Elliptic curve data - 226512.fd5

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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': '226512cq', 'Clabel': '226512cq1', 'Cnumber': 1, 'abc_quality': 0.8840474094399083, 'absD': 4963061564535140352, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6864, 'ainvs': [0, 0, 0, -418539, -149500582], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 226512, 'degree': 3932160, 'elladic_images': ['16.24.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2893494196401549390983520226', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 133, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-1532808577, 938223], 'lmfdb_iso': '226512.fd', 'lmfdb_label': '226512.fd5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -24, 63], 'min_quad_twist_disc': -132, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.2', '24.24.0-8.n.1.4', '48.48.0-48.g.1.9', '88.24.0.?', '104.24.0.?', '132.12.0.?', '156.12.0.?', '176.48.0.?', '208.48.0.?', '264.48.0.?', '286.6.0.?', '312.48.0.?', '528.96.0.?', '572.12.0.?', '624.96.0.?', '1144.48.0.?', '1716.24.0.?', '2288.96.0.?', '3432.96.0.?', '6864.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 14157], [3, 8, 25168], [11, 72, 1872], [13, 14, 17424]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15205154165303048804747450630', 'prec': 107}, 'szpiro_ratio': 4.149754385245632, '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, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 2, 0, 0, -1, -6, -4, -8, -10, 0, 6, 10, 4, 8, 10, -12, -14, 12, 0, 6, 8, -12, -2, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 226512, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '226512.fd', 'trace_hash': 283269036455684762}
• 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': '0.010268248249283949339780066959', 'prec': 107}, 'conductor': 226512, 'gens': [], 'heights': [], 'lmfdb_label': '226512.fd5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.091305709698148703437041734811', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.73044567758518962749633387848460051772', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[781, 0, 1]], 'xcoord_integral_points': [781]}
• lmfdb_label 226512.fd5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9835287
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [4]}
  • id: 9835288
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [4]}
  • id: 9835286
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '226512.fd5', 'torsion': [2, 2]}
  • id: 9835290
    {'degree': 4, 'field': [33, 0, 1, -2, 1], 'lmfdb_label': '226512.fd5', 'torsion': [8]}
  • id: 9835289
    {'degree': 4, 'field': [324, 0, -3, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [2, 4]}
  • id: 9835291
    {'degree': 4, 'field': [1329, -60, 61, -2, 1], 'lmfdb_label': '226512.fd5', 'torsion': [8]}
  • id: 9835295
    {'degree': 8, 'field': [-43923, 0, 53988, 0, 6138, 0, -143, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [6]}
  • id: 9835294
    {'degree': 8, 'field': [1764, 0, 1128, 0, 133, 0, -14, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [2, 8]}
  • id: 9835293
    {'degree': 8, 'field': [41044, 41396, -41498, 242, -215, 110, -32, -4, 1], 'lmfdb_label': '226512.fd5', 'torsion': [8]}
  • id: 9835292
    {'degree': 8, 'field': [47568, -12252, 12922, -1308, 575, 92, -26, -4, 1], 'lmfdb_label': '226512.fd5', 'torsion': [2, 4]}
  • id: 9835299
    {'degree': 16, 'field': [59049, 0, -15309, 4374, 36207, 35478, 28566, -13014, -3159, 5562, 2646, -774, -2, 110, -6, -4, 1], 'lmfdb_label': '226512.fd5', 'torsion': [2, 16]}
  • id: 9835297
    {'degree': 16, 'field': [274576, -419200, 320000, 1699568, 2895320, 984184, 383112, 423292, 127449, 96158, 48794, 3724, 855, 416, 18, -6, 1], 'lmfdb_label': '226512.fd5', 'torsion': [2, 8]}
  • id: 9835298
    {'degree': 16, 'field': [413449, 0, 633353, 0, 406540, 0, 151223, 0, 38287, 0, 6563, 0, 700, 0, 41, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [16]}
  • id: 9835296
    {'degree': 16, 'field': [14776336, 0, 0, 0, 3667304, 0, 0, 0, 193377, 0, 0, 0, 38, 0, 0, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [4, 4]}
  • id: 9835300
    {'degree': 16, 'field': [15116544, 0, -648000, 0, 107522640, 0, -4643460, 0, 1521933, 0, -161328, 0, 7290, 0, -143, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [2, 6]}
  • id: 9835302
    {'degree': 16, 'field': [864536409, 0, 209584584, 0, 12702096, 0, 48838383, 0, 3136320, 0, 28809, 0, 1089, 0, 66, 0, 1], 'lmfdb_label': '226512.fd5', 'torsion': [12]}
  • id: 9835301
    {'degree': 16, 'field': [14939928441, 0, -2042819838, 0, -207950895, 0, 1484055, 0, 548604, 0, -52626, 0, 1845, 0, -78, 0, 1], 'lmfdb_label': '226512.fd5', '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: 5615939
    {'conductor': 226512, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '226512.fd5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5615940
    {'conductor': 226512, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '226512.fd5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5615941
    {'conductor': 226512, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '226512.fd5', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5615942
    {'conductor': 226512, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '226512.fd5', 'prime': 13, '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: 3108675
    {'adelic_gens': [[1, 16, 1724, 1845], [6849, 16, 6848, 17], [1, 16, 0, 1], [15, 2, 6766, 6851], [1072, 5, 4707, 6850], [5, 4, 6860, 6861], [2287, 6848, 4568, 6735], [847, 6848, 2374, 1425], [1, 0, 16, 1], [6232, 6863, 4913, 6854]], 'adelic_image': '6864.192.1.?', 'conductor': 226512, 'lmfdb_label': '226512.fd5', 'prime': 0}
  • id: 827667
    {'conductor': 226512, 'elladic_image': '16.24.0.8', 'lmfdb_label': '226512.fd5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 226512.fd does not appear in ec_padic