Elliptic curve data - 181056.w3

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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': '181056cq', 'Clabel': '181056cq4', 'Cnumber': 4, 'abc_quality': 0.9818715313962838, 'absD': 1074611999542131818496, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 7544, 'ainvs': [0, -1, 0, -2955137, -1154736255], 'analytic_rank': 2, 'bad_primes': [2, 3, 23, 41], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 181056, 'degree': 7667712, 'elladic_images': ['8.48.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7351284794419002822882985631', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2, 4], 'jinv': [10887214909148618977, 4099319456261184], 'lmfdb_iso': '181056.w', 'lmfdb_label': '181056.w3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -46174, -2261116], 'min_quad_twist_disc': 8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.2', '8.48.0-8.c.1.10', '184.96.0.?', '328.96.0.?', '7544.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '26.197712416266299115370053698', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 60352], [23, 24, 7872], [41, 42, 4416]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6954077086019823181624503809', 'prec': 100}, 'szpiro_ratio': 4.6512603402118025, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -6, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, -1, 2, 0, -4, -6, 2, 4, -1, -6, 0, 2, 1, -4, -8, -6, 4, -6, -12, -16, 10, 8, -12, 10, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 181056, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '181056.w', 'trace_hash': 86822818255916163}
• 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': '0.0042101501834997228193089462575', 'prec': 110}, 'conductor': 181056, 'gens': [[2627, 95940, 1], [166627, 68013260, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5910887332625096167212413733', 'prec': 100}, {'__RealLiteral__': 0, 'data': '7.6222918315965078938771170960', 'prec': 100}], 'lmfdb_label': '181056.w3', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.11883426920804740164613670792', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.452744039638381447949137225260505146', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-415, 0, 1], [1889, 0, 1]], 'xcoord_integral_points': [-1473, -415, 1889, 2627, 12385, 166627]}
• lmfdb_label 181056.w3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8009375
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 4]}
  • id: 8009374
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 4]}
  • id: 8009376
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [4, 4]}
  • id: 8009380
    {'degree': 8, 'field': [-12288, 0, 3448, 0, -384, 0, 0, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 6]}
  • id: 8009379
    {'degree': 8, 'field': [5986, 6232, -5668, -1088, 445, 116, -34, -4, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 8]}
  • id: 8009378
    {'degree': 8, 'field': [58564, 0, -1252, 0, 653, 0, 26, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 8]}
  • id: 8009377
    {'degree': 8, 'field': [222786, -12, 974, -1932, 987, -28, 14, -4, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 8]}
  • id: 8009385
    {'degree': 16, 'field': [75076, 0, -222428, 0, 247297, 0, 335568, 0, 44268, 0, 354, 0, -80, 0, 16, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 12]}
  • id: 8009384
    {'degree': 16, 'field': [75076, 0, 222428, 0, 247297, 0, -335568, 0, 44268, 0, -354, 0, -80, 0, -16, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [2, 12]}
  • id: 8009381
    {'degree': 16, 'field': [325458, 449064, -604476, 117288, 567234, -1174752, 1177752, -840312, 432883, -172040, 58960, -14744, 3610, -560, 100, -8, 1], 'lmfdb_label': '181056.w3', 'torsion': [4, 8]}
  • id: 8009383
    {'degree': 16, 'field': [430336, 0, 1939136, 0, 2269764, 0, -1916180, 0, 959737, 0, 1960, 0, 1974, 0, -4, 0, 1], 'lmfdb_label': '181056.w3', 'torsion': [4, 8]}
  • id: 8009382
    {'degree': 16, 'field': [21446434, -205528, 3619220, -3782520, -4926406, 6040912, 1304896, -2360568, 14947, 338136, -23768, -22072, 2162, 672, -76, -8, 1], 'lmfdb_label': '181056.w3', 'torsion': [4, 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: 4481809
    {'conductor': 181056, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '181056.w3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4481810
    {'conductor': 181056, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '181056.w3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4481811
    {'conductor': 181056, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '181056.w3', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4481812
    {'conductor': 181056, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '181056.w3', 'prime': 41, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2829248
    {'adelic_gens': [[5, 4, 7540, 7541], [1, 0, 8, 1], [5249, 8, 5908, 33], [7541, 5654, 5662, 5], [7, 5664, 22, 1905], [7537, 8, 7536, 9], [5705, 4, 0, 1], [1, 8, 0, 1]], 'adelic_image': '7544.192.1.?', 'conductor': 181056, 'lmfdb_label': '181056.w3', 'prime': 0}
  • id: 679102
    {'conductor': 181056, 'elladic_image': '8.48.0.7', 'lmfdb_label': '181056.w3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 181056.w does not appear in ec_padic