Elliptic curve data - 39216.bk2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '39216y', 'Clabel': '39216y2', 'Cnumber': 2, 'abc_quality': 1.064464531124395, 'absD': 1641840389853806592, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 6536, 'ainvs': [0, 1, 0, 294904, -884748], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 43], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 39216, 'degree': 995328, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1846615442093435568846711122', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 36, 'isogeny_degrees': [1, 2], 'jinv': [692475290649117431, 400839938929152], 'lmfdb_iso': '39216.bk', 'lmfdb_label': '39216.bk2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 18432, 23040], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '3268.6.0.?', '6536.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1], [3, 4, 688], [19, 20, 2064], [43, 44, 912]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4915143636493982474674389907', 'prec': 100}, 'szpiro_ratio': 4.670280974630989, '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, 4, 0, 2, 0, 1, 0, -4, 0, 0, 0, 4, 0, 6, 0, -1, 0], 'aplist': [0, 1, 4, 2, -4, 0, 6, -1, -8, 6, 2, -10, 2, 1, -4, 12, 0, -8, -12, 8, -6, 10, 12, -14, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 39216, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '39216.bk', 'trace_hash': 530891146575739815}
• 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': '0.012659807238375847466201603578', 'prec': 107}, 'conductor': 39216, 'gens': [], 'heights': [], 'lmfdb_label': '39216.bk2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15878701653728543146536791300', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0811845291931338068917732159713105798', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '19': [0, 0], '43': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '39216.bk2'}
• ec_torsion_growth •

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

  
  
  • id: 1932042
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '39216.bk2', 'torsion': [2, 2]}
  • id: 1932043
    {'degree': 4, 'field': [-162, 0, 13, 0, 1], 'lmfdb_label': '39216.bk2', 'torsion': [4]}
  • id: 1932046
    {'degree': 8, 'field': [-48, 0, 65, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '39216.bk2', 'torsion': [6]}
  • id: 1932044
    {'degree': 8, 'field': [10008, -6624, 8208, -720, 1276, -96, 28, 0, 1], 'lmfdb_label': '39216.bk2', 'torsion': [2, 4]}
  • id: 1932045
    {'degree': 8, 'field': [33856, 0, 280, 0, -79, 0, 34, 0, 1], 'lmfdb_label': '39216.bk2', 'torsion': [2, 4]}
  • id: 1932048
    {'degree': 16, 'field': [66564, 0, 66564, 0, 16641, 0, 12128, 0, 1484, 0, 770, 0, 64, 0, 16, 0, 1], 'lmfdb_label': '39216.bk2', 'torsion': [2, 6]}
  • id: 1932047
    {'degree': 16, 'field': [238229895744, 0, -705992438160, 0, 289296720225, 0, -2185739097, 0, -268768319, 0, 704212, 0, 69377, 0, 439, 0, 1], 'lmfdb_label': '39216.bk2', '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: 926347
    {'conductor': 39216, 'conductor_valuation': 4, 'discriminant_valuation': 21, 'j_denominator_valuation': 9, 'kodaira_symbol': -17, 'lmfdb_label': '39216.bk2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 926348
    {'conductor': 39216, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '39216.bk2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 926349
    {'conductor': 39216, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '39216.bk2', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 926350
    {'conductor': 39216, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '39216.bk2', 'prime': 43, 'reduction_type': 1, '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: 1925602
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [4561, 4, 2586, 9], [1, 4, 0, 1], [6533, 4, 6532, 5], [2, 1, 3267, 0], [2452, 4089, 817, 5720], [3441, 4, 346, 9]], 'adelic_image': '6536.12.0.?', 'conductor': 39216, 'lmfdb_label': '39216.bk2', 'prime': 0}
  • id: 172254
    {'conductor': 39216, 'elladic_image': '8.6.0.5', 'lmfdb_label': '39216.bk2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 39216.bk does not appear in ec_padic