Elliptic curve data - 26136.bf1

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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
  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': '26136h', 'Clabel': '26136h1', 'Cnumber': 1, 'abc_quality': 0.9463948908766787, 'absD': 80339639415552, 'adelic_genus': 0, 'adelic_index': 8, 'adelic_level': 12, 'ainvs': [0, 0, 0, -13068, 718740], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 26136, 'degree': 92160, 'elladic_images': ['4.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3806582521338577045471282707', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1], 'jinv': [-3072, 1], 'lmfdb_iso': '26136.bf', 'lmfdb_label': '26136.bf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -12, 20], 'min_quad_twist_disc': 33, 'modell_images': [], 'modm_images': ['4.4.0.a.1', '6.2.0.a.1', '12.8.0.c.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2874487692510583242076397331', 'prec': 103}, 'szpiro_ratio': 3.9812585716915074, '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, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 1, 0], 'aplist': [0, 0, 4, 3, 0, -1, 4, 1, 4, 0, -4, -9, 0, 8, -12, -8, 4, 5, 11, 8, -1, 5, -8, 12, 5], 'class_deg': 1, 'class_size': 1, 'conductor': 26136, 'isogeny_matrix': [[1]], 'lmfdb_iso': '26136.bf', 'trace_hash': 1397209601164172658}
• 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': '0.063208499300546545975343164644', 'prec': 107}, 'conductor': 26136, 'gens': [], 'heights': [], 'lmfdb_label': '26136.bf1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.57560107707840752421787886527', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6048086166272601937430309221341249709', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [0, 0], '11': 'a', '13': [0, 0], '17': [0, 0], '19': [2, 0], '23': [0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '26136.bf1'}
• ec_torsion_growth •

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

  
  
  • id: 1315036
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '26136.bf1', 'torsion': [2]}
  • id: 1315037
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '26136.bf1', 'torsion': [2, 2]}
  • id: 1315038
    {'degree': 8, 'field': [-1619, -1642, -536, 186, 96, -12, 4, -4, 1], 'lmfdb_label': '26136.bf1', 'torsion': [3]}
  • id: 1315039
    {'degree': 12, 'field': [-14682, -15120, -27900, -2724, 2658, 6024, 192, -1020, -138, 66, 18, -6, 1], 'lmfdb_label': '26136.bf1', 'torsion': [4]}
• 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: 602457
    {'conductor': 26136, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '26136.bf1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 602458
    {'conductor': 26136, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '26136.bf1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 602459
    {'conductor': 26136, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '26136.bf1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1838626
    {'adelic_gens': [[9, 4, 8, 5], [4, 9, 5, 1], [2, 1, 5, 3], [8, 3, 1, 4], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '12.8.0.?', 'conductor': 26136, 'lmfdb_label': '26136.bf1', 'prime': 0}
  • id: 119001
    {'conductor': 26136, 'elladic_image': '4.4.0.1', 'lmfdb_label': '26136.bf1', 'modell_image': '2G', 'prime': 2}
• lmfdb_iso 26136.bf does not appear in ec_padic