Elliptic curve data - 63.a4

Formats: - HTML - YAML - JSON - 2023-09-21T15:50:01.505781

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '63a', 'Clabel': '63a6', 'Cnumber': 6, 'absD': 12607619787, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, -1, 0, -306, 5859], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 63, 'degree': 32, 'elladic_images': ['8.48.0.183'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.62351152772499461645588847313', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-4354703137, 17294403], 'lmfdb_iso': '63.a', 'lmfdb_label': '63.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -34, -217], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '6.6.0.a.1', '8.48.0-8.bb.2.6', '12.24.0-12.g.1.1', '24.96.0-24.bj.1.6', '112.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854669', 'prec': 107}, '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': '0.28735897654570899354538575570', 'prec': 103}, 'conductor': 63, 'gens': [], 'heights': [], 'lmfdb_label': '63.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1033104643356925070162502191', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1033104643356925070162502191141098059', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-93, 93, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '63.a4'}
• ec_torsion_growth •

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

  
  
  • id: 2203
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [4]}
  • id: 2202
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '63.a4', 'torsion': [2, 2]}
  • id: 2204
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [4]}
  • id: 2207
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [8]}
  • id: 2205
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [2, 4]}
  • id: 2208
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [8]}
  • id: 2206
    {'degree': 4, 'field': [3, 0, -3, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [2, 4]}
  • id: 2213
    {'degree': 8, 'field': [-3, -7, -5, 3, 4, 2, -3, -1, 1], 'lmfdb_label': '63.a4', 'torsion': [6]}
  • id: 2209
    {'degree': 8, 'field': [1, -4, 8, -10, 7, -2, 2, -2, 1], 'lmfdb_label': '63.a4', 'torsion': [4, 4]}
  • id: 2211
    {'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [2, 8]}
  • id: 2212
    {'degree': 8, 'field': [3, 0, 0, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [2, 8]}
  • id: 2210
    {'degree': 8, 'field': [9, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [2, 8]}
  • id: 2214
    {'degree': 16, 'field': [1, -12, 68, -232, 488, -564, 194, 396, -665, 444, -62, -152, 162, -92, 34, -8, 1], 'lmfdb_label': '63.a4', 'torsion': [4, 8]}
  • id: 2216
    {'degree': 16, 'field': [1, 0, 24, 0, -252, 0, 288, 0, 167, 0, -144, 0, -60, 0, 0, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [16]}
  • id: 2218
    {'degree': 16, 'field': [9, 0, -3, 0, -17, 0, -6, 0, 39, 0, -2, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [2, 6]}
  • id: 2215
    {'degree': 16, 'field': [9, 0, 0, 0, 54, 0, 0, 0, 87, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [4, 8]}
  • id: 2220
    {'degree': 16, 'field': [9, 0, 19, 0, 43, 0, 3, 0, 14, 0, 32, 0, 21, 0, 7, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [12]}
  • id: 2219
    {'degree': 16, 'field': [81, 0, -327, 0, 292, 0, 177, 0, -207, 0, -49, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [12]}
  • id: 2217
    {'degree': 16, 'field': [39204, 0, 64800, 0, 47628, 0, 12960, 0, 1125, 0, -360, 0, -72, 0, 0, 0, 1], 'lmfdb_label': '63.a4', 'torsion': [16]}
• 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: 327
    {'conductor': 63, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '63.a4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 328
    {'conductor': 63, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '63.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: 1666041
    {'adelic_gens': [[5, 4, 332, 333], [241, 16, 248, 129], [1, 16, 0, 1], [104, 335, 145, 326], [15, 2, 238, 323], [55, 16, 54, 73], [321, 16, 320, 17], [1, 0, 16, 1], [13, 16, 164, 105]], 'adelic_image': '336.192.1.?', 'conductor': 63, 'lmfdb_label': '63.a4', 'prime': 0}
  • id: 191
    {'conductor': 63, 'elladic_image': '8.48.0.183', 'lmfdb_label': '63.a4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 63.a does not appear in ec_padic