Elliptic curve data - 141960.r5

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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': '141960ci', 'Clabel': '141960ci3', 'Cnumber': 3, 'abc_quality': 0.9617149979611352, 'absD': 40545195600000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 21840, 'ainvs': [0, -1, 0, 40504, 9152220], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 141960, 'degree': 1179648, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8688161622294717581393640135', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1486779836, 8203125], 'lmfdb_iso': '141960.r', 'lmfdb_label': '141960.r5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 240, 4092], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '24.24.0.bz.2', '52.12.0-4.c.1.2', '56.24.0.bu.1', '80.24.0.?', '84.12.0.?', '104.24.0.?', '168.48.0.?', '240.48.0.?', '312.48.0.?', '560.48.0.?', '728.48.0.?', '1040.48.0.?', '1092.24.0.?', '1680.96.1.?', '2184.96.0.?', '3120.96.0.?', '7280.96.0.?', '21840.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 3549], [3, 4, 47320], [5, 6, 28392], [7, 8, 20280], [13, 86, 840]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0087188330320822989315935248340', 'prec': 110}, 'szpiro_ratio': 3.8425316288641973, '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, 1, 0, 1, 0, 4, 0, 0, 0, 1, 0, 2, 0, 4, 0], 'aplist': [0, -1, -1, 1, 4, 0, 2, 4, 0, -10, 0, -6, 6, -4, 8, 6, 4, -10, -4, 16, 14, 8, 4, -10, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 141960, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '141960.r', 'trace_hash': 317112757311706010}
• 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': '0.023810411774282097731525974841', 'prec': 107}, 'conductor': 141960, 'gens': [], 'heights': [], 'lmfdb_label': '141960.r5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.26173679135281736117372159174', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0938943308225388893897727338860463693', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-147, 0, 1]], 'xcoord_integral_points': [-147]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': [1, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '141960.r5'}
• ec_torsion_growth •

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

  
  
  • id: 6416875
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '141960.r5', 'torsion': [4]}
  • id: 6416874
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '141960.r5', 'torsion': [2, 2]}
  • id: 6416876
    {'degree': 2, 'field': [273, 0, 1], 'lmfdb_label': '141960.r5', 'torsion': [4]}
  • id: 6416879
    {'degree': 4, 'field': [87, -6, 7, -2, 1], 'lmfdb_label': '141960.r5', 'torsion': [8]}
  • id: 6416878
    {'degree': 4, 'field': [107, 34, -33, -2, 1], 'lmfdb_label': '141960.r5', 'torsion': [8]}
  • id: 6416877
    {'degree': 4, 'field': [597, -36, 37, -2, 1], 'lmfdb_label': '141960.r5', 'torsion': [2, 4]}
  • id: 6416883
    {'degree': 8, 'field': [-85683, 0, -202124, 0, -1014, 0, 0, 0, 1], 'lmfdb_label': '141960.r5', 'torsion': [6]}
  • id: 6416880
    {'degree': 8, 'field': [238, 28, 56, -182, 127, -46, 20, -4, 1], 'lmfdb_label': '141960.r5', 'torsion': [2, 4]}
  • id: 6416882
    {'degree': 8, 'field': [673, -692, 832, -260, 81, 56, -14, -4, 1], 'lmfdb_label': '141960.r5', 'torsion': [2, 8]}
  • id: 6416881
    {'degree': 8, 'field': [212521, 0, 46504, 0, 3702, 0, 136, 0, 1], 'lmfdb_label': '141960.r5', 'torsion': [8]}
  • id: 6416889
    {'degree': 16, 'field': [-22047, 309624, -165580, -284488, 132986, 13624, -13868, 17536, -14745, 4656, 996, -656, -194, 112, 4, -8, 1], 'lmfdb_label': '141960.r5', 'torsion': [12]}
  • id: 6416884
    {'degree': 16, 'field': [56644, 0, -25872, 0, 73780, 0, 6804, 0, 2325, 0, -1620, 0, 286, 0, -24, 0, 1], 'lmfdb_label': '141960.r5', 'torsion': [4, 4]}
  • id: 6416885
    {'degree': 16, 'field': [27265716, -31907736, 26106444, -7579656, 16453518, -1487304, 2289714, -615384, 96169, -34860, -1106, -672, 1296, -84, 28, 0, 1], 'lmfdb_label': '141960.r5', 'torsion': [2, 8]}
  • id: 6416886
    {'degree': 16, 'field': [29976921, 455909688, -363453492, -160494768, 19672058, 71359288, -21508536, -2081944, 705923, -159272, 65576, -15960, 658, 896, -108, -8, 1], 'lmfdb_label': '141960.r5', 'torsion': [16]}
  • id: 6416887
    {'degree': 16, 'field': [91757241, -160237512, 237544668, -149896368, 62875818, 15239448, -6259656, 858216, -13997, -148232, 44536, -8600, 1858, -224, 52, -8, 1], 'lmfdb_label': '141960.r5', 'torsion': [16]}
  • id: 6416890
    {'degree': 16, 'field': [52601355457, -23462763212, 46341979320, -108845620240, 92396969000, -33725502636, 7037989632, -855266976, 56487126, 2033740, -1233104, 132840, -4140, 204, 24, -8, 1], 'lmfdb_label': '141960.r5', 'torsion': [12]}
  • id: 6416888
    {'degree': 16, 'field': [54082075112116, -25239771964720, 6367574975592, -1061686707520, 150265295452, -21974602584, 2615346392, -234192800, 7425348, 339784, -145120, 51216, -7268, 1028, 12, -4, 1], 'lmfdb_label': '141960.r5', 'torsion': [2, 6]}
• 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: 3508960
    {'conductor': 141960, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '141960.r5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3508961
    {'conductor': 141960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '141960.r5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3508962
    {'conductor': 141960, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '141960.r5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3508963
    {'conductor': 141960, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '141960.r5', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3508964
    {'conductor': 141960, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '141960.r5', 'prime': 13, 'reduction_type': 0, '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: 2586817
    {'adelic_gens': [[15133, 20176, 10764, 20905], [8737, 20176, 14456, 8529], [1, 16, 0, 1], [21825, 16, 21824, 17], [7216, 11765, 12675, 8386], [6719, 0, 0, 21839], [16186, 19747, 12623, 12702], [15, 2, 21742, 21827], [1, 0, 16, 1], [5, 4, 21836, 21837], [10648, 6721, 21359, 16810]], 'adelic_image': '21840.192.1.?', 'conductor': 141960, 'lmfdb_label': '141960.r5', 'prime': 0}
  • id: 548525
    {'conductor': 141960, 'elladic_image': '8.12.0.5', 'lmfdb_label': '141960.r5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 141960.r does not appear in ec_padic