Elliptic curve data - 227136.fx2

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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': '227136r', 'Clabel': '227136r2', 'Cnumber': 2, 'abc_quality': 0.9475546814672546, 'absD': 122216637623816945664, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2184, 'ainvs': [0, 1, 0, -1476609, -441018369], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 227136, 'degree': 6193152, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5562651921024696264651348987', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 153, 'isogeny_degrees': [1, 2], 'jinv': [281397674377, 96589584], 'lmfdb_iso': '227136.fx', 'lmfdb_label': '227136.fx2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -137, 380], 'min_quad_twist_disc': -104, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0.b.1', '56.12.0-2.a.1.1', '104.12.0.?', '168.24.0.?', '312.24.0.?', '364.12.0.?', '728.24.0.?', '1092.24.0.?', '2184.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.0199220115010950117383949046', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 169], [3, 4, 75712], [7, 8, 32448], [13, 98, 1344]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.23406974253178329431254299573', 'prec': 103}, 'szpiro_ratio': 4.39698713939514, '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, 1, 0, -2, 0, -1, 0, 1, 0, 4, 0, 0, 0, -2, 0, -2, 0, 4, 0], 'aplist': [0, 1, -2, -1, 4, 0, -2, 4, 4, 2, 0, -2, -2, 4, -12, -6, 0, 10, -4, -8, 6, -8, -8, 6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 227136, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '227136.fx', 'trace_hash': 933273609455516343}
• 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': '0.0060208286224705460387946692679', 'prec': 110}, 'conductor': 227136, 'gens': [[12354, 1366365, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.0199220115010950117383949046', 'prec': 100}], 'lmfdb_label': '227136.fx2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14078223259454465641312322361', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4805899387554596049422845097987292566', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-321, 0, 1], [1343, 0, 1]], 'xcoord_integral_points': [-1023, -321, 1343, 12354]}
• lmfdb_label 227136.fx2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9860435
    {'degree': 4, 'field': [9, 0, -20, 0, 1], 'lmfdb_label': '227136.fx2', 'torsion': [2, 4]}
  • id: 9860434
    {'degree': 4, 'field': [256, 0, 46, 0, 1], 'lmfdb_label': '227136.fx2', 'torsion': [2, 4]}
  • id: 9860433
    {'degree': 4, 'field': [676, 0, -26, 0, 1], 'lmfdb_label': '227136.fx2', 'torsion': [2, 4]}
  • id: 9860436
    {'degree': 8, 'field': [-73008, 0, 3744, 0, -936, 0, 0, 0, 1], 'lmfdb_label': '227136.fx2', 'torsion': [2, 6]}
  • id: 9860438
    {'degree': 16, 'field': [144, 0, -1440, 0, 52584, 0, -43584, 0, 10321, 0, -94, 0, -153, 0, 8, 0, 1], 'lmfdb_label': '227136.fx2', 'torsion': [2, 8]}
  • id: 9860437
    {'degree': 16, 'field': [390625, 0, 0, 0, 25625, 0, 0, 0, 1056, 0, 0, 0, 41, 0, 0, 0, 1], 'lmfdb_label': '227136.fx2', 'torsion': [4, 4]}
  • id: 9860440
    {'degree': 16, 'field': [9291233, 29650096, -20656048, -25981368, 16051476, 3235568, -2372384, -501816, 333594, 58080, -51904, 8312, 84, -96, 16, -8, 1], 'lmfdb_label': '227136.fx2', 'torsion': [2, 8]}
  • id: 9860439
    {'degree': 16, 'field': [9413664, -42518736, 350402286, 239263908, 24232003, 12873916, 9829886, 768420, -108554, 181568, 71956, -20224, 7558, -936, 164, -8, 1], 'lmfdb_label': '227136.fx2', '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: 5631782
    {'conductor': 227136, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '227136.fx2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5631783
    {'conductor': 227136, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '227136.fx2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 5631784
    {'conductor': 227136, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '227136.fx2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5631785
    {'conductor': 227136, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '227136.fx2', 'prime': 13, '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: 3112708
    {'adelic_gens': [[1, 0, 4, 1], [471, 2, 778, 1091], [1, 4, 0, 1], [1593, 2182, 1850, 1093], [1819, 2180, 1454, 2175], [1091, 0, 0, 2183], [2181, 4, 2180, 5], [547, 2, 0, 1], [1095, 2180, 1096, 2179]], 'adelic_image': '2184.48.0.?', 'conductor': 227136, 'lmfdb_label': '227136.fx2', 'prime': 0}
  • id: 829816
    {'conductor': 227136, 'elladic_image': '2.6.0.1', 'lmfdb_label': '227136.fx2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 227136.fx does not appear in ec_padic