Elliptic curve data - 12274.b1

Formats: - HTML - YAML - JSON - 2024-04-29T01:47:04.275793

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '12274f', 'Clabel': '12274f1', 'Cnumber': 1, 'abc_quality': 0.9354352331857968, 'absD': 1335043923526928, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1292, 'ainvs': [1, 0, 1, -27805, 304488], 'analytic_rank': 0, 'bad_primes': [2, 17, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12274, 'degree': 69120, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5924586481466438949982274329', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [50529889873, 28377488], 'lmfdb_iso': '12274.b', 'lmfdb_label': '12274.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -77, -77], 'min_quad_twist_disc': -19, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '34.6.0.a.1', '76.6.0.?', '1292.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.12023915856342366499371371696', 'prec': 103}, 'szpiro_ratio': 4.49404067973809, '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, -2, 1, 2, 2, 0, -1, 1, -2, -4, -2, -2, 0, -4, 1, -1, -1, 0, 2], 'aplist': [-1, -2, 2, 0, -4, -2, -1, 0, 8, 8, 2, 8, -4, 4, 8, -2, 12, 2, -12, -14, 6, 10, -12, -6, -4], 'class_deg': 2, 'class_size': 2, 'conductor': 12274, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12274.b', 'trace_hash': 2294460396142404133}
• 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': '0.041381668076790867410764518353', 'prec': 107}, 'conductor': 12274, 'gens': [], 'heights': [], 'lmfdb_label': '12274.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41626500143153453571021516282', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.83253000286306907142043032564387509388', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[11, -6, 1]], 'xcoord_integral_points': [11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '17': [0, 0], '19': 'a'}, 'iwp0': 3, 'lmfdb_label': '12274.b1'}
• ec_torsion_growth •

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

  
  
  • id: 633595
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '12274.b1', 'torsion': [2, 2]}
  • id: 633596
    {'degree': 4, 'field': [4, 2, 1, -1, 1], 'lmfdb_label': '12274.b1', 'torsion': [4]}
  • id: 633599
    {'degree': 8, 'field': [-2, -139, 118, 41, -17, -7, 7, -4, 1], 'lmfdb_label': '12274.b1', 'torsion': [6]}
  • id: 633597
    {'degree': 8, 'field': [101, -162, 203, -162, 110, -36, 9, 0, 1], 'lmfdb_label': '12274.b1', 'torsion': [2, 4]}
  • id: 633598
    {'degree': 8, 'field': [494, 722, 229, 480, 260, -16, -42, -2, 1], 'lmfdb_label': '12274.b1', 'torsion': [2, 4]}
  • id: 633601
    {'degree': 16, 'field': [289444, 0, 601679, 0, 84934, 0, -268435, 0, 52879, 0, -4363, 0, 463, 0, -34, 0, 1], 'lmfdb_label': '12274.b1', 'torsion': [2, 6]}
  • id: 633600
    {'degree': 16, 'field': [471268, -138872, 158690, -56800, 77721, -76612, 53344, -22388, 6042, -3648, 3814, -1360, -16, 84, 8, -8, 1], 'lmfdb_label': '12274.b1', '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: 265182
    {'conductor': 12274, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12274.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 265183
    {'conductor': 12274, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '12274.b1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 265184
    {'conductor': 12274, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '12274.b1', 'prime': 19, '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: 1745400
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1289, 4, 1288, 5], [1, 4, 0, 1], [477, 4, 954, 9], [686, 1, 303, 0], [325, 970, 968, 323]], 'adelic_image': '1292.12.0.?', 'conductor': 12274, 'lmfdb_label': '12274.b1', 'prime': 0}
  • id: 58499
    {'conductor': 12274, 'elladic_image': '2.3.0.1', 'lmfdb_label': '12274.b1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12274.b does not appear in ec_padic