Elliptic curve data - 228888.j2

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• 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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '228888bk', 'Clabel': '228888bk2', 'Cnumber': 2, 'abc_quality': 0.8581857641551086, 'absD': 11341662808101931008, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4488, 'ainvs': [0, 0, 0, -375411, 184640366], 'analytic_rank': 2, 'bad_primes': [2, 3, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 228888, 'degree': 4128768, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3458836048555192944515643039', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [-162365474, 314721], 'lmfdb_iso': '228888.j', 'lmfdb_label': '228888.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -144, -1440], 'min_quad_twist_disc': -51, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '2244.6.0.?', '4488.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '5.8388994649648775365194720071', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2601], [3, 8, 25432], [11, 12, 20808], [17, 162, 792]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.25541412701992679166995506817', 'prec': 107}, 'szpiro_ratio': 4.180458343409191, '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, 0, 0, 0, -2, 0, -4, 0, 0, 0, -1, 0, -4, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, -2, -4, -1, -4, 0, 0, 0, -8, -2, 8, -10, 0, -2, 4, 0, -6, -4, 12, 6, -4, 4, 6, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 228888, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '228888.j', 'trace_hash': 1930284465377112815}
• 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': '0.0091704656919595060270137347212', 'prec': 110}, 'conductor': 228888, 'gens': [[-170, 15606, 1], [374, 9826, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3758331941225774983923290196', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.4639095410080963167088839341', 'prec': 100}], 'lmfdb_label': '228888.j2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.20216979118757447498640864076', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.4435926847775169243035659219198586083', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-782, 0, 1]], 'xcoord_integral_points': [-782, -254, -170, 374, 1330]}
• lmfdb_label 228888.j2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9931928
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '228888.j2', 'torsion': [2, 2]}
  • id: 9931929
    {'degree': 4, 'field': [-50, 0, 19, 0, 1], 'lmfdb_label': '228888.j2', 'torsion': [4]}
  • id: 9931932
    {'degree': 8, 'field': [-632043, 0, 413304, 0, 2754, 0, 0, 0, 1], 'lmfdb_label': '228888.j2', 'torsion': [6]}
  • id: 9931930
    {'degree': 8, 'field': [7056, 0, 624, 0, 361, 0, 46, 0, 1], 'lmfdb_label': '228888.j2', 'torsion': [2, 4]}
  • id: 9931931
    {'degree': 8, 'field': [10404, 0, 4896, 0, 2566, 0, -8, 0, 1], 'lmfdb_label': '228888.j2', 'torsion': [2, 4]}
  • id: 9931933
    {'degree': 16, 'field': [14400, 0, -896832, 0, -1705308, 0, 2248344, 0, -789650, 0, 58244, 0, -693, 0, -46, 0, 1], 'lmfdb_label': '228888.j2', 'torsion': [8]}
  • id: 9931934
    {'degree': 16, 'field': [182223001, 0, 6932120344, 0, 2578246564, 0, -68728988, 0, 1060798, 0, -104696, 0, 1384, 0, 4, 0, 1], 'lmfdb_label': '228888.j2', '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: 5676446
    {'conductor': 228888, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '228888.j2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5676447
    {'conductor': 228888, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '228888.j2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5676448
    {'conductor': 228888, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '228888.j2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5676449
    {'conductor': 228888, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '228888.j2', 'prime': 17, '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: 3123539
    {'adelic_gens': [[409, 4, 818, 9], [1057, 4, 2114, 9], [1, 2, 2, 5], [4485, 4, 4484, 5], [1, 4, 0, 1], [2993, 4, 1498, 9], [1, 0, 4, 1], [1684, 2809, 561, 3928], [2, 1, 2243, 0], [3, 4, 8, 11]], 'adelic_image': '4488.12.0.?', 'conductor': 228888, 'lmfdb_label': '228888.j2', 'prime': 0}
  • id: 835469
    {'conductor': 228888, 'elladic_image': '8.6.0.5', 'lmfdb_label': '228888.j2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 228888.j does not appear in ec_padic