Elliptic curve data - 63.a3

Formats: - HTML - YAML - JSON - 2023-09-25T23:06:28.101843

• 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': '63a3', 'Cnumber': 3, 'absD': 33480783, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [1, -1, 0, -351, -2430], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 63, 'degree': 16, 'elladic_images': ['16.48.0.98'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.27693793744502196174727241240', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6570725617, 45927], 'lmfdb_iso': '63.a', 'lmfdb_label': '63.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -39, 90], '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', '16.48.0-8.bb.1.8', '24.48.0-8.bb.1.2', '28.12.0.h.1', '48.96.0-48.bf.1.1', '56.48.0.bl.2', '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': 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': '-0.27236820688903288395035020606', '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': '0.57471795309141798709077151139', 'prec': 103}, 'conductor': 63, 'gens': [], 'heights': [], 'lmfdb_label': '63.a3', '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': [[-45, 45, 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.a3'}
• ec_torsion_growth •

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

  
  
  • id: 2162
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [2, 2]}
  • id: 2164
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '63.a3', 'torsion': [8]}
  • id: 2163
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [4]}
  • id: 2166
    {'degree': 4, 'field': [7, 0, -5, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [16]}
  • id: 2165
    {'degree': 4, 'field': [49, 0, 7, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [2, 8]}
  • id: 2167
    {'degree': 8, 'field': [-111, 84, 172, 56, 13, -28, -10, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [2, 4]}
  • id: 2170
    {'degree': 8, 'field': [-3, -7, -5, 3, 4, 2, -3, -1, 1], 'lmfdb_label': '63.a3', 'torsion': [6]}
  • id: 2168
    {'degree': 8, 'field': [49, 0, 0, 0, 98, 0, 0, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [8]}
  • id: 2169
    {'degree': 8, 'field': [81, -54, 36, 36, -21, 12, 4, -2, 1], 'lmfdb_label': '63.a3', 'torsion': [2, 16]}
  • id: 2176
    {'degree': 16, 'field': [9, 0, -3, 0, -17, 0, -6, 0, 39, 0, -2, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [24]}
  • id: 2173
    {'degree': 16, 'field': [2401, 0, -6860, 0, 9751, 0, -8036, 0, 3955, 0, -1148, 0, 199, 0, -20, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [32]}
  • id: 2172
    {'degree': 16, 'field': [2401, 0, 0, 0, -1715, 0, 0, 0, 1176, 0, 0, 0, -35, 0, 0, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [2, 16]}
  • id: 2171
    {'degree': 16, 'field': [3249, 0, 9012, 0, 7864, 0, 2084, 0, -114, 0, -212, 0, 24, 0, -4, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [4, 8]}
  • id: 2174
    {'degree': 16, 'field': [21609, 0, -44590, 0, 46501, 0, -28371, 0, 10388, 0, -2345, 0, 336, 0, -28, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [2, 6]}
  • id: 2175
    {'degree': 16, 'field': [21609, 0, 116277, 0, 61936, 0, 25725, 0, 7203, 0, 1120, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '63.a3', 'torsion': [12]}
• 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: 321
    {'conductor': 63, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '63.a3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 322
    {'conductor': 63, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '63.a3', '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: 1666040
    {'adelic_gens': [[5, 4, 332, 333], [1, 16, 0, 1], [15, 2, 238, 323], [321, 16, 320, 17], [1, 16, 92, 213], [218, 263, 43, 54], [223, 320, 104, 207], [1, 0, 16, 1], [248, 1, 223, 10]], 'adelic_image': '336.192.1.?', 'conductor': 63, 'lmfdb_label': '63.a3', 'prime': 0}
  • id: 190
    {'conductor': 63, 'elladic_image': '16.48.0.98', 'lmfdb_label': '63.a3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 63.a does not appear in ec_padic