Elliptic curve data - 81312.bm1

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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': '81312r', 'Clabel': '81312r2', 'Cnumber': 2, 'abc_quality': 1.0353155241318501, 'absD': 9133406652262573506405888, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 616, 'ainvs': [0, 1, 0, -197777928, -1060715168856], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 81312, 'degree': 19353600, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6053405505523143192500670303', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 38, 'isogeny_degrees': [1, 2], 'jinv': [943259332190261813000, 10069472554261659], 'lmfdb_iso': '81312.bm', 'lmfdb_label': '81312.bm1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1634528, -796336632], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '88.6.0.?', '616.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.4018462406922398980615886963', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 121], [3, 4, 3872], [7, 8, 11616], [11, 72, 672]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8865325287331700651561711502', 'prec': 100}, 'szpiro_ratio': 6.095990728713923, '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, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0, -4, 0, 6, 0], 'aplist': [0, 1, 0, -1, 0, 2, -4, 6, -4, 2, 10, -6, 12, 12, -6, -6, 0, -6, -4, -8, -8, -16, 2, 10, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 81312, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '81312.bm', 'trace_hash': 595537284960113582}
• 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': '0.00073865388611584933134800415371', 'prec': 113}, 'conductor': 81312, 'gens': [[16290, 201318, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '8.4018462406922398980615886963', 'prec': 100}], 'lmfdb_label': '81312.bm1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.040284239418158478911333381071', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.1230876523504230772868876730823607332', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-7473, 0, 1]], 'xcoord_integral_points': [-7473, 16290]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '81312.bm1'}
• ec_torsion_growth •

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

  
  
  • id: 3822871
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '81312.bm1', 'torsion': [2, 2]}
  • id: 3822872
    {'degree': 4, 'field': [8, -1, -3, -1, 1], 'lmfdb_label': '81312.bm1', 'torsion': [4]}
  • id: 3822875
    {'degree': 8, 'field': [-3267, 0, 1496, 0, -198, 0, 0, 0, 1], 'lmfdb_label': '81312.bm1', 'torsion': [6]}
  • id: 3822874
    {'degree': 8, 'field': [196, 0, 476, 0, 53, 0, -10, 0, 1], 'lmfdb_label': '81312.bm1', 'torsion': [2, 4]}
  • id: 3822873
    {'degree': 8, 'field': [6561, 0, -2916, 0, -922, 0, -36, 0, 1], 'lmfdb_label': '81312.bm1', 'torsion': [2, 4]}
  • id: 3822877
    {'degree': 16, 'field': [66474, -189720, 271068, -302928, 298596, -218896, 105656, -49720, 36788, -18292, 2048, 1348, -518, 148, -20, -8, 1], 'lmfdb_label': '81312.bm1', 'torsion': [2, 6]}
  • id: 3822876
    {'degree': 16, 'field': [687698176, 0, 352715968, 0, 67121560, 0, 5150728, 0, 18016, 0, -17300, 0, -608, 0, 10, 0, 1], 'lmfdb_label': '81312.bm1', 'torsion': [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: 1978885
    {'conductor': 81312, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81312.bm1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1978886
    {'conductor': 81312, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '81312.bm1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1978887
    {'conductor': 81312, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '81312.bm1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1978888
    {'conductor': 81312, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '81312.bm1', 'prime': 11, 'reduction_type': 0, '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: 2199981
    {'adelic_gens': [[1, 0, 4, 1], [353, 4, 90, 9], [3, 4, 8, 11], [613, 4, 612, 5], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 307, 0], [540, 81, 385, 232], [114, 1, 559, 0]], 'adelic_image': '616.12.0.?', 'conductor': 81312, 'lmfdb_label': '81312.bm1', 'prime': 0}
  • id: 333311
    {'conductor': 81312, 'elladic_image': '2.3.0.1', 'lmfdb_label': '81312.bm1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 4191978
    {'lmfdb_iso': '81312.bm', 'p': 13, 'prec': 20, 'unit': 1020159850187960826871, 'val': 1}
  • id: 4191980
    {'lmfdb_iso': '81312.bm', 'p': 17, 'prec': 20, 'unit': 140109034916301914143274, 'val': 1}
  • id: 4191981
    {'lmfdb_iso': '81312.bm', 'p': 19, 'prec': 20, 'unit': 541880808082289290825253, 'val': 1}
  • id: 4191984
    {'lmfdb_iso': '81312.bm', 'p': 23, 'prec': 20, 'unit': 39563858222254778792884229, 'val': 1}
  • id: 4191977
    {'lmfdb_iso': '81312.bm', 'p': 29, 'prec': 20, 'unit': 5733304164295574768898168263, 'val': 1}
  • id: 4191988
    {'lmfdb_iso': '81312.bm', 'p': 31, 'prec': 20, 'unit': 17668021366696078790086084971, 'val': 1}
  • id: 4191973
    {'lmfdb_iso': '81312.bm', 'p': 37, 'prec': 20, 'unit': 393917296448846619325794162182, 'val': 1}
  • id: 4191975
    {'lmfdb_iso': '81312.bm', 'p': 41, 'prec': 20, 'unit': 1983953793061660261835871340441, 'val': 1}
  • id: 4191976
    {'lmfdb_iso': '81312.bm', 'p': 43, 'prec': 20, 'unit': 5933062284713466594013197217101, 'val': 1}
  • id: 4191979
    {'lmfdb_iso': '81312.bm', 'p': 47, 'prec': 20, 'unit': 8829211849006193140775587276502, 'val': 1}
  • id: 4191982
    {'lmfdb_iso': '81312.bm', 'p': 53, 'prec': 20, 'unit': 514239620520523134827278275826473, 'val': 1}
  • id: 4191987
    {'lmfdb_iso': '81312.bm', 'p': 61, 'prec': 20, 'unit': 7794029503176785420916790268713989, 'val': 1}
  • id: 4191972
    {'lmfdb_iso': '81312.bm', 'p': 67, 'prec': 20, 'unit': 20338161123243540882087697371602653, 'val': 1}
  • id: 4191974
    {'lmfdb_iso': '81312.bm', 'p': 71, 'prec': 20, 'unit': 119258619107064099094443190968171220, 'val': 1}
  • id: 4191983
    {'lmfdb_iso': '81312.bm', 'p': 73, 'prec': 20, 'unit': 13719607633582807551542835583765317, 'val': 1}
  • id: 4191986
    {'lmfdb_iso': '81312.bm', 'p': 79, 'prec': 20, 'unit': 218843031442437039500664550975452218, 'val': 1}
  • id: 4191971
    {'lmfdb_iso': '81312.bm', 'p': 83, 'prec': 20, 'unit': 145746631549657465663582093682896607, 'val': 1}
  • id: 4191985
    {'lmfdb_iso': '81312.bm', 'p': 89, 'prec': 20, 'unit': 2920017347249582375147109347442530145, 'val': 1}
  • id: 4191970
    {'lmfdb_iso': '81312.bm', 'p': 97, 'prec': 20, 'unit': 9898002887626911176683281461829844984, 'val': 1}