Elliptic curve data - 69.a1

Formats: - HTML - YAML - JSON - 2024-05-28T03:09:20.209855

• 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': '69a', 'Clabel': '69a2', 'Cnumber': 2, 'abc_quality': 0.9246304097924353, 'absD': 1587, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [1, 0, 1, -16, -25], 'analytic_rank': 0, 'bad_primes': [3, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 69, 'degree': 4, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.52739354827166909392101445569', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [413493625, 1587], 'lmfdb_iso': '69.a', 'lmfdb_label': '69.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -16, -25], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '92.6.0.?', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, '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': '-0.52739354827166909392101445569', 'prec': 107}, 'szpiro_ratio': 4.685794425245767, '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, 1, -1, 0, 1, -2, -3, 1, 0, 4, -1, -6, -2, 0, -1, 4, 1, 2, 0], 'aplist': [1, 1, 0, -2, 4, -6, 4, 2, -1, 2, 4, 2, 2, 10, 0, -12, -12, -6, -10, 8, -14, 10, 12, -16, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 69, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '69.a', 'trace_hash': 538245996156256486}
• 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': '2.8713637655492899020652867990', 'prec': 100}, 'conductor': 69, 'gens': [], 'heights': [], 'lmfdb_label': '69.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.4058638675609891988009602024', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2029319337804945994004801012147073770', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[-9, 5, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 0], '23': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '69.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2446
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '69.a1', 'torsion': [2, 2]}
  • id: 2447
    {'degree': 4, 'field': [4, 2, 2, -1, 1], 'lmfdb_label': '69.a1', 'torsion': [4]}
  • id: 2450
    {'degree': 8, 'field': [-27, 81, -90, 17, -5, -7, 7, -4, 1], 'lmfdb_label': '69.a1', 'torsion': [6]}
  • id: 2449
    {'degree': 8, 'field': [-11, 24, 80, 36, -39, -24, 2, 0, 1], 'lmfdb_label': '69.a1', 'torsion': [2, 4]}
  • id: 2448
    {'degree': 8, 'field': [144, 72, 126, -126, 49, -6, -4, 0, 1], 'lmfdb_label': '69.a1', 'torsion': [2, 4]}
  • id: 2452
    {'degree': 16, 'field': [9, 0, -3816, 0, 3438, 0, -2436, 0, 2103, 0, -879, 0, 136, 0, -7, 0, 1], 'lmfdb_label': '69.a1', 'torsion': [2, 6]}
  • id: 2451
    {'degree': 16, 'field': [20736, 0, -6912, 0, 14400, 0, -12816, 0, 5379, 0, -1068, 0, 100, 0, -4, 0, 1], 'lmfdb_label': '69.a1', '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: 376
    {'conductor': 69, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '69.a1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 377
    {'conductor': 69, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '69.a1', 'prime': 23, 'reduction_type': -1, '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: 1666059
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [97, 4, 194, 9], [273, 4, 272, 5], [208, 73, 69, 208], [1, 0, 4, 1], [3, 4, 8, 11], [94, 1, 91, 0]], 'adelic_image': '276.12.0.?', 'conductor': 69, 'lmfdb_label': '69.a1', 'prime': 0}
  • id: 216
    {'conductor': 69, 'elladic_image': '2.3.0.1', 'lmfdb_label': '69.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 69.a does not appear in ec_padic