Elliptic curve data - 3136.e1

Formats: - HTML - YAML - JSON - 2024-10-06T17:43:26.871775

• 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': '3136k', 'Clabel': '3136k6', 'Cnumber': 6, 'abc_quality': 1.0648884149541868, 'absD': 773738492592128, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 504, 'ainvs': [0, 1, 0, -8562913, 9641661567], 'analytic_rank': 0, 'bad_primes': [2, 7], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 3136, 'degree': 55296, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4257768257906590742593069087', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 18, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [2251439055699625, 25088], 'lmfdb_iso': '3136.e', 'lmfdb_label': '3136.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2731, -55146], 'min_quad_twist_disc': -56, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '12.24.0-6.a.1.7', '18.36.0.a.1', '24.48.0-24.y.1.10', '28.6.0.c.1', '36.72.0-18.a.1.5', '42.24.0-6.a.1.1', '56.12.0.k.1', '63.36.0.d.1', '72.144.1.?', '84.48.0.?', '126.216.2.?', '168.96.1.?', '252.432.7.?', '504.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 49], [7, 32, 64]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.41310098042308445758078235479', 'prec': 103}, 'szpiro_ratio': 7.39096366018861, '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, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, -6, 0, 2, 0], 'aplist': [0, -2, 0, 0, 0, -4, -6, 2, 0, 6, 4, -2, -6, -8, 12, -6, -6, 8, 4, 0, -2, 8, -6, 6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 3136, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '3136.e', 'trace_hash': 1422146765026648502}
• 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': '0.0078162244213750481741007588359', 'prec': 110}, 'conductor': 3136, 'gens': [], 'heights': [], 'lmfdb_label': '3136.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.35425243486158037401123451882', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.70850486972316074802246903763197407034', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[1689, 0, 1]], 'xcoord_integral_points': [1689]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '7': 'a'}, 'iwp0': 5, 'lmfdb_label': '3136.e1'}
• ec_torsion_growth •

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

  
  
  • id: 162501
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [6]}
  • id: 162500
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 2]}
  • id: 162502
    {'degree': 4, 'field': [2, 0, -1, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [4]}
  • id: 162503
    {'degree': 4, 'field': [7, 14, -13, -2, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 6]}
  • id: 162505
    {'degree': 6, 'field': [-10752, 0, 1764, 0, -84, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [18]}
  • id: 162504
    {'degree': 6, 'field': [56, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [6]}
  • id: 162507
    {'degree': 8, 'field': [1, 0, 2, 0, 10, 0, 2, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 4]}
  • id: 162508
    {'degree': 8, 'field': [121, 0, -26, 0, 26, 0, -10, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [12]}
  • id: 162506
    {'degree': 8, 'field': [196, 0, -224, 0, 58, 0, -8, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 4]}
  • id: 162512
    {'degree': 12, 'field': [-188, 4032, -11364, 4648, 11349, -5124, -5410, 756, 879, -28, -54, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 18]}
  • id: 162511
    {'degree': 12, 'field': [225, 0, 648, 0, 660, 0, -146, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 6]}
  • id: 162509
    {'degree': 12, 'field': [3249, -342, -819, 2190, -750, -462, 253, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '3136.e1', 'torsion': [3, 6]}
  • id: 162510
    {'degree': 12, 'field': [153664, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [18]}
  • id: 162515
    {'degree': 16, 'field': [1, 0, -2, 0, -6, 0, -16, 0, 95, 0, -16, 0, -6, 0, -2, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 12]}
  • id: 162514
    {'degree': 16, 'field': [256, 0, -1024, 0, 1056, 0, -320, 0, 20, 0, -80, 0, 66, 0, -16, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [2, 12]}
  • id: 162513
    {'degree': 16, 'field': [784, 0, -392, 0, 161, 0, 126, 0, -59, 0, 24, 0, 5, 0, -2, 0, 1], 'lmfdb_label': '3136.e1', 'torsion': [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: 56284
    {'conductor': 3136, 'conductor_valuation': 6, 'discriminant_valuation': 27, 'j_denominator_valuation': 9, 'kodaira_symbol': -21, 'lmfdb_label': '3136.e1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 56285
    {'conductor': 3136, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '3136.e1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1684292
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [397, 36, 88, 29], [127, 36, 262, 361], [469, 36, 468, 37], [476, 477, 447, 206], [257, 468, 262, 497], [19, 36, 216, 91], [1, 18, 14, 253]], 'adelic_image': '504.864.21.?', 'conductor': 3136, 'lmfdb_label': '3136.e1', 'prime': 0}
  • id: 15593
    {'conductor': 3136, 'elladic_image': '8.6.0.6', 'lmfdb_label': '3136.e1', 'modell_image': '2B', 'prime': 2}
  • id: 15594
    {'conductor': 3136, 'elladic_image': '9.12.0.1', 'lmfdb_label': '3136.e1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 3136.e does not appear in ec_padic