Elliptic curve data - 28224.es2

Formats: - HTML - YAML - JSON - 2023-12-01T17:34:01.591874

• 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': '28224fw', 'Clabel': '28224fw4', 'Cnumber': 4, 'absD': 485836746572169216, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 168, 'ainvs': [0, 0, 0, -1383564, 625494800], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 28224, 'degree': 393216, 'elladic_images': ['8.48.0.76'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2896137828125965784257969663', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 122, 'isogeny_degrees': [1, 2, 4], 'jinv': [13027640977, 21609], 'lmfdb_iso': '28224.es', 'lmfdb_label': '28224.es2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -49, -136], 'min_quad_twist_disc': -168, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.e.1.13', '12.24.0.c.1', '24.96.0-24.j.2.12', '56.96.0-56.u.1.9', '168.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020607', '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, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 2, 0, -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': 28224, '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': '28224.es', 'trace_hash': 1210649544045141312}
• 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': '0.010262820590918178340906634132', 'prec': 107}, 'conductor': 28224, 'gens': [], 'heights': [], 'lmfdb_label': '28224.es2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29487212491333079155708746451', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1794884996533231662283498580268883419', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[658, 0, 1], [700, 0, 1]], 'xcoord_integral_points': [-1358, 658, 700]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '28224.es2'}
• ec_torsion_growth •

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

  
  
  • id: 1415168
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 4]}
  • id: 1415171
    {'degree': 4, 'field': [22, -16, 17, -2, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 8]}
  • id: 1415169
    {'degree': 4, 'field': [49, 0, 28, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 4]}
  • id: 1415170
    {'degree': 4, 'field': [196, 0, 14, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 4]}
  • id: 1415175
    {'degree': 8, 'field': [-2352, 0, 1680, 0, 252, 0, 28, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 6]}
  • id: 1415173
    {'degree': 8, 'field': [9, 0, -120, 0, 79, 0, -16, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 8]}
  • id: 1415172
    {'degree': 8, 'field': [2401, 0, 0, 0, -49, 0, 0, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [4, 4]}
  • id: 1415174
    {'degree': 8, 'field': [2401, 0, 1372, 0, 147, 0, -14, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 8]}
  • id: 1415177
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [4, 8]}
  • id: 1415176
    {'degree': 16, 'field': [2241, 2808, -3654, -5796, 3642, 4812, -978, -2256, 319, 528, -142, -24, 36, -12, -4, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 8]}
  • id: 1415178
    {'degree': 16, 'field': [133921, -1090268, 2836206, -1439824, 1486194, -403368, 335254, -61048, 53319, -7844, 6022, -672, 504, -68, 36, -4, 1], 'lmfdb_label': '28224.es2', 'torsion': [4, 8]}
  • id: 1415179
    {'degree': 16, 'field': [1679616, 0, 279936, 0, 285768, 0, 204120, 0, 65457, 0, 10584, 0, 1008, 0, 48, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 16]}
  • id: 1415180
    {'degree': 16, 'field': [4108729, 0, -15984310, 0, -4546127, 0, -497152, 0, 41806, 0, 13190, 0, 1024, 0, 56, 0, 1], 'lmfdb_label': '28224.es2', 'torsion': [2, 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: 654287
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '28224.es2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654288
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '28224.es2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654289
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '28224.es2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1852493
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [79, 124, 104, 75], [161, 8, 160, 9], [161, 120, 6, 47], [5, 4, 164, 165], [95, 160, 44, 135], [49, 166, 18, 5]], 'adelic_image': '168.192.1.?', 'conductor': 28224, 'lmfdb_label': '28224.es2', 'prime': 0}
  • id: 127600
    {'conductor': 28224, 'elladic_image': '8.48.0.76', 'lmfdb_label': '28224.es2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 28224.es does not appear in ec_padic