Elliptic curve data - 3192.b4

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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': '3192c', 'Clabel': '3192c1', 'Cnumber': 1, 'abc_quality': 1.0129345940863133, 'absD': 4488567692112, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1064, 'ainvs': [0, -1, 0, -4359, -41940], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3192, 'degree': 6144, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1210068920925358955358551106', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [572616640141312, 280535480757], 'lmfdb_iso': '3192.b', 'lmfdb_label': '3192.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4359, -41940], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '28.12.0-4.c.1.2', '56.24.0-56.ba.1.2', '76.12.0.?', '152.24.0.?', '266.6.0.?', '532.24.0.?', '1064.48.0.?'], '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, 133], [3, 4, 152], [7, 8, 456], [19, 20, 168]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.88995783190588745906344440345', 'prec': 103}, 'szpiro_ratio': 4.555278966582307, '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, -1, 0, 1, 0, -4, 0, 2, 0, 2, 0, -6, 0, 1, 0], 'aplist': [0, -1, -2, -1, -4, 2, -6, 1, 0, -10, 8, -2, 6, 4, -8, 6, -4, -10, 8, 12, -14, -4, -4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 3192, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '3192.b', 'trace_hash': 2278949429915027169}
• 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': '0.10624433564395054390338240349', 'prec': 103}, 'conductor': 3192, 'gens': [], 'heights': [], 'lmfdb_label': '3192.b4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.61750109449594611849769173845', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.61750109449594611849769173845055423355', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-60, 0, 1]], 'xcoord_integral_points': [-60]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': [0, 0], '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '3192.b4'}
• ec_torsion_growth •

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

  
  
  • id: 166409
    {'degree': 2, 'field': [-33, -1, 1], 'lmfdb_label': '3192.b4', 'torsion': [2, 2]}
  • id: 166411
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '3192.b4', 'torsion': [4]}
  • id: 166410
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '3192.b4', 'torsion': [4]}
  • id: 166412
    {'degree': 4, 'field': [9, 0, 13, 0, 1], 'lmfdb_label': '3192.b4', 'torsion': [2, 4]}
  • id: 166413
    {'degree': 4, 'field': [133, 0, 19, 0, 1], 'lmfdb_label': '3192.b4', 'torsion': [8]}
  • id: 166417
    {'degree': 8, 'field': [-12, 0, -20, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '3192.b4', 'torsion': [6]}
  • id: 166414
    {'degree': 8, 'field': [81, 0, -7150, 0, -877, 0, -26, 0, 1], 'lmfdb_label': '3192.b4', 'torsion': [2, 4]}
  • id: 166415
    {'degree': 8, 'field': [1138, -1068, 1360, -614, 383, -94, 36, -4, 1], 'lmfdb_label': '3192.b4', 'torsion': [8]}
  • id: 166416
    {'degree': 8, 'field': [11473, -3794, 4540, -1538, 885, -142, 52, -4, 1], 'lmfdb_label': '3192.b4', 'torsion': [2, 8]}
  • id: 166419
    {'degree': 16, 'field': [1849, 9202, 22898, 85952, 118017, -99478, 41170, -3314, -7052, 3608, -536, 22, 81, -20, 8, -4, 1], 'lmfdb_label': '3192.b4', 'torsion': [2, 8]}
  • id: 166423
    {'degree': 16, 'field': [6164, -3344, -5156, 15680, -3772, -7392, 7864, -7504, 6521, -4864, 2988, -1432, 542, -168, 44, -8, 1], 'lmfdb_label': '3192.b4', 'torsion': [12]}
  • id: 166422
    {'degree': 16, 'field': [801113, -246608, 352840, -326752, 485918, -496920, 369784, -219352, 115643, -49168, 19056, -5800, 1634, -336, 68, -8, 1], 'lmfdb_label': '3192.b4', 'torsion': [12]}
  • id: 166418
    {'degree': 16, 'field': [2229049, 0, -1867304, 0, 603778, 0, -96936, 0, 5523, 0, -168, 0, 238, 0, 16, 0, 1], 'lmfdb_label': '3192.b4', 'torsion': [4, 4]}
  • id: 166420
    {'degree': 16, 'field': [77849032877, -72040639132, 21371946032, -853281356, -1055407826, 273771164, 34818020, -26885420, 1728990, 967828, -107192, -30724, 4682, 604, -116, -4, 1], 'lmfdb_label': '3192.b4', 'torsion': [16]}
  • id: 166421
    {'degree': 16, 'field': [1437631117689, 339912594576, -304211692936, -69235033840, 29283141518, 6172126408, -1681504136, -310266824, 62895291, 9449616, -1562352, -173912, 25042, 1792, -236, -8, 1], 'lmfdb_label': '3192.b4', 'torsion': [2, 6]}
• 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: 57627
    {'conductor': 3192, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '3192.b4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57628
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '3192.b4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57629
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '3192.b4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 57630
    {'conductor': 3192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3192.b4', 'prime': 19, '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: 1684720
    {'adelic_gens': [[460, 1, 783, 6], [624, 3, 789, 2], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1057, 8, 1056, 9], [7, 6, 1058, 1059], [673, 668, 670, 135], [403, 402, 146, 675]], 'adelic_image': '1064.48.0.?', 'conductor': 3192, 'lmfdb_label': '3192.b4', 'prime': 0}
  • id: 15991
    {'conductor': 3192, 'elladic_image': '8.12.0.6', 'lmfdb_label': '3192.b4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3192.b does not appear in ec_padic