Elliptic curve data - 14.a4

Formats: - HTML - YAML - JSON - 2024-04-16T12:47:27.290708

• 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': '14a', 'Clabel': '14a6', 'Cnumber': 6, 'abc_quality': 0.9676277689392396, 'absD': 98, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 504, 'ainvs': [1, 0, 1, -11, 12], 'analytic_rank': 0, 'bad_primes': [2, 7], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 14, 'degree': 6, 'elladic_images': ['8.6.0.6', '9.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288209', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [128787625, 98], 'lmfdb_iso': '14.a', 'lmfdb_label': '14.a4', 'lmfdb_number': 4, 'manin_constant': 3, 'min_quad_twist_ainvs': [1, 0, 1, -11, 12], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '6.24.0-6.a.1.4', '8.6.0.b.1', '9.24.0-9.a.1.2', '18.72.0-18.a.1.1', '24.48.0-24.y.1.15', '28.6.0.c.1', '56.12.0.k.1', '63.72.0-63.d.2.4', '72.144.1.?', '84.48.0.?', '126.216.2.?', '168.96.1.?', '252.432.7.?', '504.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288209', 'prec': 107}, 'szpiro_ratio': 7.075888453908073, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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, 0, 2, 1, -1, 1, 0, 0, -2, -4, -1, 0, 1, 6, -1, 2, 0], 'aplist': [-1, -2, 0, 1, 0, -4, 6, 2, 0, -6, -4, 2, 6, 8, -12, 6, -6, 8, -4, 0, 2, 8, -6, -6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 14, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '14.a', 'trace_hash': 1459918945821948014}
• 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': '3.9393771083730242797467824533', 'prec': 100}, 'conductor': 14, 'gens': [], 'heights': [], 'lmfdb_label': '14.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '5.9440258682006497025087150302', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.33022365934448053902826194612222809986', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[0, 3, 1]], 'xcoord_integral_points': [0, 2]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '3': [0, 0], '7': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '14.a4'}
• ec_torsion_growth •

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

  
  
  • id: 108
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [2, 6]}
  • id: 109
    {'degree': 3, 'field': [1, -2, -1, 1], 'lmfdb_label': '14.a4', 'torsion': [18]}
  • id: 110
    {'degree': 4, 'field': [2, 0, -1, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [12]}
  • id: 113
    {'degree': 6, 'field': [-8, 0, 24, 0, -10, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [2, 18]}
  • id: 112
    {'degree': 6, 'field': [1, 1, -2, -1, 4, -3, 1], 'lmfdb_label': '14.a4', 'torsion': [18]}
  • id: 111
    {'degree': 6, 'field': [27, 9, -8, -3, 4, -3, 1], 'lmfdb_label': '14.a4', 'torsion': [3, 6]}
  • id: 115
    {'degree': 8, 'field': [1, 0, 2, 0, 10, 0, 2, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [2, 12]}
  • id: 114
    {'degree': 8, 'field': [4, 0, -16, 0, 18, 0, -8, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [2, 12]}
  • id: 117
    {'degree': 12, 'field': [4, 0, -8, 0, 16, 0, -22, 0, 16, 0, -6, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [2, 18]}
  • id: 118
    {'degree': 12, 'field': [8, 0, -12, 0, 4, 0, 1, 0, 2, 0, -3, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [36]}
  • id: 116
    {'degree': 12, 'field': [36, 0, 48, 0, 52, 0, 28, 0, 12, 0, -2, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [6, 6]}
  • id: 119
    {'degree': 16, 'field': [64, 0, -192, 0, 164, 0, 72, 0, -86, 0, -12, 0, 31, 0, -10, 0, 1], 'lmfdb_label': '14.a4', 'torsion': [24]}
  • id: 120
    {'degree': 18, 'field': [1, -4, 14, -31, 64, -100, 146, -176, 202, -205, 202, -176, 146, -100, 64, -31, 14, -4, 1], 'lmfdb_label': '14.a4', 'torsion': [3, 18]}
• 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: 13
    {'conductor': 14, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '14.a4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 14
    {'conductor': 14, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '14.a4', 'prime': 7, '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: 1665894
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [281, 36, 0, 1], [127, 36, 262, 361], [469, 36, 468, 37], [19, 36, 216, 91], [28, 27, 57, 298], [313, 36, 426, 265], [1, 18, 14, 253]], 'adelic_image': '504.864.21.?', 'conductor': 14, 'lmfdb_label': '14.a4', 'prime': 0}
  • id: 9
    {'conductor': 14, 'elladic_image': '8.6.0.6', 'lmfdb_label': '14.a4', 'modell_image': '2B', 'prime': 2}
  • id: 10
    {'conductor': 14, 'elladic_image': '9.24.0.1', 'lmfdb_label': '14.a4', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 14.a does not appear in ec_padic