Elliptic curve data - 65.a2

Formats: - HTML - YAML - JSON - 2023-03-28T05:16:00.130150

• 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': '65a', 'Clabel': '65a2', 'Cnumber': 2, 'absD': 4225, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [1, 0, 0, 4, 1], 'analytic_rank': 1, 'bad_primes': [5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 65, 'degree': 4, 'elladic_images': ['8.12.0.37'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.61504164701218906692326327839', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [6967871, 4225], 'lmfdb_iso': '65.a', 'lmfdb_label': '65.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 4, 1], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['1.1.0.1', '2.3.0.1', '4.6.0.5', '8.12.0.37', '260.12.0.?', '520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.18775704933063316090223643841', 'prec': 103}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61504164701218906692326327839', 'prec': 107}, '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, -2, -1, -1, 2, -4, 3, 1, 1, 2, 2, -1, 4, 2, -1, 2, -1, -6, 1], 'aplist': [-1, -2, -1, -4, 2, -1, 2, -6, -6, 2, -10, -2, -6, 10, 4, 2, 6, 2, -4, 6, -6, -12, -16, 2, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 65, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '65.a', 'trace_hash': 1364169308829084149}
• 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': '3.4215145161344667838159895157', 'prec': 100}, 'conductor': 65, 'gens': [[1, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.18775704933063316090223643841', 'prec': 103}], 'lmfdb_label': '65.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.6914267352859004970576117647', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.50533434230685977745953442460952885255', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-1, 1, 2]], 'xcoord_integral_points': [0, 1, 3, 11, 16, 393]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [3, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '65.a2'}
• ec_torsion_growth •

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

  
  
  • id: 2286
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '65.a2', 'torsion': [2, 2]}
  • id: 2287
    {'degree': 4, 'field': [-16, 0, -1, 0, 1], 'lmfdb_label': '65.a2', 'torsion': [4]}
  • id: 2290
    {'degree': 8, 'field': [-3, 0, -1, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '65.a2', 'torsion': [6]}
  • id: 2288
    {'degree': 8, 'field': [16, -56, 98, -86, 33, 6, 8, -4, 1], 'lmfdb_label': '65.a2', 'torsion': [2, 4]}
  • id: 2289
    {'degree': 8, 'field': [16, 0, -32, 0, 25, 0, -8, 0, 1], 'lmfdb_label': '65.a2', 'torsion': [2, 4]}
  • id: 2293
    {'degree': 16, 'field': [9, 0, 522, 0, -375, 0, 16, 0, -130, 0, 34, 0, 40, 0, 8, 0, 1], 'lmfdb_label': '65.a2', 'torsion': [2, 6]}
  • id: 2292
    {'degree': 16, 'field': [256, 0, 2896, 0, 3360, 0, -11821, 0, 689, 0, 1574, 0, 210, 0, -29, 0, 1], 'lmfdb_label': '65.a2', 'torsion': [8]}
  • id: 2291
    {'degree': 16, 'field': [3136, -2240, 8272, -16448, 18642, -10628, -502, 4868, -2023, -812, 1302, -372, -120, 56, 12, -8, 1], 'lmfdb_label': '65.a2', 'torsion': [4, 4]}
• 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: 335
    {'conductor': 65, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '65.a2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 336
    {'conductor': 65, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '65.a2', '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: 1666045
    {'adelic_gens': [[391, 8, 327, 17], [1, 0, 8, 1], [5, 8, 48, 77], [513, 8, 512, 9], [3, 8, 10, 27], [261, 8, 2, 17], [41, 2, 0, 1], [417, 6, 0, 1], [1, 8, 0, 1]], 'adelic_image': '520.48.0.?', 'conductor': 65, 'lmfdb_label': '65.a2', 'prime': 0}
  • id: 195
    {'conductor': 65, 'elladic_image': '8.12.0.37', 'lmfdb_label': '65.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 146
    {'lmfdb_iso': '65.a', 'p': 7, 'prec': 20, 'unit': 4411326274457138, 'val': 1}
  • id: 151
    {'lmfdb_iso': '65.a', 'p': 11, 'prec': 20, 'unit': 53616304024270417680, 'val': 1}
  • id: 152
    {'lmfdb_iso': '65.a', 'p': 17, 'prec': 20, 'unit': 185600086133575968586802, 'val': 1}
  • id: 153
    {'lmfdb_iso': '65.a', 'p': 19, 'prec': 20, 'unit': 671515904808903286998549, 'val': 1}
  • id: 157
    {'lmfdb_iso': '65.a', 'p': 23, 'prec': 20, 'unit': 10908928486152077139816067, 'val': 1}
  • id: 149
    {'lmfdb_iso': '65.a', 'p': 29, 'prec': 20, 'unit': 2762682662788971549263589731, 'val': 1}
  • id: 162
    {'lmfdb_iso': '65.a', 'p': 31, 'prec': 20, 'unit': 11622374795445317990719935680, 'val': 1}
  • id: 145
    {'lmfdb_iso': '65.a', 'p': 37, 'prec': 20, 'unit': 112295101785203693824955901564, 'val': 1}
  • id: 147
    {'lmfdb_iso': '65.a', 'p': 41, 'prec': 20, 'unit': 1320213556133048310585441892698, 'val': 1}
  • id: 148
    {'lmfdb_iso': '65.a', 'p': 43, 'prec': 20, 'unit': 225225489231719442733305558427, 'val': 2}
  • id: 160
    {'lmfdb_iso': '65.a', 'p': 47, 'prec': 20, 'unit': 55503566341700265131205610198083, 'val': 1}
  • id: 154
    {'lmfdb_iso': '65.a', 'p': 53, 'prec': 20, 'unit': 554974440453417248817556655110299, 'val': 1}
  • id: 155
    {'lmfdb_iso': '65.a', 'p': 59, 'prec': 20, 'unit': 646307799242231367814023307232522, 'val': 1}
  • id: 161
    {'lmfdb_iso': '65.a', 'p': 61, 'prec': 20, 'unit': 1294115125720408135927297731340031, 'val': 1}
  • id: 144
    {'lmfdb_iso': '65.a', 'p': 67, 'prec': 20, 'unit': 9606395249362291727859342863035516, 'val': 1}
  • id: 159
    {'lmfdb_iso': '65.a', 'p': 71, 'prec': 20, 'unit': 41548533125207347882492704702900941, 'val': 1}
  • id: 156
    {'lmfdb_iso': '65.a', 'p': 73, 'prec': 20, 'unit': 169630053180748402640755689659677009, 'val': 1}
  • id: 150
    {'lmfdb_iso': '65.a', 'p': 79, 'prec': 20, 'unit': 202251586041674838798708536045972580, 'val': 1}
  • id: 143
    {'lmfdb_iso': '65.a', 'p': 83, 'prec': 20, 'unit': 133152453144030652648785815248932021, 'val': 1}
  • id: 158
    {'lmfdb_iso': '65.a', 'p': 89, 'prec': 20, 'unit': 8267550566144888309272320917725438729, 'val': 1}
  • id: 142
    {'lmfdb_iso': '65.a', 'p': 97, 'prec': 20, 'unit': 35590272891399152235039219601062111116, 'val': 1}