Elliptic curve data - 14161.b2

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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': '14161b', 'Clabel': '14161b2', 'Cnumber': 2, 'abc_quality': 1.0296285559493121, 'absD': 820690887176209, 'adelic_genus': 53, 'adelic_index': 1536, 'adelic_level': 3808, 'ainvs': [1, -1, 1, -80541, 8709236], 'analytic_rank': 0, 'bad_primes': [7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 14161, 'degree': 41472, 'elladic_images': ['16.48.0.20'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6663520353344485570113946157', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [20346417, 289], 'lmfdb_iso': '14161.b', 'lmfdb_label': '14161.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -6, -4], 'min_quad_twist_disc': -119, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.a.1', '8.24.0.f.1', '16.48.0.c.2', '28.24.0-4.a.1.2', '56.48.0-8.f.1.4', '68.24.0.b.1', '112.96.0.?', '136.96.3.?', '272.384.21.?', '476.48.0.?', '544.768.53.?', '952.192.3.?', '1904.768.21.?', '3808.1536.53.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.72320971122131613566604906496', 'prec': 107}, 'szpiro_ratio': 4.760617340168213, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, -1, -2, 0, 0, 3, -3, 2, 0, 0, 2, 0, 0, -1, 0, 3, 4, 2], 'aplist': [-1, 0, -2, 0, 0, 2, 0, 4, -4, -6, 4, 2, -6, 4, 0, 6, 12, -10, 4, 4, -6, -12, 4, -10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 14161, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '14161.b', 'trace_hash': 2266761599506173569}
• 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': '0.035696448723781228244633917135', 'prec': 107}, 'conductor': 14161, 'gens': [], 'heights': [], 'lmfdb_label': '14161.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.50340298455688871174773446677', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.50340298455688871174773446677154470605', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-327, 163, 1], [149, -75, 1]], 'xcoord_integral_points': [-327, 149]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '7': 'a', '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '14161.b2'}
• ec_torsion_growth •

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

  
  
  • id: 728479
    {'degree': 4, 'field': [2, 22, -21, -2, 1], 'lmfdb_label': '14161.b2', 'torsion': [2, 4]}
  • id: 728478
    {'degree': 4, 'field': [36, 0, -5, 0, 1], 'lmfdb_label': '14161.b2', 'torsion': [2, 4]}
  • id: 728480
    {'degree': 4, 'field': [900, 0, -59, 0, 1], 'lmfdb_label': '14161.b2', 'torsion': [2, 4]}
  • id: 728482
    {'degree': 8, 'field': [-5729, -5644, 289, 1343, 34, -85, 4, -4, 1], 'lmfdb_label': '14161.b2', 'torsion': [2, 6]}
  • id: 728481
    {'degree': 8, 'field': [72, -288, 470, -390, 261, -82, 32, -4, 1], 'lmfdb_label': '14161.b2', 'torsion': [4, 4]}
  • id: 728483
    {'degree': 16, 'field': [5167, -12772, 25806, -33932, 39898, -37620, 32386, -23652, 15691, -9012, 4658, -2036, 764, -224, 52, -8, 1], 'lmfdb_label': '14161.b2', 'torsion': [2, 8]}
  • id: 728484
    {'degree': 16, 'field': [1679616, 0, -3359232, 0, 2375568, 0, -943488, 0, 212056, 0, -26208, 0, 1833, 0, -72, 0, 1], 'lmfdb_label': '14161.b2', 'torsion': [2, 8]}
  • id: 728485
    {'degree': 16, 'field': [28090000, 0, -19941648, 0, 6467148, 0, -1278300, 0, 170577, 0, -15896, 0, 1030, 0, -44, 0, 1], 'lmfdb_label': '14161.b2', 'torsion': [2, 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: 310626
    {'conductor': 14161, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '14161.b2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 310627
    {'conductor': 14161, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '14161.b2', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1758184
    {'adelic_gens': [[1, 0, 32, 1], [2143, 2310, 1904, 1], [1, 32, 0, 1], [543, 0, 0, 3807], [3667, 1064, 3542, 1259], [3613, 84, 2968, 169], [3777, 32, 3776, 33], [29, 8, 444, 1173], [9, 32, 3752, 3609]], 'adelic_image': '3808.1536.53.?', 'conductor': 14161, 'lmfdb_label': '14161.b2', 'prime': 0}
  • id: 67035
    {'conductor': 14161, 'elladic_image': '16.48.0.20', 'lmfdb_label': '14161.b2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 14161.b does not appear in ec_padic