Elliptic curve data - 159936.bn4

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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': '159936df', 'Clabel': '159936df3', 'Cnumber': 3, 'abc_quality': 1.0143831157402887, 'absD': 416366962425699812868096, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, -1, 0, 8627071, 29470659009], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 159936, 'degree': 14155776, 'elladic_images': ['8.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2140955821751865289865096643', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 39, 'isogeny_degrees': [1, 2, 4], 'jinv': [18419405270942584, 108003564029403], 'lmfdb_iso': '159936.bn', 'lmfdb_label': '159936.bn4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 44016, -10755756], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.2', '24.24.0-24.v.1.5', '56.24.0-56.ba.1.9', '84.12.0.?', '168.48.0.?'], '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, 147], [3, 4, 53312], [7, 32, 3264], [17, 18, 9408]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3747065319475982396622931408', 'prec': 100}, 'szpiro_ratio': 5.152223090973486, '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, 0, 0, 1, 0, 4, 0, 2, 0, 2, 0, 1, 0, -4, 0], 'aplist': [0, -1, -2, 0, 4, 2, 1, -4, 4, 2, -8, 2, 2, -8, 0, -6, 4, 2, 8, 4, 6, 0, -4, -6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 159936, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '159936.bn', 'trace_hash': 57568677151548123}
• 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': '0.0016153701325085727985056942014', 'prec': 110}, 'conductor': 159936, 'gens': [], 'heights': [], 'lmfdb_label': '159936.bn4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.068306695033321193822493943887', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0929071205331391011599031021931584629', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-2193, 0, 1]], 'xcoord_integral_points': [-2193]}
• lmfdb_label 159936.bn4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7153856
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '159936.bn4', 'torsion': [4]}
  • id: 7153855
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [2, 2]}
  • id: 7153857
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [4]}
  • id: 7153858
    {'degree': 4, 'field': [4, 0, 10, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [2, 4]}
  • id: 7153862
    {'degree': 8, 'field': [-28812, 0, 13720, 0, -588, 0, 0, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [6]}
  • id: 7153860
    {'degree': 8, 'field': [484, 0, -992, 0, 108, 0, 16, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [8]}
  • id: 7153861
    {'degree': 8, 'field': [161618, 79952, 28028, 5656, -66, -128, -32, -4, 1], 'lmfdb_label': '159936.bn4', 'torsion': [8]}
  • id: 7153859
    {'degree': 8, 'field': [47872897, -5623056, 499192, -8160, 13938, -816, -8, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [2, 4]}
  • id: 7153867
    {'degree': 16, 'field': [144, 0, -2400, 0, 4912, 0, -2400, 0, -6180, 0, 4400, 0, -276, 0, 0, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [12]}
  • id: 7153868
    {'degree': 16, 'field': [3753, 21708, 44564, 35028, 21678, 49328, 29400, -10516, 27316, -11780, 7164, -2204, 806, -160, 44, -4, 1], 'lmfdb_label': '159936.bn4', 'torsion': [12]}
  • id: 7153864
    {'degree': 16, 'field': [20736, 0, -82944, 0, 119232, 0, -77760, 0, 28548, 0, -6120, 0, 702, 0, -36, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [2, 8]}
  • id: 7153866
    {'degree': 16, 'field': [848313, -628560, -444636, 41040, 1079334, -1148724, 755376, -335592, 92404, -13408, -1892, 1592, -282, -20, 28, -8, 1], 'lmfdb_label': '159936.bn4', 'torsion': [2, 6]}
  • id: 7153865
    {'degree': 16, 'field': [38574925713, -4846744404, 4828834008, 65522580, -107069696, 89254536, -29692572, -449740, 610889, -330880, 63800, 2492, -1386, 420, -40, -8, 1], 'lmfdb_label': '159936.bn4', 'torsion': [2, 8]}
  • id: 7153863
    {'degree': 16, 'field': [9282009196321, 2147953614336, 248529420288, -4841962032, -21187971374, -3698606088, -287316864, -5661408, 18516183, 2139144, 83232, 4896, -6890, -408, 0, 0, 1], 'lmfdb_label': '159936.bn4', 'torsion': [4, 4]}
• 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: 3955904
    {'conductor': 159936, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '159936.bn4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3955905
    {'conductor': 159936, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '159936.bn4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3955906
    {'conductor': 159936, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '159936.bn4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3955907
    {'conductor': 159936, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '159936.bn4', 'prime': 17, '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: 2698262
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [64, 3, 61, 2], [7, 6, 162, 163], [161, 8, 160, 9], [113, 108, 110, 23], [95, 160, 44, 135], [1, 4, 4, 17], [104, 13, 143, 114]], 'adelic_image': '168.48.0.?', 'conductor': 159936, 'lmfdb_label': '159936.bn4', 'prime': 0}
  • id: 609144
    {'conductor': 159936, 'elladic_image': '8.12.0.12', 'lmfdb_label': '159936.bn4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 159936.bn does not appear in ec_padic