Elliptic curve data - 26.b1

Formats: - HTML - YAML - JSON - 2022-06-27T04:53:31.557558

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  absD	numeric
  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[]
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '26b', 'Clabel': '26b2', 'Cnumber': 2, 'absD': 125497034, 'ainvs': [1, -1, 1, -213, -1257], 'analytic_rank': 0, 'bad_primes': [2, 13], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 26, 'degree': 14, 'elladic_images': ['7.48.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.28979452610338456519600707002', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 7, 'iso_nlabel': 1, 'isogeny_degrees': [1, 7], 'jinv': [-1064019559329, 125497034], 'lmfdb_iso': '26.b', 'lmfdb_label': '26.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -213, -1257], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.3'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.28979452610338456519600707002', 'prec': 103}, '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, 1, -3, 1, -1, -3, 1, 1, 6, -1, -2, -3, -1, 1, 3, 1, -3, 6, 6, -1], 'aplist': [1, -3, -1, 1, -2, -1, -3, 6, -4, 2, 4, 3, 0, -5, 13, 12, -10, -8, -2, -5, -10, -4, 0, 6, 14], 'class_deg': 7, 'class_size': 2, 'conductor': 26, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '26.b', 'trace_hash': 1458165707980378714}
• 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': '0.56012850284733550649814539019', 'prec': 103}, 'conductor': 26, 'gens': [], 'heights': [], 'lmfdb_label': '26.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.62096534954905546637586267270', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.62096534954905546637586267270088986448', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [0, 0, 0], '5': [0, 0], '7': [4, 1], '13': [0, 0]}, 'iwp0': 11, 'lmfdb_label': '26.b1'}
• ec_torsion_growth •

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

  
  
  • id: 622
    {'degree': 3, 'field': [-2, -1, 0, 1], 'lmfdb_label': '26.b1', 'torsion': [2]}
  • id: 624
    {'degree': 6, 'field': [1, -1, 1, -1, 1, -1, 1], 'lmfdb_label': '26.b1', 'torsion': [7]}
  • id: 623
    {'degree': 6, 'field': [26, 0, 29, 0, 8, 0, 1], 'lmfdb_label': '26.b1', 'torsion': [2, 2]}
  • id: 625
    {'degree': 7, 'field': [-2, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '26.b1', 'torsion': [7]}
  • id: 626
    {'degree': 8, 'field': [-2, -4, -2, 11, -2, -7, 7, -4, 1], 'lmfdb_label': '26.b1', 'torsion': [3]}
  • id: 627
    {'degree': 12, 'field': [-16, 112, -28, 264, -228, 28, 119, -90, 25, -8, 11, -6, 1], 'lmfdb_label': '26.b1', 'torsion': [4]}
  • id: 628
    {'degree': 18, 'field': [64, 32, 16, -24, -28, -22, 1, -28, -3, -2, 13, 8, 5, -4, 1, -2, 1, 0, 1], 'lmfdb_label': '26.b1', 'torsion': [14]}
  • id: 629
    {'degree': 21, 'field': [32, 0, 0, 0, 0, 0, 0, 1294, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '26.b1', 'torsion': [14]}
• 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: 78
    {'conductor': 26, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '26.b1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 79
    {'conductor': 26, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '26.b1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'conductor': 26, 'elladic_image': '7.48.0.5', 'lmfdb_label': '26.b1', 'modell_image': '7B.1.3', 'prime': 7}
• lmfdb_iso 26.b does not appear in ec_padic