Elliptic curve data - 86640.j1

Formats: - HTML - YAML - JSON - 2024-04-25T08:55:38.482352

• 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': '86640bw', 'Clabel': '86640bw4', 'Cnumber': 4, 'abc_quality': 0.962838731498289, 'absD': 8581168694400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, -1, 0, -3587016, -2609861520], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 86640, 'degree': 2211840, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5282842193947194742821832967', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4], 'jinv': [26487576322129, 44531250], 'lmfdb_iso': '86640.j', 'lmfdb_label': '86640.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -621, -6207], 'min_quad_twist_disc': 76, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.12.0-4.c.1.2', '24.24.0-8.m.1.1', '152.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.5206697907114020299968809728', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.36291754925155393486043745930', 'prec': 103}, 'szpiro_ratio': 5.003915078781729, '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, -1, 0, -1, 0, 0, 0, 1, 0, -4, 0, -2, 0, 1, 0, 2, 0, 0, 0], 'aplist': [0, -1, -1, 0, -4, -2, 2, 0, -4, -6, 4, 6, -10, 4, 12, -6, -12, -2, 4, 8, -6, -4, 12, -10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 86640, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '86640.j', 'trace_hash': 421911429191430110}
• 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': '0.0063673720929900697459446943013', 'prec': 110}, 'conductor': 86640, 'gens': [[180826, 76537054, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '8.5206697907114020299968809728', 'prec': 100}], 'lmfdb_label': '86640.j1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10971350037349878328213521623', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7393300330627008247904687075965400003', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-1127, 0, 1]], 'xcoord_integral_points': [-1127]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [1, 3, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': 'a', '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': '86640.j1'}
• ec_torsion_growth •

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

  
  
  • id: 4058461
    {'degree': 2, 'field': [-114, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [2, 2]}
  • id: 4058463
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '86640.j1', 'torsion': [4]}
  • id: 4058462
    {'degree': 2, 'field': [38, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [4]}
  • id: 4058464
    {'degree': 4, 'field': [1444, 0, -38, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [2, 4]}
  • id: 4058466
    {'degree': 8, 'field': [729, 0, -108, 0, -12, 0, 4, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [8]}
  • id: 4058467
    {'degree': 8, 'field': [3364, 0, -536, 0, 177, 0, -23, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [8]}
  • id: 4058465
    {'degree': 8, 'field': [12996, 0, 0, 0, -1596, 0, 0, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [2, 4]}
  • id: 4058468
    {'degree': 8, 'field': [122160, -128184, 46118, -6480, 600, -98, -12, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [6]}
  • id: 4058471
    {'degree': 16, 'field': [6561, 0, 2916, 0, 8748, 0, -3960, 0, 8239, 0, -440, 0, 108, 0, 4, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [2, 8]}
  • id: 4058472
    {'degree': 16, 'field': [2782224, 0, 19655424, 0, 32128416, 0, -11651664, 0, 892200, 0, -79536, 0, 2569, 0, -64, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [2, 6]}
  • id: 4058470
    {'degree': 16, 'field': [8020224, 0, 2405376, 0, -1126176, 0, -29664, 0, 94321, 0, -16250, 0, 1455, 0, -62, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [2, 8]}
  • id: 4058474
    {'degree': 16, 'field': [91527489, -22444182, 22819986, -10678260, 8664904, -4400934, -140292, -788912, 271071, 31986, 24984, -2340, -228, -260, 12, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [12]}
  • id: 4058469
    {'degree': 16, 'field': [174900625, 0, 18038900, 0, -1234154, 0, 424976, 0, 46987, 0, -3664, 0, -218, 0, -4, 0, 1], 'lmfdb_label': '86640.j1', 'torsion': [4, 4]}
  • id: 4058473
    {'degree': 16, 'field': [10306939392, 8865004032, 28008159168, -8951088288, 2720751716, -539088192, 151947120, -34881240, 8995488, -1892448, 319792, -38352, 3312, -4, -24, 0, 1], 'lmfdb_label': '86640.j1', '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: 2114493
    {'conductor': 86640, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '86640.j1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2114494
    {'conductor': 86640, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '86640.j1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2114495
    {'conductor': 86640, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '86640.j1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2114496
    {'conductor': 86640, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '86640.j1', 'prime': 19, 'reduction_type': 0, '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: 2234749
    {'adelic_gens': [[160, 3, 157, 2], [449, 8, 448, 9], [1, 0, 8, 1], [136, 453, 427, 454], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 450, 451], [288, 65, 163, 150], [277, 284, 238, 51]], 'adelic_image': '456.48.0.?', 'conductor': 86640, 'lmfdb_label': '86640.j1', 'prime': 0}
  • id: 353165
    {'conductor': 86640, 'elladic_image': '8.12.0.11', 'lmfdb_label': '86640.j1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4476823
    {'lmfdb_iso': '86640.j', 'p': 11, 'prec': 20, 'unit': 5910916730623462706, 'val': 1}
  • id: 4476829
    {'lmfdb_iso': '86640.j', 'p': 13, 'prec': 20, 'unit': 89753463304083675897, 'val': 2}
  • id: 4476831
    {'lmfdb_iso': '86640.j', 'p': 17, 'prec': 20, 'unit': 1403925800108758644952, 'val': 1}
  • id: 4476836
    {'lmfdb_iso': '86640.j', 'p': 23, 'prec': 20, 'unit': 3044762526815985858614245, 'val': 1}
  • id: 4476828
    {'lmfdb_iso': '86640.j', 'p': 29, 'prec': 20, 'unit': 107613583273699553739062661, 'val': 1}
  • id: 4476840
    {'lmfdb_iso': '86640.j', 'p': 31, 'prec': 20, 'unit': 7149210799994691069415463177, 'val': 1}
  • id: 4476824
    {'lmfdb_iso': '86640.j', 'p': 37, 'prec': 20, 'unit': 538078483945949896886657079071, 'val': 1}
  • id: 4476826
    {'lmfdb_iso': '86640.j', 'p': 41, 'prec': 20, 'unit': 3129563045777552977814987802768, 'val': 1}
  • id: 4476827
    {'lmfdb_iso': '86640.j', 'p': 43, 'prec': 20, 'unit': 5310578587225755379073126546346, 'val': 1}
  • id: 4476838
    {'lmfdb_iso': '86640.j', 'p': 47, 'prec': 20, 'unit': 16684046565562844778042061354535, 'val': 1}
  • id: 4476833
    {'lmfdb_iso': '86640.j', 'p': 53, 'prec': 20, 'unit': 17825108432569690132211295975275, 'val': 1}
  • id: 4476834
    {'lmfdb_iso': '86640.j', 'p': 59, 'prec': 20, 'unit': 1205846783682647851667677197237662, 'val': 1}
  • id: 4476839
    {'lmfdb_iso': '86640.j', 'p': 61, 'prec': 20, 'unit': 6215262653990222015850012871268687, 'val': 1}
  • id: 4476832
    {'lmfdb_iso': '86640.j', 'p': 67, 'prec': 20, 'unit': 36296620703562576881842380448042337, 'val': 1}
  • id: 4476825
    {'lmfdb_iso': '86640.j', 'p': 71, 'prec': 20, 'unit': 111184925206130695255094297597666936, 'val': 1}
  • id: 4476835
    {'lmfdb_iso': '86640.j', 'p': 73, 'prec': 20, 'unit': 142511027355578692283108155099195706, 'val': 1}
  • id: 4476830
    {'lmfdb_iso': '86640.j', 'p': 79, 'prec': 20, 'unit': 867995139575944211182445901896639162, 'val': 1}
  • id: 4476822
    {'lmfdb_iso': '86640.j', 'p': 83, 'prec': 20, 'unit': 2409661685927096306582920199749975424, 'val': 1}
  • id: 4476837
    {'lmfdb_iso': '86640.j', 'p': 89, 'prec': 20, 'unit': 5989682439368019265300863136982775658, 'val': 1}
  • id: 4476821
    {'lmfdb_iso': '86640.j', 'p': 97, 'prec': 20, 'unit': 1135014884163055975084763360358467758, 'val': 1}