Elliptic curve data - 286650.jx5

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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': '286650jx', 'Clabel': '286650jx2', 'Cnumber': 2, 'abc_quality': 1.0081936394487907, 'absD': 1472731368654873600000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 21840, 'ainvs': [1, -1, 1, -3852576230, 92040598049397], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 286650, 'degree': 150994944, 'elladic_images': ['16.48.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.0172576964692799350704782324', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 257, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4718909406724749250561, 1098974822400], 'lmfdb_iso': '286650.jx', 'lmfdb_label': '286650.jx5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -349440, 79361697], 'min_quad_twist_disc': 105, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.i.1', '16.48.0.d.2', '56.48.0.ba.2', '112.96.1.?', '120.48.0.?', '156.24.0.?', '240.96.0.?', '312.48.0.?', '420.24.0.?', '520.48.0.?', '624.96.0.?', '840.96.0.?', '1040.192.5.?', '1560.96.0.?', '1680.192.1.?', '1820.24.0.?', '2184.96.0.?', '3120.384.5.?', '3640.96.1.?', '4368.192.1.?', '5460.48.0.?', '7280.384.13.?', '10920.192.1.?', '21840.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 14, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2748943805786716203844492532', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 11025], [3, 8, 31850], [5, 18, 11466], [7, 32, 5850], [13, 14, 22050]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6902775213905182495197995756', 'prec': 100}, 'szpiro_ratio': 6.193659080092528, '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, 1, 0, 1, 0, 0, 0, 1, 0, 0, -4, 0, 1, 0, 0, 1, -2, 0, 4, 0], 'aplist': [1, 0, 0, 0, -4, 1, -2, 4, 0, 2, -8, -6, -6, -4, 0, 6, -12, 2, -4, 0, 10, 0, -4, 10, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 286650, 'isogeny_matrix': [[1, 16, 2, 4, 8, 8, 16, 4], [16, 1, 8, 4, 2, 8, 4, 16], [2, 8, 1, 2, 4, 4, 8, 2], [4, 4, 2, 1, 2, 2, 4, 4], [8, 2, 4, 2, 1, 4, 2, 8], [8, 8, 4, 2, 4, 1, 8, 8], [16, 4, 8, 4, 2, 8, 1, 16], [4, 16, 2, 4, 8, 8, 16, 1]], 'lmfdb_iso': '286650.jx', 'trace_hash': 1555645274581442648}
• 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': '0.00032408154461150584372180792376', 'prec': 113}, 'conductor': 286650, 'gens': [[36329, 143835, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2748943805786716203844492532', 'prec': 100}], 'lmfdb_label': '286650.jx5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.067647622979016722570087507314', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.039177522617988753286096662387124837', 'prec': 130}, 'tamagawa_product': 2048, 'torsion_generators': [[-71671, 35835, 1], [35849, -17925, 1]], 'xcoord_integral_points': [-71671, 30249, 35345, 35849, 35913, 36329, 41729, 79949]}
• lmfdb_label 286650.jx5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12182494
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 4]}
  • id: 12182497
    {'degree': 4, 'field': [-26, -143, -55, -1, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 8]}
  • id: 12182495
    {'degree': 4, 'field': [1296, 0, 33, 0, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 4]}
  • id: 12182496
    {'degree': 4, 'field': [9130, -230, 231, -2, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 4]}
  • id: 12182499
    {'degree': 8, 'field': [904, 288, -218, -134, 53, 14, 0, -4, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 8]}
  • id: 12182500
    {'degree': 8, 'field': [27556, 0, -26693, 0, 3359, 0, -127, 0, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 16]}
  • id: 12182498
    {'degree': 8, 'field': [75280, -43880, 49754, -11894, 6313, -442, 152, -4, 1], 'lmfdb_label': '286650.jx5', 'torsion': [4, 4]}
  • id: 12182501
    {'degree': 8, 'field': [1066024, -192900, 96142, -8699, -4395, -206, 100, -3, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 6]}
  • id: 12182505
    {'degree': 16, 'field': [2119936, 0, -53774448, 0, 1868252360, 0, -107122223, 0, 4524789, 0, -142502, 0, 5010, 0, -107, 0, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 16]}
  • id: 12182504
    {'degree': 16, 'field': [16777216, 0, 6887488, 0, 2049968, 0, 325260, 0, 36281, 0, 1860, 0, 158, 0, -8, 0, 1], 'lmfdb_label': '286650.jx5', 'torsion': [4, 8]}
  • id: 12182503
    {'degree': 16, 'field': [17587003456, 0, 2169361728, 0, 273390868, 0, 122789796, 0, 12543705, 0, 111576, 0, -2042, 0, -12, 0, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 8]}
  • id: 12182506
    {'degree': 16, 'field': [200410219584, 0, -81420080688, 0, 9686444140, 0, -678591201, 0, 32546490, 0, -1015009, 0, 19293, 0, -210, 0, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 12]}
  • id: 12182502
    {'degree': 16, 'field': [16183907141220, -11558428670880, 4535181869400, -936181908480, 206493181456, -44559703000, 9053029028, -1583818368, 280029829, -38712068, 4705336, -523076, 41242, -3276, 236, -4, 1], 'lmfdb_label': '286650.jx5', 'torsion': [2, 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: 7101098
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '286650.jx5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 7101099
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '286650.jx5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7101100
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '286650.jx5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 7101101
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '286650.jx5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7101102
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '286650.jx5', '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: 3471050
    {'adelic_gens': [[17365, 14568, 19518, 21709], [1, 16, 0, 1], [21825, 16, 21824, 17], [3119, 14544, 18714, 21743], [17459, 7272, 7350, 14603], [1, 0, 16, 1], [1, 16, 4, 65], [7285, 7296, 7284, 5473], [14575, 7296, 14784, 21169], [7279, 0, 0, 21839]], 'adelic_image': '21840.768.13.?', 'conductor': 286650, 'lmfdb_label': '286650.jx5', 'prime': 0}
  • id: 1016939
    {'conductor': 286650, 'elladic_image': '16.48.0.3', 'lmfdb_label': '286650.jx5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 286650.jx does not appear in ec_padic