Elliptic curve data - 63.a6

Formats: - HTML - YAML - JSON - 2024-04-25T16:43:35.148358

• 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': '63a', 'Clabel': '63a1', 'Cnumber': 1, 'abc_quality': 0.9786808587681587, 'absD': 45927, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, -1, 0, 9, 0], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 63, 'degree': 4, 'elladic_images': ['16.48.0.84'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.41620924311492334766995970906', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [103823, 63], 'lmfdb_iso': '63.a', 'lmfdb_label': '63.a6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1, 0], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.1', '12.12.0-4.c.1.2', '14.6.0.b.1', '16.48.0-16.e.1.1', '24.48.0-24.bz.1.7', '28.12.0.g.1', '48.96.0-48.bd.1.1', '56.48.0-56.bf.1.4', '84.24.0.?', '112.96.0.?', '168.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, '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': '-0.96551538744897819336758232752', 'prec': 107}, 'szpiro_ratio': 4.378838182976427, '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, -3, 0, 2, -4, 0, -2, -1, 0, -1, 6, 0, 4, -2], 'aplist': [1, 0, 2, -1, -4, -2, 6, 4, 0, 2, 0, 6, -2, -4, 0, -6, -12, -2, 4, 0, -6, -16, 12, 14, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 63, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '63.a', 'trace_hash': 2278490076300767204}
• 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': '2.2988718123656719483630860456', 'prec': 100}, 'conductor': 63, 'gens': [], 'heights': [], 'lmfdb_label': '63.a6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.2066209286713850140325004382', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1033104643356925070162502191141098059', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '63.a6'}
• ec_torsion_growth •

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

  
  
  • id: 2139
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '63.a6', 'torsion': [4]}
  • id: 2140
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '63.a6', 'torsion': [8]}
  • id: 2138
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '63.a6', 'torsion': [2, 2]}
  • id: 2142
    {'degree': 4, 'field': [1, 2, 0, -1, 1], 'lmfdb_label': '63.a6', 'torsion': [16]}
  • id: 2141
    {'degree': 4, 'field': [4, -2, -1, -1, 1], 'lmfdb_label': '63.a6', 'torsion': [2, 8]}
  • id: 2146
    {'degree': 8, 'field': [-3, -7, -5, 3, 4, 2, -3, -1, 1], 'lmfdb_label': '63.a6', 'torsion': [6]}
  • id: 2144
    {'degree': 8, 'field': [-3, 18, -20, 6, -7, 2, 4, -4, 1], 'lmfdb_label': '63.a6', 'torsion': [8]}
  • id: 2145
    {'degree': 8, 'field': [1, -3, 4, -3, 3, -3, 4, -3, 1], 'lmfdb_label': '63.a6', 'torsion': [2, 16]}
  • id: 2143
    {'degree': 8, 'field': [22, -26, 29, -30, 14, -12, 8, -2, 1], 'lmfdb_label': '63.a6', 'torsion': [2, 4]}
  • id: 2151
    {'degree': 16, 'field': [-3, 27, -92, 161, -128, 14, -41, -7, 38, 70, 44, -98, -22, 49, -8, -4, 1], 'lmfdb_label': '63.a6', 'torsion': [12]}
  • id: 2147
    {'degree': 16, 'field': [1, -2, 2, -12, 13, 8, 30, -26, -12, -26, 30, 8, 13, -12, 2, -2, 1], 'lmfdb_label': '63.a6', 'torsion': [4, 8]}
  • id: 2149
    {'degree': 16, 'field': [3, 6, -9, -114, 501, -1062, 1485, -1572, 1393, -1106, 802, -512, 274, -116, 37, -8, 1], 'lmfdb_label': '63.a6', 'torsion': [32]}
  • id: 2148
    {'degree': 16, 'field': [9, -72, 198, -126, -354, 486, 462, -1188, 457, 350, -142, -160, 67, 28, -13, -2, 1], 'lmfdb_label': '63.a6', 'torsion': [2, 16]}
  • id: 2152
    {'degree': 16, 'field': [9, 0, -3, 0, -17, 0, -6, 0, 39, 0, -2, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '63.a6', 'torsion': [24]}
  • id: 2150
    {'degree': 16, 'field': [23, -86, 195, -343, 570, -750, 804, -704, 531, -365, 249, -174, 120, -70, 30, -8, 1], 'lmfdb_label': '63.a6', '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: 317
    {'conductor': 63, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '63.a6', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 318
    {'conductor': 63, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '63.a6', '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: 1666043
    {'adelic_gens': [[1, 16, 92, 213], [15, 2, 238, 323], [1, 16, 0, 1], [160, 5, 243, 322], [305, 16, 74, 207], [5, 4, 332, 333], [321, 16, 320, 17], [1, 0, 16, 1], [211, 320, 32, 315]], 'adelic_image': '336.192.1.?', 'conductor': 63, 'lmfdb_label': '63.a6', 'prime': 0}
  • id: 193
    {'conductor': 63, 'elladic_image': '16.48.0.84', 'lmfdb_label': '63.a6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 63.a does not appear in ec_padic