Elliptic curve data - 26.a2

Formats: - HTML - YAML - JSON - 2023-09-28T15:26:36.705105

• ec_curvedata •

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

  
  {'Ciso': '26a', 'Clabel': '26a1', 'Cnumber': 1, 'absD': 17576, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 936, 'ainvs': [1, 0, 1, -5, -8], 'analytic_rank': 0, 'bad_primes': [2, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 26, 'degree': 2, 'elladic_images': ['3.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.49491971820067818992441210777', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [-10218313, 17576], 'lmfdb_iso': '26.a', 'lmfdb_label': '26.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5, -8], 'min_quad_twist_disc': 1, 'modell_images': ['3Cs.1.1'], 'modm_images': ['3.24.0-3.a.1.1', '104.2.0.?', '117.72.0.?', '312.48.1.?', '936.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.49491971820067818992441210777', 'prec': 107}, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 1, 1, -3, -1, -1, -1, -2, 3, 6, 1, 1, 1, -3, 1, -3, 2, 2, -3], 'aplist': [-1, 1, -3, -1, 6, 1, -3, 2, 0, 6, -4, -7, 0, -1, 3, 0, -6, 8, 14, -3, 2, 8, 12, -6, -10], 'class_deg': 9, 'class_size': 3, 'conductor': 26, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '26.a', 'trace_hash': 2069639601307544454}
• 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': '2.6908023927466443508254527535', 'prec': 100}, 'conductor': 26, 'gens': [], 'heights': [], 'lmfdb_label': '26.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.5467299538318833526303052273', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.51557665127729445087676840909457345498', 'prec': 133}, 'tamagawa_product': 3, 'torsion_generators': [[4, 4, 1]], 'xcoord_integral_points': [4]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [0, 1], '13': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '26.a2'}
• ec_torsion_growth •

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

  
  
  • id: 581
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '26.a2', 'torsion': [3, 3]}
  • id: 582
    {'degree': 3, 'field': [-2, -1, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [6]}
  • id: 584
    {'degree': 6, 'field': [4, -2, 1, -4, 1, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [3, 6]}
  • id: 583
    {'degree': 6, 'field': [26, 0, 29, 0, 8, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [2, 6]}
  • id: 585
    {'degree': 9, 'field': [-1, 0, 0, -10, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [9]}
  • id: 586
    {'degree': 12, 'field': [-2, -2, -1, -4, 3, 2, -11, 0, -1, -10, -1, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [12]}
  • id: 587
    {'degree': 12, 'field': [1, 0, 0, 0, 0, 0, 106, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [6, 6]}
  • id: 590
    {'degree': 18, 'field': [1, 0, 0, 6, 0, 0, 1, 0, 0, -22, 0, 0, 25, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [3, 9]}
  • id: 589
    {'degree': 18, 'field': [25, -15, 264, -1187, 3858, -7140, 8797, -7785, 5337, -3127, 1956, -1473, 1114, -711, 369, -150, 45, -9, 1], 'lmfdb_label': '26.a2', 'torsion': [3, 9]}
  • id: 588
    {'degree': 18, 'field': [19683, 0, 0, -18954, 0, 0, 7803, 0, 0, -1872, 0, 0, 289, 0, 0, -26, 0, 0, 1], 'lmfdb_label': '26.a2', 'torsion': [3, 9]}
• 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: 70
    {'conductor': 26, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '26.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 71
    {'conductor': 26, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '26.a2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1665929
    {'adelic_gens': [[469, 18, 477, 163], [13, 18, 153, 511], [1, 18, 0, 1], [1, 0, 18, 1], [713, 486, 306, 541], [919, 18, 918, 19], [1, 12, 0, 1], [1, 6, 6, 37], [1, 9, 9, 82], [703, 18, 711, 163]], 'adelic_image': '936.144.3.?', 'conductor': 26, 'lmfdb_label': '26.a2', 'prime': 0}
  • id: 51
    {'conductor': 26, 'elladic_image': '3.24.0.1', 'lmfdb_label': '26.a2', 'modell_image': '3Cs.1.1', 'prime': 3}
• lmfdb_iso 26.a does not appear in ec_padic