Elliptic curve data - 14.a1

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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': '14a', 'Clabel': '14a5', 'Cnumber': 5, 'abc_quality': 1.0648884149541868, 'absD': 25088, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 504, 'ainvs': [1, 0, 1, -2731, -55146], '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', '9.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.41310098042308445758078235484', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 18, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [2251439055699625, 25088], 'lmfdb_iso': '14.a', 'lmfdb_label': '14.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2731, -55146], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '6.24.0-6.a.1.2', '8.6.0.b.1', '9.24.0-9.a.1.1', '18.72.0-18.a.1.2', '24.48.0-24.y.1.13', '28.6.0.c.1', '56.12.0.k.1', '63.72.0-63.d.1.3', '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': 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': '0.41310098042308445758078235484', 'prec': 103}, 'szpiro_ratio': 13.395065575232227, '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, -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': '0.43770856759700269774964249481', 'prec': 103}, 'conductor': 14, 'gens': [], 'heights': [], 'lmfdb_label': '14.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.66044731868896107805652389225', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.33022365934448053902826194612222809986', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[-121, 117, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '3': [0, 2], '7': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '14.a1'}
• ec_torsion_growth •

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

  
  
  • id: 88
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 2]}
  • id: 89
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '14.a1', 'torsion': [6]}
  • id: 90
    {'degree': 3, 'field': [-7, 0, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [6]}
  • id: 91
    {'degree': 4, 'field': [2, 0, -1, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [4]}
  • id: 92
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 6]}
  • id: 95
    {'degree': 6, 'field': [7, 0, 0, -4, 0, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [18]}
  • id: 96
    {'degree': 6, 'field': [41, -84, 12, -14, -6, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 6]}
  • id: 93
    {'degree': 6, 'field': [64, -24, -15, 7, 6, -3, 1], 'lmfdb_label': '14.a1', 'torsion': [3, 6]}
  • id: 94
    {'degree': 6, 'field': [343, 0, 0, -28, 0, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [18]}
  • id: 98
    {'degree': 8, 'field': [1, 0, 2, 0, 10, 0, 2, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 4]}
  • id: 97
    {'degree': 8, 'field': [4, 0, -16, 0, 18, 0, -8, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 4]}
  • id: 99
    {'degree': 8, 'field': [4, 0, 2, 0, -1, 0, 1, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [12]}
  • id: 103
    {'degree': 12, 'field': [392, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [12]}
  • id: 100
    {'degree': 12, 'field': [1681, 3444, 6564, -140, -786, 1176, 350, 0, 24, -28, 6, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [6, 6]}
  • id: 102
    {'degree': 12, 'field': [3136, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 18]}
  • id: 101
    {'degree': 12, 'field': [116929, 144732, 55956, -13720, -4314, 1848, 1526, -504, 24, -56, 6, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 18]}
  • id: 106
    {'degree': 16, 'field': [1, 0, -2, 0, -6, 0, -16, 0, 95, 0, -16, 0, -6, 0, -2, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 12]}
  • id: 105
    {'degree': 16, 'field': [16, 0, 64, 0, 184, 0, 224, 0, 192, 0, 112, 0, 46, 0, 8, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [2, 12]}
  • id: 104
    {'degree': 16, 'field': [64, 0, -192, 0, 164, 0, 72, 0, -86, 0, -12, 0, 31, 0, -10, 0, 1], 'lmfdb_label': '14.a1', 'torsion': [8]}
  • id: 107
    {'degree': 18, 'field': [2512, -15720, 47184, -95718, 150321, -188391, 198099, -175122, 133758, -87574, 50088, -24600, 10548, -3822, 1194, -300, 63, -9, 1], 'lmfdb_label': '14.a1', '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: 11
    {'conductor': 14, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '14.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12
    {'conductor': 14, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '14.a1', '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: 1665891
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [397, 36, 88, 29], [127, 36, 262, 361], [469, 36, 468, 37], [247, 36, 242, 7], [19, 36, 216, 91], [28, 27, 57, 298], [1, 18, 14, 253]], 'adelic_image': '504.864.21.?', 'conductor': 14, 'lmfdb_label': '14.a1', 'prime': 0}
  • id: 3
    {'conductor': 14, 'elladic_image': '8.6.0.6', 'lmfdb_label': '14.a1', 'modell_image': '2B', 'prime': 2}
  • id: 4
    {'conductor': 14, 'elladic_image': '9.24.0.3', 'lmfdb_label': '14.a1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 14.a does not appear in ec_padic