Elliptic curve data - 192192.du2

Formats: - HTML - YAML - JSON - 2026-04-20T00:10:12.680423

• 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': '192192df', 'Clabel': '192192df1', 'Cnumber': 1, 'abc_quality': 0.8308135130066956, 'absD': 595137134592, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 8008, 'ainvs': [0, -1, 0, -2497, 61537], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 192192, 'degree': 196608, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.97076278268151317044566939587', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 98, 'isogeny_degrees': [1, 2], 'jinv': [-6570725617, 2270268], 'lmfdb_iso': '192192.du', 'lmfdb_label': '192192.du2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -39, -135], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.d.1', '286.6.0.?', '8008.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 143], [3, 4, 64064], [7, 8, 27456], [11, 12, 17472], [13, 14, 14784]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.068957988158404793680178786317', 'prec': 110}, 'szpiro_ratio': 2.9220749503545846, '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, 1, 0, -1, 0, -2, 0, 0, 0, 4, 0], 'aplist': [0, -1, 2, 1, 1, -1, 0, 4, 4, 0, -4, 8, 6, -4, 4, -6, 6, -2, 0, 2, -2, -2, 4, 16, -4], 'class_deg': 2, 'class_size': 2, 'conductor': 192192, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '192192.du', 'trace_hash': 739619623052598808}
• 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': '0.14348488714905755397923861112', 'prec': 103}, 'conductor': 192192, 'gens': [], 'heights': [], 'lmfdb_label': '192192.du2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.86464827218731917367316160953', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4585930887492766946926464381099854610', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-59, 0, 1]], 'xcoord_integral_points': [-59]}
• lmfdb_label 192192.du2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8457313
    {'degree': 2, 'field': [36, -1, 1], 'lmfdb_label': '192192.du2', 'torsion': [2, 2]}
  • id: 8457314
    {'degree': 4, 'field': [-10, 4, -3, -2, 1], 'lmfdb_label': '192192.du2', 'torsion': [4]}
  • id: 8457317
    {'degree': 8, 'field': [-13872, 0, -12830, 0, 408, 0, 0, 0, 1], 'lmfdb_label': '192192.du2', 'torsion': [6]}
  • id: 8457316
    {'degree': 8, 'field': [44108, -37676, 13917, -1178, 543, -128, 15, -2, 1], 'lmfdb_label': '192192.du2', 'torsion': [2, 4]}
  • id: 8457315
    {'degree': 8, 'field': [116964, 0, -24732, 0, 3053, 0, 18, 0, 1], 'lmfdb_label': '192192.du2', 'torsion': [2, 4]}
  • id: 8457318
    {'degree': 16, 'field': [324648324, 0, 1731457728, 0, 2012862852, 0, 763122360, 0, 59895397, 0, -573444, 0, -16090, 0, -36, 0, 1], 'lmfdb_label': '192192.du2', 'torsion': [8]}
  • id: 8457319
    {'degree': 16, 'field': [28229754196224, 0, 1065168161064, 0, -11932484508, 0, -1053596376, 0, -570540, 0, 249628, 0, -1860, 0, 0, 0, 1], 'lmfdb_label': '192192.du2', '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: 4757910
    {'conductor': 192192, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '192192.du2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4757911
    {'conductor': 192192, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '192192.du2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4757912
    {'conductor': 192192, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '192192.du2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4757913
    {'conductor': 192192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '192192.du2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4757914
    {'conductor': 192192, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '192192.du2', 'prime': 13, '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: 2897550
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [3433, 4, 6866, 9], [4005, 4, 2, 9], [1, 4, 0, 1], [730, 1, 3639, 0], [8005, 4, 8004, 5], [1850, 1, 3079, 0], [5009, 3004, 1000, 7007]], 'adelic_image': '8008.12.0.?', 'conductor': 192192, 'lmfdb_label': '192192.du2', 'prime': 0}
  • id: 715961
    {'conductor': 192192, 'elladic_image': '2.3.0.1', 'lmfdb_label': '192192.du2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 192192.du does not appear in ec_padic