Elliptic curve data - 2448.p4

Formats: - HTML - YAML - JSON - 2023-09-26T19:11:18.590356

• 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': '2448n', 'Clabel': '2448n2', 'Cnumber': 2, 'absD': 90588973694976, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 408, 'ainvs': [0, 0, 0, -16419, -667870], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 2448, 'degree': 6144, 'elladic_images': ['8.48.0.89'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3963844299755270999354496751', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [163936758817, 30338064], 'lmfdb_iso': '2448.p', 'lmfdb_label': '2448.p4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -114, -396], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.h.2', '12.24.0-4.b.1.1', '24.96.0-8.h.2.1', '68.24.0.c.1', '136.96.1.?', '204.48.0.?', '408.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.0171748911622799015839055954', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.15393110508152694482059493518', 'prec': 103}, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -1, 0, -4, 0], 'aplist': [0, 0, 2, 0, -4, -2, -1, -4, 0, 10, -8, -2, -10, -12, 0, -6, 12, -10, 12, 0, 10, 8, 4, 6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 2448, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '2448.p', 'trace_hash': 1538785435641431420}
• 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': '0.061251382403982695380060598876', 'prec': 107}, 'conductor': 2448, 'gens': [[-97, 110, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.0171748911622799015839055954', 'prec': 100}], 'lmfdb_label': '2448.p4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.42714622496304481522812719590', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4318421795525965639822134407750288898', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-47, 0, 1], [145, 0, 1]], 'xcoord_integral_points': [-98, -97, -47, 145, 12295]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '2448.p4'}
• ec_torsion_growth •

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

  
  
  • id: 125498
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 4]}
  • id: 125501
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 8]}
  • id: 125499
    {'degree': 4, 'field': [16, 4, 5, -1, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 4]}
  • id: 125500
    {'degree': 4, 'field': [289, 0, -17, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 4]}
  • id: 125503
    {'degree': 8, 'field': [-50, 180, -38, -260, 71, 68, -18, -4, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 8]}
  • id: 125504
    {'degree': 8, 'field': [-12, 0, 177, 0, 63, 0, -17, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 6]}
  • id: 125502
    {'degree': 8, 'field': [256, 0, -144, 0, 65, 0, -9, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [4, 4]}
  • id: 125509
    {'degree': 16, 'field': [-12, -168, -672, -144, 2460, 1140, -3884, -1048, 3104, 68, -1206, 326, 41, -30, 20, -8, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 12]}
  • id: 125508
    {'degree': 16, 'field': [16, 0, 96, 0, 80, 0, -312, 0, 9, 0, 156, 0, 20, 0, -12, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 16]}
  • id: 125505
    {'degree': 16, 'field': [256, 0, 416, 0, 788, 0, -246, 0, -19, 0, -66, 0, 11, 0, 2, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [2, 8]}
  • id: 125506
    {'degree': 16, 'field': [256, 128, 32, 720, -92, -476, 786, -334, -27, 182, -120, 34, 7, -12, 8, -4, 1], 'lmfdb_label': '2448.p4', 'torsion': [4, 8]}
  • id: 125507
    {'degree': 16, 'field': [65536, 0, 0, 0, -12544, 0, 0, 0, 2145, 0, 0, 0, -49, 0, 0, 0, 1], 'lmfdb_label': '2448.p4', 'torsion': [4, 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: 41874
    {'conductor': 2448, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '2448.p4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 41875
    {'conductor': 2448, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '2448.p4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 41876
    {'conductor': 2448, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2448.p4', '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: 1679880
    {'adelic_gens': [[271, 0, 0, 407], [1, 0, 8, 1], [5, 4, 404, 405], [55, 138, 150, 403], [131, 300, 6, 245], [401, 8, 400, 9], [1, 8, 0, 1], [73, 312, 144, 37]], 'adelic_image': '408.192.1.?', 'conductor': 2448, 'lmfdb_label': '2448.p4', 'prime': 0}
  • id: 12109
    {'conductor': 2448, 'elladic_image': '8.48.0.89', 'lmfdb_label': '2448.p4', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 75394
    {'lmfdb_iso': '2448.p', 'p': 5, 'prec': 20, 'unit': 1774226430238, 'val': 1}
  • id: 75401
    {'lmfdb_iso': '2448.p', 'p': 11, 'prec': 20, 'unit': 57250848248025176333, 'val': 1}
  • id: 75399
    {'lmfdb_iso': '2448.p', 'p': 13, 'prec': 20, 'unit': 921861889820929935031, 'val': 1}
  • id: 75402
    {'lmfdb_iso': '2448.p', 'p': 19, 'prec': 20, 'unit': 495039285642591839228534, 'val': 1}
  • id: 75398
    {'lmfdb_iso': '2448.p', 'p': 29, 'prec': 20, 'unit': 5305100445640011528626506962, 'val': 1}
  • id: 75395
    {'lmfdb_iso': '2448.p', 'p': 31, 'prec': 20, 'unit': 21167955518629585536228021950, 'val': 1}
  • id: 75408
    {'lmfdb_iso': '2448.p', 'p': 37, 'prec': 20, 'unit': 285595912928634975108876757193, 'val': 1}
  • id: 75396
    {'lmfdb_iso': '2448.p', 'p': 41, 'prec': 20, 'unit': 2665833358689486505587775638713, 'val': 1}
  • id: 75397
    {'lmfdb_iso': '2448.p', 'p': 43, 'prec': 20, 'unit': 9327799234365198183948134107951, 'val': 1}
  • id: 75403
    {'lmfdb_iso': '2448.p', 'p': 53, 'prec': 20, 'unit': 331000859338879297918577156524880, 'val': 1}
  • id: 75406
    {'lmfdb_iso': '2448.p', 'p': 59, 'prec': 20, 'unit': 1241741273932923986789934575236985, 'val': 1}
  • id: 75407
    {'lmfdb_iso': '2448.p', 'p': 61, 'prec': 20, 'unit': 2416233209694400760369394259603408, 'val': 1}
  • id: 75393
    {'lmfdb_iso': '2448.p', 'p': 67, 'prec': 20, 'unit': 31960215400315397725296472760511561, 'val': 1}
  • id: 75404
    {'lmfdb_iso': '2448.p', 'p': 73, 'prec': 20, 'unit': 165773366720971281245560483407047119, 'val': 1}
  • id: 75400
    {'lmfdb_iso': '2448.p', 'p': 79, 'prec': 20, 'unit': 713100317882009038802900079487890917, 'val': 1}
  • id: 75392
    {'lmfdb_iso': '2448.p', 'p': 83, 'prec': 20, 'unit': 2765838474621030719325871488938186250, 'val': 1}
  • id: 75405
    {'lmfdb_iso': '2448.p', 'p': 89, 'prec': 20, 'unit': 3782640173672948886978909104635662889, 'val': 1}
  • id: 75391
    {'lmfdb_iso': '2448.p', 'p': 97, 'prec': 20, 'unit': 26325447968743833702328113770301641270, 'val': 1}