Elliptic curve data - 2448.p6

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '2448n', 'Clabel': '2448n4', 'Cnumber': 4, 'abc_quality': 1.0301007930420596, 'absD': 8740503770775552, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 816, 'ainvs': [0, 0, 0, 32541, -3889438], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 2448, 'degree': 12288, 'elladic_images': ['16.48.0.132'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7429580202554997546440657359', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1276229915423, 2927177028], 'lmfdb_iso': '2448.p', 'lmfdb_label': '2448.p6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 226, -2232], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.ba.2', '12.12.0-4.c.1.1', '16.48.0.y.2', '24.48.0-8.ba.2.5', '48.96.0-16.y.2.6', '68.12.0.h.1', '136.48.0.?', '204.24.0.?', '272.96.1.?', '408.96.0.?', '816.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.0343497823245598031678111908', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.50050469536149959952921099598', 'prec': 103}, 'szpiro_ratio': 5.622266590324776, '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, 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': '0.030625691201991347690030299438', 'prec': 107}, 'conductor': 2448, 'gens': [[2471, 67606, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '8.0343497823245598031678111908', 'prec': 100}], 'lmfdb_label': '2448.p6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21357311248152240761406359795', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4318421795525965639822134407750288898', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[94, 0, 1]], 'xcoord_integral_points': [94]}
• 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.p6'}
• ec_torsion_growth •

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

  
  
  • id: 125523
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [4]}
  • id: 125524
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '2448.p6', 'torsion': [4]}
  • id: 125522
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [2, 2]}
  • id: 125527
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [8]}
  • id: 125525
    {'degree': 4, 'field': [25, 0, 7, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [2, 4]}
  • id: 125526
    {'degree': 4, 'field': [289, 0, -68, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [8]}
  • id: 125532
    {'degree': 8, 'field': [-12, 0, 177, 0, 63, 0, -17, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [6]}
  • id: 125528
    {'degree': 8, 'field': [256, 128, -96, 144, 100, -36, -6, -2, 1], 'lmfdb_label': '2448.p6', 'torsion': [2, 4]}
  • id: 125530
    {'degree': 8, 'field': [297, 468, 96, 72, 145, -12, 22, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [2, 8]}
  • id: 125531
    {'degree': 8, 'field': [2817, -504, -888, 240, 118, -24, -8, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [16]}
  • id: 125529
    {'degree': 8, 'field': [4624, 0, 0, 0, 68, 0, 0, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [8]}
  • id: 125535
    {'degree': 16, 'field': [-6145703, 50656600, -1832480, -12472016, -2233632, -3601688, -2323184, -305184, 219958, 69768, 5408, 816, -784, -136, -16, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [16]}
  • id: 125538
    {'degree': 16, 'field': [-12, -168, -672, -144, 2460, 1140, -3884, -1048, 3104, 68, -1206, 326, 41, -30, 20, -8, 1], 'lmfdb_label': '2448.p6', 'torsion': [12]}
  • id: 125533
    {'degree': 16, 'field': [256, 128, 32, 720, -92, -476, 786, -334, -27, 182, -120, 34, 7, -12, 8, -4, 1], 'lmfdb_label': '2448.p6', 'torsion': [4, 4]}
  • id: 125536
    {'degree': 16, 'field': [1089, 0, 6636, 0, 109840, 0, -25200, 0, 10719, 0, -2048, 0, 144, 0, -12, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [2, 16]}
  • id: 125537
    {'degree': 16, 'field': [24964, 0, -165279, 0, 209818, 0, 209095, 0, 46095, 0, 5935, 0, 667, 0, 42, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [2, 6]}
  • id: 125534
    {'degree': 16, 'field': [104976, 0, 64800, 0, 27040, 0, 10592, 0, 2076, 0, -560, 0, -24, 0, -4, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [2, 8]}
  • id: 125539
    {'degree': 16, 'field': [389376, 0, -358464, 0, 169744, 0, -47904, 0, 8688, 0, -728, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '2448.p6', 'torsion': [12]}
• 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: 41880
    {'conductor': 2448, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '2448.p6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 41881
    {'conductor': 2448, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '2448.p6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 41882
    {'conductor': 2448, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2448.p6', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1679882
    {'adelic_gens': [[5, 4, 812, 813], [1, 16, 0, 1], [271, 0, 0, 815], [15, 2, 718, 803], [13, 288, 60, 121], [638, 333, 417, 386], [568, 273, 543, 10], [1, 0, 16, 1], [801, 16, 800, 17]], 'adelic_image': '816.192.1.?', 'conductor': 2448, 'lmfdb_label': '2448.p6', 'prime': 0}
  • id: 12111
    {'conductor': 2448, 'elladic_image': '16.48.0.132', 'lmfdb_label': '2448.p6', 'modell_image': '2B', '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}