Elliptic curve data - 63.a5

Formats: - HTML - YAML - JSON - 2023-09-28T15:11:19.372074

• 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': '63a2', 'Cnumber': 2, 'absD': 2893401, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 168, 'ainvs': [1, -1, 0, -36, 27], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 63, 'degree': 8, 'elladic_images': ['8.48.0.66'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.069635652834950692961343648325', 'prec': 110}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [7189057, 3969], 'lmfdb_iso': '63.a', 'lmfdb_label': '63.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -4, -1], 'min_quad_twist_disc': -3, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.e.2.6', '12.24.0-4.b.1.3', '24.96.0-24.w.2.1', '28.24.0.c.1', '56.96.0-56.i.1.9', '84.48.0.?', '168.192.1.?'], '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': '-0.61894179716900553865896626679', 'prec': 107}, '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, -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': '1.1494359061828359741815430228', 'prec': 100}, 'conductor': 63, 'gens': [], 'heights': [], 'lmfdb_label': '63.a5', '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': 8, 'torsion_generators': [[-6, 3, 1], [6, -3, 1]], 'xcoord_integral_points': [-6, 6]}
• 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.a5'}
• ec_torsion_growth •

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

  
  
  • id: 2153
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '63.a5', 'torsion': [2, 8]}
  • id: 2154
    {'degree': 4, 'field': [1, 0, -5, 0, 1], 'lmfdb_label': '63.a5', 'torsion': [2, 4]}
  • id: 2155
    {'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '63.a5', 'torsion': [2, 4]}
  • id: 2158
    {'degree': 8, 'field': [-3, -7, -5, 3, 4, 2, -3, -1, 1], 'lmfdb_label': '63.a5', 'torsion': [2, 6]}
  • id: 2157
    {'degree': 8, 'field': [1, 0, 2, 0, 0, 0, -1, 0, 1], 'lmfdb_label': '63.a5', 'torsion': [2, 16]}
  • id: 2156
    {'degree': 8, 'field': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'lmfdb_label': '63.a5', 'torsion': [4, 8]}
  • id: 2159
    {'degree': 16, 'field': [9, 0, -120, 0, 457, 0, -440, 0, 80, 0, 88, 0, -31, 0, -8, 0, 1], 'lmfdb_label': '63.a5', 'torsion': [2, 8]}
  • id: 2161
    {'degree': 16, 'field': [9, 0, -3, 0, -17, 0, -6, 0, 39, 0, -2, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '63.a5', 'torsion': [2, 24]}
  • id: 2160
    {'degree': 16, 'field': [16, 0, 80, 0, 161, 0, -84, 0, 56, 0, -84, 0, 56, 0, -4, 0, 1], 'lmfdb_label': '63.a5', '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: 319
    {'conductor': 63, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '63.a5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 320
    {'conductor': 63, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '63.a5', '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: 1666042
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [7, 6, 66, 163], [161, 8, 160, 9], [5, 4, 164, 165], [55, 164, 0, 167], [5, 132, 162, 35], [89, 48, 36, 77]], 'adelic_image': '168.192.1.?', 'conductor': 63, 'lmfdb_label': '63.a5', 'prime': 0}
  • id: 192
    {'conductor': 63, 'elladic_image': '8.48.0.66', 'lmfdb_label': '63.a5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 63.a does not appear in ec_padic