Elliptic curve data - 8281.d2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '8281g', 'Clabel': '8281g3', 'Cnumber': 3, 'abc_quality': 0.9802957926219806, 'absD': 194779153450063, 'ainvs': [1, -1, 1, -18115, 1158434], 'analytic_rank': 0, 'bad_primes': [7, 13], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 8281, 'degree': 16464, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4562913642028026034551083828', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 7, 'intrinsic_torsion': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '8281.d', 'lmfdb_label': '8281.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': -91, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1183], [7, 20, 169], [13, 86, 49]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 4.593411888295552, '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, 0, 0, 0, 3, -3, 0, -4, 0, 0, 0, 0, -1, 0, 3, 0, 0], 'aplist': [-1, 0, 0, 0, -4, 0, 0, 0, 8, 2, 0, 6, 0, -12, 0, -10, 0, 0, -4, -16, 0, 8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 8281, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '8281.d', 'trace_hash': 1771063166617640388}
• 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': '0.054335215387720293807672494156', 'prec': 107}, 'conductor': 8281, 'gens': [], 'heights': [], 'lmfdb_label': '8281.d2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.53620419123508888195587905170', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.53620419123508888195587905169855104996', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-159, 79, 1]], 'xcoord_integral_points': [-159]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': [0, 0, 0], '5': [0, 0, 0], '7': 'a', '13': 'a'}, 'iwp0': 11, 'lmfdb_label': '8281.d2'}
• ec_torsion_growth •

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

  
  
  • id: 433567
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '8281.d2', 'torsion': [2, 2]}
  • id: 433568
    {'degree': 4, 'field': [-248, -88, -2, -2, 1], 'lmfdb_label': '8281.d2', 'torsion': [4]}
  • id: 433569
    {'degree': 4, 'field': [296, -46, 24, -1, 1], 'lmfdb_label': '8281.d2', 'torsion': [2, 4]}
  • id: 433570
    {'degree': 6, 'field': [-1, -16, 35, 9, -14, -1, 1], 'lmfdb_label': '8281.d2', 'torsion': [14]}
  • id: 433573
    {'degree': 8, 'field': [-16253, -5234, 4159, 1195, -308, -68, 1, -2, 1], 'lmfdb_label': '8281.d2', 'torsion': [6]}
  • id: 433571
    {'degree': 8, 'field': [3844, 2728, 968, -80, 125, 46, 2, -2, 1], 'lmfdb_label': '8281.d2', 'torsion': [4, 4]}
  • id: 433572
    {'degree': 8, 'field': [21904, 0, -6933, 0, 825, 0, -45, 0, 1], 'lmfdb_label': '8281.d2', 'torsion': [2, 8]}
  • id: 433574
    {'degree': 12, 'field': [729, 243, 324, 189, 171, 120, 97, -40, 19, -7, 4, -1, 1], 'lmfdb_label': '8281.d2', 'torsion': [2, 14]}
  • id: 433575
    {'degree': 16, 'field': [14818756, -6895384, 4388788, 5015216, -2472262, -155560, 240038, -159228, 34333, 8064, -5894, 2148, -176, -112, 36, -8, 1], 'lmfdb_label': '8281.d2', 'torsion': [8]}
  • id: 433576
    {'degree': 16, 'field': [30738184, -1300952, 2651884, -2701244, 1385730, -145328, 222404, -153970, 46673, -8750, 5094, -1902, 408, -70, 30, -8, 1], 'lmfdb_label': '8281.d2', 'torsion': [4, 8]}
  • id: 433577
    {'degree': 16, 'field': [215590489, 0, -84747293, 0, 19711868, 0, -2827457, 0, 292026, 0, -21429, 0, 1164, 0, -41, 0, 1], 'lmfdb_label': '8281.d2', 'torsion': [2, 16]}
  • id: 433578
    {'degree': 16, 'field': [264160009, 85068202, 94990983, 17076464, 18545987, 2851065, 2320579, 224836, 209154, 5002, 15640, -105, 173, 134, 3, -2, 1], 'lmfdb_label': '8281.d2', 'torsion': [6, 6]}
  • id: 433579
    {'degree': 20, 'field': [27778159711, 17038017814, 6342631671, -1144870468, -87670111, -143712065, -16898855, 19766269, 8140696, -2473867, -97899, -142599, 43163, 2870, 5758, -1600, 150, -40, 0, -2, 1], 'lmfdb_label': '8281.d2', 'torsion': [2, 22]}
• 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: 172419
    {'conductor': 8281, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '8281.d2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 172420
    {'conductor': 8281, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8281.d2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• lmfdb_label 8281.d2 does not appear in ec_galrep
• lmfdb_iso 8281.d does not appear in ec_padic