Elliptic curve data - 83655.bb1

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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': '83655t', 'Clabel': '83655t4', 'Cnumber': 4, 'abc_quality': 1.0771710471613196, 'absD': 24191363356875, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 17160, 'ainvs': [1, -1, 0, -90024, -10371295], 'analytic_rank': 1, 'bad_primes': [3, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 83655, 'degree': 294912, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5461153430900643130613789296', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2, 4], 'jinv': [22930509321, 6875], 'lmfdb_iso': '83655.bb', 'lmfdb_label': '83655.bb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -59, 190], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '40.12.0.z.1', '44.12.0.h.1', '156.12.0.?', '440.24.0.?', '1560.24.0.?', '1716.24.0.?', '17160.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.6563504924139759461292173172', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 16731], [3, 6, 9295], [5, 6, 16731], [11, 12, 7605], [13, 86, 495]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.28566547997475890066298740965', 'prec': 107}, 'szpiro_ratio': 4.044049585735749, '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, 1, 0, -1, 1, 0, 0, -3, 0, 1, -1, 0, 0, 0, 0, -1, -6, 0, 4, -1], 'aplist': [1, 0, 1, 0, -1, 0, -6, 4, -4, -6, 8, 2, 2, 4, -12, 2, 4, -10, 16, 8, -14, 8, -4, 10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 83655, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '83655.bb', 'trace_hash': 2121056191770627470}
• 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': '0.045400566947603602033374195239', 'prec': 107}, 'conductor': 83655, 'gens': [[-2755, 8625, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '6.6563504924139759461292173172', 'prec': 100}], 'lmfdb_label': '83655.bb1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27562433954011355921633426825', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.3386088328764471614515075769418404231', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-701, 701, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': 'a', '5': [2, 0], '7': [1, 1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [3, 0]}, 'iwp0': 0, 'lmfdb_label': '83655.bb1'}
• ec_torsion_growth •

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

  
  
  • id: 3925824
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '83655.bb1', 'torsion': [2, 2]}
  • id: 3925826
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '83655.bb1', 'torsion': [4]}
  • id: 3925825
    {'degree': 2, 'field': [429, 0, 1], 'lmfdb_label': '83655.bb1', 'torsion': [4]}
  • id: 3925827
    {'degree': 4, 'field': [430, 2, -1, -2, 1], 'lmfdb_label': '83655.bb1', 'torsion': [2, 4]}
  • id: 3925831
    {'degree': 8, 'field': [-3393, -702, 1260, -369, 372, -177, 24, -3, 1], 'lmfdb_label': '83655.bb1', 'torsion': [6]}
  • id: 3925828
    {'degree': 8, 'field': [-3275, 10340, -3132, -616, 701, -44, -50, 0, 1], 'lmfdb_label': '83655.bb1', 'torsion': [2, 4]}
  • id: 3925830
    {'degree': 8, 'field': [31555, -4810, 5334, -1074, 603, -82, 32, -4, 1], 'lmfdb_label': '83655.bb1', 'torsion': [8]}
  • id: 3925829
    {'degree': 8, 'field': [331021636, 0, 5834620, 0, 69773, 0, 440, 0, 1], 'lmfdb_label': '83655.bb1', 'torsion': [8]}
  • id: 3925835
    {'degree': 16, 'field': [-33684395, 89095470, -79748395, 40797786, -18772205, 2241774, -1865557, 74982, -62891, -55470, 51422, -6714, 688, -300, 35, -6, 1], 'lmfdb_label': '83655.bb1', 'torsion': [2, 6]}
  • id: 3925837
    {'degree': 16, 'field': [496105, -470070, 1413650, -746073, 570568, -420333, 291089, -153918, 68452, -21762, 6362, -915, 307, 0, 20, 0, 1], 'lmfdb_label': '83655.bb1', 'torsion': [12]}
  • id: 3925832
    {'degree': 16, 'field': [69722500, 0, -69925624, 0, 33322424, 0, -6213228, 0, 705053, 0, -51072, 0, 2522, 0, -76, 0, 1], 'lmfdb_label': '83655.bb1', 'torsion': [4, 4]}
  • id: 3925836
    {'degree': 16, 'field': [196856685, -447434370, 407223090, -177477876, 84355182, -26708994, 13278033, -4018536, 1266789, -373524, 95235, -19584, 3141, -498, 57, -6, 1], 'lmfdb_label': '83655.bb1', 'torsion': [12]}
  • id: 3925834
    {'degree': 16, 'field': [965855320, -950523280, 1696324496, -1454191728, 630702178, 123654244, -54380214, 10986788, -2347855, -313268, 111190, -27972, 5936, -616, 108, -8, 1], 'lmfdb_label': '83655.bb1', 'torsion': [2, 8]}
  • id: 3925833
    {'degree': 16, 'field': [2507755045, -1499074460, 1196758504, -471127820, 215940022, -62868104, 21184364, -4894204, 1340007, -249296, 56468, -7964, 1646, -236, 60, -8, 1], 'lmfdb_label': '83655.bb1', '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: 2037955
    {'conductor': 83655, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '83655.bb1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2037956
    {'conductor': 83655, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '83655.bb1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2037957
    {'conductor': 83655, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '83655.bb1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2037958
    {'conductor': 83655, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '83655.bb1', '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: 2215018
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [10297, 7488, 2028, 12793], [1, 4, 4, 17], [16888, 9633, 11193, 15640], [14519, 0, 0, 17159], [6124, 3081, 10023, 15406], [7099, 7098, 16458, 12715], [7, 6, 17154, 17155], [17153, 8, 17152, 9], [5719, 0, 0, 17159]], 'adelic_image': '17160.48.0.?', 'conductor': 83655, 'lmfdb_label': '83655.bb1', 'prime': 0}
  • id: 342064
    {'conductor': 83655, 'elladic_image': '4.6.0.1', 'lmfdb_label': '83655.bb1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4313074
    {'lmfdb_iso': '83655.bb', 'p': 17, 'prec': 20, 'unit': 81139844123439246041773, 'val': 1}
  • id: 4313065
    {'lmfdb_iso': '83655.bb', 'p': 19, 'prec': 20, 'unit': 716913559055541255534641, 'val': 1}
  • id: 4313079
    {'lmfdb_iso': '83655.bb', 'p': 23, 'prec': 20, 'unit': 72340133174514431278906415, 'val': 1}
  • id: 4313072
    {'lmfdb_iso': '83655.bb', 'p': 29, 'prec': 20, 'unit': 3445550345731282974487425631, 'val': 1}
  • id: 4313083
    {'lmfdb_iso': '83655.bb', 'p': 31, 'prec': 20, 'unit': 843272751041275714132195761, 'val': 1}
  • id: 4313068
    {'lmfdb_iso': '83655.bb', 'p': 37, 'prec': 20, 'unit': 37631663939854466458631075471, 'val': 1}
  • id: 4313070
    {'lmfdb_iso': '83655.bb', 'p': 41, 'prec': 20, 'unit': 2800091304094372233126319280898, 'val': 1}
  • id: 4313071
    {'lmfdb_iso': '83655.bb', 'p': 43, 'prec': 20, 'unit': 4554297842817827299989157846270, 'val': 1}
  • id: 4313081
    {'lmfdb_iso': '83655.bb', 'p': 47, 'prec': 20, 'unit': 655789983945174802838855607417, 'val': 2}
  • id: 4313076
    {'lmfdb_iso': '83655.bb', 'p': 53, 'prec': 20, 'unit': 738072483437450200855946235539, 'val': 2}
  • id: 4313077
    {'lmfdb_iso': '83655.bb', 'p': 59, 'prec': 20, 'unit': 3911427018746618466742228809817275, 'val': 1}
  • id: 4313082
    {'lmfdb_iso': '83655.bb', 'p': 61, 'prec': 20, 'unit': 7679513041677757548482151177097125, 'val': 1}
  • id: 4313067
    {'lmfdb_iso': '83655.bb', 'p': 67, 'prec': 20, 'unit': 12582496168987848070120825287766818, 'val': 1}
  • id: 4313069
    {'lmfdb_iso': '83655.bb', 'p': 71, 'prec': 20, 'unit': 20796415508197128082035655304126517, 'val': 1}
  • id: 4313078
    {'lmfdb_iso': '83655.bb', 'p': 73, 'prec': 20, 'unit': 154221119017806845402917794528562235, 'val': 1}
  • id: 4313073
    {'lmfdb_iso': '83655.bb', 'p': 79, 'prec': 20, 'unit': 644053233380472014798184873705584097, 'val': 1}
  • id: 4313075
    {'lmfdb_iso': '83655.bb', 'p': 83, 'prec': 20, 'unit': 1742195417666829200741364829782123135, 'val': 1}
  • id: 4313080
    {'lmfdb_iso': '83655.bb', 'p': 89, 'prec': 20, 'unit': 10707006143057668807451568629709813873, 'val': 1}
  • id: 4313066
    {'lmfdb_iso': '83655.bb', 'p': 97, 'prec': 20, 'unit': 1068232179786345604378302057480519360, 'val': 1}