Elliptic curve data - 87616.k2

Formats: - HTML - YAML - JSON - 2025-09-24T13:48:18.743515

• 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': '87616bn', 'Clabel': '87616bn2', 'Cnumber': 2, 'abc_quality': 0.9847633793256833, 'absD': 94076963651584, 'adelic_genus': 6, 'adelic_index': 288, 'adelic_level': 2664, 'ainvs': [0, 1, 0, 8831, -337281], 'analytic_rank': 0, 'bad_primes': [2, 37], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 87616, 'degree': 331776, 'elladic_images': ['4.2.0.1', '9.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3673528416331824381734902514', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 10, 'isogeny_degrees': [1, 3], 'jinv': [212207543, 262144], 'lmfdb_iso': '87616.k', 'lmfdb_label': '87616.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 138, 676], 'min_quad_twist_disc': -8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '4.2.0.a.1', '9.12.0.b.1', '12.16.0.b.2', '36.48.0.b.2', '296.4.0.?', '333.36.0.?', '888.32.0.?', '1332.144.6.?', '2664.288.6.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1369], [37, 254, 64]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27418758131410626668037387596', 'prec': 107}, 'szpiro_ratio': 3.4266612101191827, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, 3, 0, 4, 0, 1, 0, -6, 0, 2, 0, -6, 0, -3, 0, -2, 0], 'aplist': [0, -2, 3, 4, -6, 2, -3, -2, 6, 3, 2, 0, 3, 4, 6, 6, 0, -1, 2, 12, -10, 14, 6, -3, 13], 'class_deg': 3, 'class_size': 2, 'conductor': 87616, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '87616.k', 'trace_hash': 1126775155782826761}
• 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': '0.064913109306983687381213634171', 'prec': 107}, 'conductor': 87616, 'gens': [], 'heights': [], 'lmfdb_label': '87616.k2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.32214720019942725688649755441', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5771776015954180550919804352953930065', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': 'a', '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '87616.k2'}
• ec_torsion_growth •

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

  
  
  • id: 4107035
    {'degree': 2, 'field': [-222, 0, 1], 'lmfdb_label': '87616.k2', 'torsion': [3]}
  • id: 4107036
    {'degree': 3, 'field': [26, -12, -1, 1], 'lmfdb_label': '87616.k2', 'torsion': [2]}
  • id: 4107039
    {'degree': 6, 'field': [-71928, 0, 4329, 0, 0, 0, 1], 'lmfdb_label': '87616.k2', 'torsion': [6]}
  • id: 4107038
    {'degree': 6, 'field': [296, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '87616.k2', 'torsion': [3]}
  • id: 4107037
    {'degree': 6, 'field': [676, 0, 196, 0, 25, 0, 1], 'lmfdb_label': '87616.k2', 'torsion': [2, 2]}
  • id: 4107040
    {'degree': 12, 'field': [-5476, 0, -21904, 0, -4107, 0, -1184, 0, -37, 0, 0, 0, 1], 'lmfdb_label': '87616.k2', 'torsion': [4]}
  • id: 4107041
    {'degree': 12, 'field': [88209, -1782, -4419, 11790, -4350, -1902, 733, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '87616.k2', 'torsion': [3, 3]}
  • id: 4107042
    {'degree': 12, 'field': [5815282564, 0, -587464608, 0, 20811516, 0, -178468, 0, 8673, 0, 6, 0, 1], 'lmfdb_label': '87616.k2', 'torsion': [2, 6]}
  • id: 4107043
    {'degree': 18, 'field': [-6837362792, 0, 0, -8609942040, 0, 0, 1291871985, 0, 0, -21298700, 0, 0, -204294, 0, 0, -60, 0, 0, 1], 'lmfdb_label': '87616.k2', 'torsion': [9]}
  • id: 4107044
    {'degree': 18, 'field': [142745472, -285692160, 263458176, -144741376, 50579920, -11768608, 2432976, -899400, 375250, -76572, 4631, -3470, 3239, -1406, 294, -42, 17, -6, 1], 'lmfdb_label': '87616.k2', 'torsion': [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: 2141340
    {'conductor': 87616, 'conductor_valuation': 6, 'discriminant_valuation': 36, 'j_denominator_valuation': 18, 'kodaira_symbol': -30, 'lmfdb_label': '87616.k2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2141341
    {'conductor': 87616, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '87616.k2', 'prime': 37, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2241441
    {'adelic_gens': [[2651, 2658, 1382, 1355], [1, 36, 0, 1], [1, 36, 12, 433], [2645, 2637, 2007, 1520], [1, 0, 36, 1], [1466, 2637, 2541, 1951], [1367, 2628, 1368, 2627], [1331, 0, 0, 2663], [19, 27, 657, 2476], [2032, 2637, 1911, 1831], [2629, 36, 2628, 37], [13, 6, 2614, 2641], [1997, 2628, 2313, 2015]], 'adelic_image': '2664.288.6.?', 'conductor': 87616, 'lmfdb_label': '87616.k2', 'prime': 0}
  • id: 357212
    {'conductor': 87616, 'elladic_image': '4.2.0.1', 'lmfdb_label': '87616.k2', 'modell_image': '2G', 'prime': 2}
  • id: 357213
    {'conductor': 87616, 'elladic_image': '9.12.0.2', 'lmfdb_label': '87616.k2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 87616.k does not appear in ec_padic