Elliptic curve data - 27456.bn1

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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': '27456co', 'Clabel': '27456co2', 'Cnumber': 2, 'abc_quality': 1.0688232684606453, 'absD': 16034122602381312, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 3432, 'ainvs': [0, 1, 0, -471809, 124431615], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 27456, 'degree': 387072, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0138103149872042175370647925', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2], 'jinv': [44308125149913793, 61165323648], 'lmfdb_iso': '27456.bn', 'lmfdb_label': '27456.bn1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -7372, -243952], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '88.6.0.?', '156.6.0.?', '3432.12.0.?'], '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': '0.90821847218213274009868268451', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 11], [3, 4, 704], [11, 12, 2496], [13, 14, 2112]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.97408954414728625341121661031', 'prec': 103}, 'szpiro_ratio': 4.9711255893456014, '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, -2, 0, -4, 0, 1, 0, 1, 0, 1, 0, -2, 0, -8, 0, -6, 0], 'aplist': [0, 1, -2, -4, 1, 1, -8, -6, 6, 2, 2, -4, 2, 4, -4, 8, 12, 2, 12, 16, 0, 8, 4, 10, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 27456, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '27456.bn', 'trace_hash': 1440493020831453994}
• 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': '0.017816672015316039138672815252', 'prec': 107}, 'conductor': 27456, 'gens': [[1087, 29952, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.90821847218213274009868268451', 'prec': 103}], 'lmfdb_label': '27456.bn1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.39119441959443302004207217381', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2634799770827855446520486670808733292', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[385, 0, 1]], 'xcoord_integral_points': [34, 385, 1087]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [2, 0], '13': [2, 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': '27456.bn1'}
• ec_torsion_growth •

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

  
  
  • id: 1375942
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '27456.bn1', 'torsion': [2, 2]}
  • id: 1375943
    {'degree': 4, 'field': [198, 0, -21, 0, 1], 'lmfdb_label': '27456.bn1', 'torsion': [4]}
  • id: 1375946
    {'degree': 8, 'field': [-12, 0, -1390, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '27456.bn1', 'torsion': [6]}
  • id: 1375944
    {'degree': 8, 'field': [4251, -780, 518, 560, -369, 104, -30, -4, 1], 'lmfdb_label': '27456.bn1', 'torsion': [2, 4]}
  • id: 1375945
    {'degree': 8, 'field': [55038, -65076, 33262, -8448, 1095, -44, -6, 0, 1], 'lmfdb_label': '27456.bn1', 'torsion': [2, 4]}
  • id: 1375948
    {'degree': 16, 'field': [795664, 0, -752624, 0, 241300, 0, -44480, 0, 3796, 0, -524, 0, 136, 0, -26, 0, 1], 'lmfdb_label': '27456.bn1', 'torsion': [2, 6]}
  • id: 1375947
    {'degree': 16, 'field': [21083040000, 0, -309729024, 0, -189422112, 0, -168432, 0, -454223, 0, 15092, 0, 5340, 0, 20, 0, 1], 'lmfdb_label': '27456.bn1', '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: 634256
    {'conductor': 27456, 'conductor_valuation': 6, 'discriminant_valuation': 25, 'j_denominator_valuation': 7, 'kodaira_symbol': -19, 'lmfdb_label': '27456.bn1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 634257
    {'conductor': 27456, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '27456.bn1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 634258
    {'conductor': 27456, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27456.bn1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 634259
    {'conductor': 27456, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '27456.bn1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

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

  
  
  • id: 1847111
    {'adelic_gens': [[1, 2, 2, 5], [2, 1, 1715, 0], [1874, 1, 2495, 0], [1, 4, 0, 1], [2641, 4, 1850, 9], [1145, 4, 2290, 9], [1, 0, 4, 1], [3429, 4, 3428, 5], [3, 4, 8, 11], [3004, 433, 2145, 1288]], 'adelic_image': '3432.12.0.?', 'conductor': 27456, 'lmfdb_label': '27456.bn1', 'prime': 0}
  • id: 124252
    {'conductor': 27456, 'elladic_image': '2.3.0.1', 'lmfdb_label': '27456.bn1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1315690
    {'lmfdb_iso': '27456.bn', 'p': 5, 'prec': 20, 'unit': 6743484605556, 'val': 1}
  • id: 1315691
    {'lmfdb_iso': '27456.bn', 'p': 7, 'prec': 20, 'unit': 733834458499746, 'val': 1}
  • id: 1315697
    {'lmfdb_iso': '27456.bn', 'p': 17, 'prec': 20, 'unit': 36936452005229803372409, 'val': 1}
  • id: 1315687
    {'lmfdb_iso': '27456.bn', 'p': 19, 'prec': 20, 'unit': 160766609049510555297217, 'val': 1}
  • id: 1315701
    {'lmfdb_iso': '27456.bn', 'p': 23, 'prec': 20, 'unit': 50641932823129175882337451, 'val': 1}
  • id: 1315695
    {'lmfdb_iso': '27456.bn', 'p': 29, 'prec': 20, 'unit': 550011526018454711477599331, 'val': 1}
  • id: 1315692
    {'lmfdb_iso': '27456.bn', 'p': 31, 'prec': 20, 'unit': 6483956628850346488715180382, 'val': 1}
  • id: 1315706
    {'lmfdb_iso': '27456.bn', 'p': 37, 'prec': 20, 'unit': 379354676259600531711448857768, 'val': 1}
  • id: 1315693
    {'lmfdb_iso': '27456.bn', 'p': 41, 'prec': 20, 'unit': 4219280924888370604413766590037, 'val': 1}
  • id: 1315694
    {'lmfdb_iso': '27456.bn', 'p': 43, 'prec': 20, 'unit': 8083277311539094429983176387258, 'val': 1}
  • id: 1315704
    {'lmfdb_iso': '27456.bn', 'p': 47, 'prec': 20, 'unit': 118862533720414517864321810441, 'val': 1}
  • id: 1315699
    {'lmfdb_iso': '27456.bn', 'p': 53, 'prec': 20, 'unit': 51407841946547051257692838860997, 'val': 1}
  • id: 1315700
    {'lmfdb_iso': '27456.bn', 'p': 59, 'prec': 20, 'unit': 3862345109186934172800331154142947, 'val': 1}
  • id: 1315705
    {'lmfdb_iso': '27456.bn', 'p': 61, 'prec': 20, 'unit': 131037593535949435507752830244156, 'val': 1}
  • id: 1315689
    {'lmfdb_iso': '27456.bn', 'p': 67, 'prec': 20, 'unit': 40483829805440044379170295602731399, 'val': 1}
  • id: 1315703
    {'lmfdb_iso': '27456.bn', 'p': 71, 'prec': 20, 'unit': 73808651607952426582458342828642250, 'val': 1}
  • id: 1315696
    {'lmfdb_iso': '27456.bn', 'p': 79, 'prec': 20, 'unit': 255636313048479389343077704927447188, 'val': 1}
  • id: 1315698
    {'lmfdb_iso': '27456.bn', 'p': 83, 'prec': 20, 'unit': 2519461559501547248846037474573764841, 'val': 1}
  • id: 1315702
    {'lmfdb_iso': '27456.bn', 'p': 89, 'prec': 20, 'unit': 8928053904972113286488255422326583531, 'val': 1}
  • id: 1315688
    {'lmfdb_iso': '27456.bn', 'p': 97, 'prec': 20, 'unit': 1517428399855193894505689405053286854, 'val': 1}