Elliptic curve data - 126.a5

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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': '126b', 'Clabel': '126b1', 'Cnumber': 1, 'abc_quality': 0.9822408596528094, 'absD': 11757312, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, -1, 0, -36, -176], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 126, 'degree': 32, 'elladic_images': ['16.48.0.102'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.045260157191830045121861551471', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-7189057, 16128], 'lmfdb_iso': '126.a', 'lmfdb_label': '126.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -4, 5], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '12.12.0-4.c.1.2', '14.6.0.b.1', '16.48.0.z.1', '24.48.0-8.bb.1.2', '28.12.0.g.1', '48.96.0-16.z.1.2', '56.48.0.bh.2', '84.24.0.?', '112.96.1.?', '168.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50404598714222480057576106699', 'prec': 107}, 'szpiro_ratio': 4.955086460660417, '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, 0, 1, 2, 0, -1, -1, 0, -2, 4, 0, 6, 1, 0, 1, -2, 0, -4, 2], 'aplist': [-1, 0, 2, -1, 4, 6, -2, -4, -8, 2, 0, -10, 6, -4, 0, -6, -4, 6, 4, -8, 10, 0, 4, 6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 126, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '126.a', 'trace_hash': 16903396746378590}
• 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': '0.91345577742135273012299306070', 'prec': 103}, 'conductor': 126, 'gens': [], 'heights': [], 'lmfdb_label': '126.a5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.91047373686992849677187200164', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.91047373686992849677187200163496359111', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[8, -4, 1]], 'xcoord_integral_points': [8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '126.a5'}
• ec_torsion_growth •

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

  
  
  • id: 4835
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '126.a5', 'torsion': [4]}
  • id: 4836
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '126.a5', 'torsion': [8]}
  • id: 4834
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '126.a5', 'torsion': [2, 2]}
  • id: 4837
    {'degree': 4, 'field': [4, -2, -1, -1, 1], 'lmfdb_label': '126.a5', 'torsion': [2, 8]}
  • id: 4841
    {'degree': 8, 'field': [-4, 28, -20, 20, -2, -2, 5, -2, 1], 'lmfdb_label': '126.a5', 'torsion': [6]}
  • id: 4839
    {'degree': 8, 'field': [-3, 18, -20, 6, -7, 2, 4, -4, 1], 'lmfdb_label': '126.a5', 'torsion': [8]}
  • id: 4840
    {'degree': 8, 'field': [1, -2, 3, 2, -4, 2, 3, -2, 1], 'lmfdb_label': '126.a5', 'torsion': [16]}
  • id: 4838
    {'degree': 8, 'field': [22, -26, 29, -30, 14, -12, 8, -2, 1], 'lmfdb_label': '126.a5', 'torsion': [2, 4]}
  • id: 4842
    {'degree': 16, 'field': [1, -2, 2, -12, 13, 8, 30, -26, -12, -26, 30, 8, 13, -12, 2, -2, 1], 'lmfdb_label': '126.a5', 'torsion': [4, 8]}
  • id: 4847
    {'degree': 16, 'field': [1, 0, 8, 0, -14, 0, 28, 0, -49, 0, 28, 0, -14, 0, 8, 0, 1], 'lmfdb_label': '126.a5', 'torsion': [12]}
  • id: 4843
    {'degree': 16, 'field': [4, -24, 98, -268, 503, -6, 65, -338, 132, -62, 109, -22, 24, -10, 7, -2, 1], 'lmfdb_label': '126.a5', 'torsion': [2, 16]}
  • id: 4845
    {'degree': 16, 'field': [4, 32, 40, -168, -175, 140, 294, 4, -122, -58, -42, 28, 14, 0, -2, -2, 1], 'lmfdb_label': '126.a5', 'torsion': [16]}
  • id: 4848
    {'degree': 16, 'field': [16, -64, 192, -264, 288, -84, 121, -100, -3, 66, -15, -18, 17, -14, 9, -4, 1], 'lmfdb_label': '126.a5', 'torsion': [24]}
  • id: 4844
    {'degree': 16, 'field': [16, 0, 24, 0, 32, 0, 38, 0, 21, 0, -16, 0, 15, 0, -4, 0, 1], 'lmfdb_label': '126.a5', 'torsion': [2, 16]}
  • id: 4846
    {'degree': 16, 'field': [32, 240, 520, 276, 316, -700, 176, 86, -40, 141, -64, -77, 55, -11, 7, -4, 1], 'lmfdb_label': '126.a5', 'torsion': [2, 6]}
• 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: 870
    {'conductor': 126, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '126.a5', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 871
    {'conductor': 126, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '126.a5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 872
    {'conductor': 126, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '126.a5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1666272
    {'adelic_gens': [[193, 240, 258, 271], [5, 4, 332, 333], [1, 16, 0, 1], [15, 2, 238, 323], [321, 16, 320, 17], [223, 0, 0, 335], [1, 240, 84, 85], [1, 0, 16, 1], [136, 225, 111, 10]], 'adelic_image': '336.192.1.?', 'conductor': 126, 'lmfdb_label': '126.a5', 'prime': 0}
  • id: 463
    {'conductor': 126, 'elladic_image': '16.48.0.102', 'lmfdb_label': '126.a5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 126.a does not appear in ec_padic