Elliptic curve data - 286650.k2

Formats: - HTML - YAML - JSON - 2025-10-05T14:06:19.983282

• 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': '286650k', 'Clabel': '286650k3', 'Cnumber': 3, 'abc_quality': 0.9896845589755124, 'absD': 97801991769326276250000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 5460, 'ainvs': [1, -1, 0, -96911817, 366924753341], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 286650, 'degree': 47775744, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3322204586858469763804878155', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [2781982314427707, 2703013040], 'lmfdb_iso': '286650.k', 'lmfdb_label': '286650.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -8790, 319140], 'min_quad_twist_disc': 105, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0-6.a.1.1', '105.8.0.?', '156.48.0.?', '210.48.0.?', '1820.6.0.?', '5460.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9581717090675776945394733862', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3675], [3, 2, 2450], [5, 18, 11466], [7, 32, 5850], [13, 14, 22050]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.73058721144005786798099784947', 'prec': 103}, 'szpiro_ratio': 5.3144554739635606, '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, -1, 0, 0, -6, 0, 1, 0, 0, 1, 0, 0, 4, 0], 'aplist': [-1, 0, 0, 0, -6, 1, 0, 4, 0, 0, 4, 4, -6, 10, -6, -6, 0, 10, 4, 6, 2, -4, -6, -6, -10], 'class_deg': 6, 'class_size': 4, 'conductor': 286650, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '286650.k', 'trace_hash': 1178231523701761285}
• 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': '0.0012754695197543602931724226167', 'prec': 110}, 'conductor': 286650, 'gens': [[5833, 5683, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9581717090675776945394733862', 'prec': 100}], 'lmfdb_label': '286650.k2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10602282501001543976504811270', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9826615148008316932123924174418509066', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-11366, 5683, 1]], 'xcoord_integral_points': [-11366, 5534, 5833, 78035]}
• lmfdb_label 286650.k2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12179065
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '286650.k2', 'torsion': [2, 6]}
  • id: 12179066
    {'degree': 4, 'field': [13, -26, 27, -2, 1], 'lmfdb_label': '286650.k2', 'torsion': [4]}
  • id: 12179067
    {'degree': 6, 'field': [560, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '286650.k2', 'torsion': [6]}
  • id: 12179068
    {'degree': 8, 'field': [-4394, -338, 325, 52, 664, -2, -50, -2, 1], 'lmfdb_label': '286650.k2', 'torsion': [2, 12]}
  • id: 12179069
    {'degree': 8, 'field': [626704, 154336, 19540, -236, 4237, -74, 103, -2, 1], 'lmfdb_label': '286650.k2', 'torsion': [2, 12]}
  • id: 12179070
    {'degree': 12, 'field': [314721, -3366, -8379, 22350, -8310, -3486, 1261, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '286650.k2', 'torsion': [6, 6]}
  • id: 12179071
    {'degree': 16, 'field': [222727363600, 0, 23991839200, 0, 2372442524, 0, 154163896, 0, 6870649, 0, 229232, 0, 4586, 0, 56, 0, 1], 'lmfdb_label': '286650.k2', 'torsion': [8]}
  • id: 12179072
    {'degree': 18, 'field': [-5011849549824, 2935935535104, 2066550576480, -1064003534100, -106538572764, 78572718432, 6501544158, -764656506, -2035389996, 47329731, 97262865, -353880, -2197716, -48546, 25944, 1134, -204, -9, 1], 'lmfdb_label': '286650.k2', 'torsion': [2, 18]}
• 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: 7098978
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '286650.k2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7098979
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '286650.k2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7098980
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '286650.k2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7098981
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '286650.k2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7098982
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '286650.k2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

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

  
  
  • id: 3471059
    {'adelic_gens': [[5449, 12, 5448, 13], [459, 2278, 3206, 5021], [1, 0, 12, 1], [3628, 5449, 3675, 32], [5450, 5457, 1119, 8], [3890, 5457, 3147, 8], [1, 6, 6, 37], [1, 12, 0, 1], [4201, 12, 3366, 73], [11, 2, 5410, 5451]], 'adelic_image': '5460.96.1.?', 'conductor': 286650, 'lmfdb_label': '286650.k2', 'prime': 0}
  • id: 1016949
    {'conductor': 286650, 'elladic_image': '2.3.0.1', 'lmfdb_label': '286650.k2', 'modell_image': '2B', 'prime': 2}
  • id: 1016950
    {'conductor': 286650, 'elladic_image': '3.4.0.1', 'lmfdb_label': '286650.k2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 286650.k does not appear in ec_padic