 82179646665, 24262726215, -7466149376, -1254729705, 321485245, 30211755, -7026170, -369798, 80305, 2205, -455, -5, 1], 'lmfdb_label': '16731.a1', 'torsion': [25]}
• 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: 372313
    {'conductor': 16731, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '16731.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 372314
    {'conductor': 16731, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '16731.a1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 372315
    {'conductor': 16731, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '16731.a1', 'prime': 13, 'reduction_type': 0, '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: 1775455
    {'adelic_gens': [[2536, 17745, 20865, 18916], [38, 41, 18891, 18689], [9790, 14859, 9477, 13963], [14299, 0, 0, 21449], [1649, 0, 0, 21449], [1, 50, 0, 1], [1, 0, 50, 1], [21401, 50, 21400, 51]], 'adelic_image': '21450.1200.37.?', 'conductor': 16731, 'lmfdb_label': '16731.a1', 'prime': 0}
  • id: 78495
    {'conductor': 16731, 'elladic_image': '25.60.0.2', 'lmfdb_label': '16731.a1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 761488
    {'lmfdb_iso': '16731.a', 'p': 5, 'prec': 20, 'unit': 11783453688226, 'val': 1}
  • id: 761473
    {'lmfdb_iso': '16731.a', 'p': 7, 'prec': 20, 'unit': 2613885509550864, 'val': 1}
  • id: 761478
    {'lmfdb_iso': '16731.a', 'p': 17, 'prec': 20, 'unit': 2104568123276122504997, 'val': 1}
  • id: 761483
    {'lmfdb_iso': '16731.a', 'p': 23, 'prec': 20, 'unit': 1671725769062556615122154333, 'val': -1}
  • id: 761474
    {'lmfdb_iso': '16731.a', 'p': 31, 'prec': 20, 'unit': 8038669249024638124241175939, 'val': 1}
  • id: 761472
    {'lmfdb_iso': '16731.a', 'p': 37, 'prec': 20, 'unit': 614567323901903011388325422078, 'val': 1}
  • id: 761475
    {'lmfdb_iso': '16731.a', 'p': 41, 'prec': 20, 'unit': 748408925365051046800128090147, 'val': 1}
  • id: 761476
    {'lmfdb_iso': '16731.a', 'p': 43, 'prec': 20, 'unit': 8719334216426829260630775277588, 'val': 1}
  • id: 761486
    {'lmfdb_iso': '16731.a', 'p': 47, 'prec': 20, 'unit': 23174000824661060145613977756170, 'val': 1}
  • id: 761480
    {'lmfdb_iso': '16731.a', 'p': 53, 'prec': 20, 'unit': 503112259459423022253453685616499, 'val': 1}
  • id: 761481
    {'lmfdb_iso': '16731.a', 'p': 59, 'prec': 20, 'unit': 68969424004226364182255502823892, 'val': 1}
  • id: 761487
    {'lmfdb_iso': '16731.a', 'p': 61, 'prec': 20, 'unit': 1261571856501014924984807401643627, 'val': 1}
  • id: 761471
    {'lmfdb_iso': '16731.a', 'p': 67, 'prec': 20, 'unit': 29260602314356152514161113603836562, 'val': 1}
  • id: 761485
    {'lmfdb_iso': '16731.a', 'p': 71, 'prec': 20, 'unit': 18433782866001534201054229511790867, 'val': 1}
  • id: 761482
    {'lmfdb_iso': '16731.a', 'p': 73, 'prec': 20, 'unit': 50141722070804822121645801298556744, 'val': 1}
  • id: 761477
    {'lmfdb_iso': '16731.a', 'p': 79, 'prec': 20, 'unit': 336330661803052923679470762816104868, 'val': 1}
  • id: 761479
    {'lmfdb_iso': '16731.a', 'p': 83, 'prec': 20, 'unit': 319046506988897045656423997233136542, 'val': 1}
  • id: 761484
    {'lmfdb_iso': '16731.a', 'p': 89, 'prec': 20, 'unit': 497241965998284130828240929349348657, 'val': 1}
  • id: 761470
    {'lmfdb_iso': '16731.a', 'p': 97, 'prec': 20, 'unit': 32490452428120155997788014543904879526, 'val': 1}