Elliptic curve data - 188760.cb4

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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': '188760u', 'Clabel': '188760u4', 'Cnumber': 4, 'abc_quality': 1.0213953201021033, 'absD': 27636351600000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3432, 'ainvs': [0, 1, 0, 75464, -528640], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 188760, 'degree': 1966080, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8442678616112127657125924971', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 53, 'isogeny_degrees': [1, 2, 4], 'jinv': [26198797244, 15234375], 'lmfdb_iso': '188760.cb', 'lmfdb_label': '188760.cb4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 624, 624], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '78.6.0.?', '88.12.0.?', '104.12.0.?', '132.12.0.?', '156.12.0.?', '264.24.0.?', '312.24.0.?', '572.12.0.?', '1144.24.0.?', '1716.24.0.?', '3432.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 4719], [3, 4, 62920], [5, 6, 37752], [11, 62, 1560], [13, 14, 14520]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.067697574745406402500593940235', 'prec': 107}, 'szpiro_ratio': 3.729581728699229, '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, -1, 0, 4, 0, 1, 0, 0, 0, -1, 0, -1, 0, 6, 0, 0, 0], 'aplist': [0, 1, -1, 4, 0, -1, 6, 0, -8, -6, -4, -2, 10, 4, -8, -2, 12, 2, -16, -8, 6, 16, -4, -2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 188760, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '188760.cb', 'trace_hash': 2050059263539266262}
• 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': '0.025008594749343573242224118647', 'prec': 107}, 'conductor': 188760, 'gens': [], 'heights': [], 'lmfdb_label': '188760.cb4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22160979664617368115995844868', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5457567463387788985593351788725385586', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[7, 0, 1]], 'xcoord_integral_points': [7]}
• lmfdb_label 188760.cb4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8318383
    {'degree': 2, 'field': [-143, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [4]}
  • id: 8318382
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '188760.cb4', 'torsion': [2, 2]}
  • id: 8318384
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [4]}
  • id: 8318385
    {'degree': 4, 'field': [562, -86, 87, -2, 1], 'lmfdb_label': '188760.cb4', 'torsion': [2, 4]}
  • id: 8318389
    {'degree': 8, 'field': [-3557763, 0, 910404, 0, -6534, 0, 0, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [6]}
  • id: 8318388
    {'degree': 8, 'field': [1, 0, 146, 0, 51, 0, 14, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [8]}
  • id: 8318387
    {'degree': 8, 'field': [103041, 0, -26384, 0, 1662, 0, -96, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [8]}
  • id: 8318386
    {'degree': 8, 'field': [389376, 0, 0, 0, 6396, 0, 0, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [2, 4]}
  • id: 8318391
    {'degree': 16, 'field': [43261, -94822, 219066, -289250, 264036, -195888, 164212, -108986, 61413, -29176, 12796, -4530, 1392, -322, 66, -8, 1], 'lmfdb_label': '188760.cb4', 'torsion': [2, 8]}
  • id: 8318392
    {'degree': 16, 'field': [417752721, 0, 609620580, 0, 332336340, 0, 46183980, 0, 515686, 0, -190340, 0, 7860, 0, -140, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [2, 8]}
  • id: 8318390
    {'degree': 16, 'field': [517016644, 0, 475829960, 0, -59024288, 0, 8953988, 0, 2659909, 0, 6452, 0, -3170, 0, 8, 0, 1], 'lmfdb_label': '188760.cb4', 'torsion': [4, 4]}
  • id: 8318394
    {'degree': 16, 'field': [2397258548073, -442883129184, -395179356024, 68107077852, 113658228060, -19668305868, -3630092108, 81691492, -140551390, -16604392, 1176964, 533532, 48028, -2780, -280, -4, 1], 'lmfdb_label': '188760.cb4', 'torsion': [12]}
  • id: 8318395
    {'degree': 16, 'field': [4704372885796, -2349298381184, 1133638387400, -328970083104, 92113576268, -18809261992, 3893992712, -534182192, 101179812, -7621088, 1830448, -55864, 24888, -436, 236, -4, 1], 'lmfdb_label': '188760.cb4', 'torsion': [12]}
  • id: 8318393
    {'degree': 16, 'field': [252482324301120, -98125504992768, 11336230245312, -1818855392064, 166738081632, 29854025568, 3717653200, -776068768, 36868788, -4112288, -197980, -102132, 7892, -32, 72, -4, 1], 'lmfdb_label': '188760.cb4', '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: 4672572
    {'conductor': 188760, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '188760.cb4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4672573
    {'conductor': 188760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '188760.cb4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4672574
    {'conductor': 188760, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '188760.cb4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4672575
    {'conductor': 188760, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '188760.cb4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4672576
    {'conductor': 188760, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '188760.cb4', '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: 2876553
    {'adelic_gens': [[7, 6, 3426, 3427], [3425, 8, 3424, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1915, 352, 2090, 45], [892, 2497, 1463, 2190], [1915, 1914, 2002, 595], [2608, 627, 1045, 2498], [2495, 0, 0, 3431]], 'adelic_image': '3432.48.0.?', 'conductor': 188760, 'lmfdb_label': '188760.cb4', 'prime': 0}
  • id: 704776
    {'conductor': 188760, 'elladic_image': '4.6.0.1', 'lmfdb_label': '188760.cb4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 188760.cb does not appear in ec_padic