Elliptic curve data - 169050.ee1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '169050gt', 'Clabel': '169050gt5', 'Cnumber': 5, 'abc_quality': 0.9812234956880324, 'absD': 168178127595525468750, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 38640, 'ainvs': [1, 0, 1, -103745276, 406715630948], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 169050, 'degree': 18874368, 'elladic_images': ['8.12.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1551038079546656266105109467', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 108, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [67176973097223766561, 91487391870], 'lmfdb_iso': '169050.ee', 'lmfdb_label': '169050.ee1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -84690, -9493338], 'min_quad_twist_disc': -35, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '48.24.0-8.n.1.3', '80.24.0.?', '112.24.0.?', '120.24.0.?', '140.12.0.?', '168.24.0.?', '184.24.0.?', '240.48.0.?', '280.24.0.?', '336.48.0.?', '560.48.0.?', '840.48.0.?', '1104.48.0.?', '1680.96.0.?', '1840.48.0.?', '2576.48.0.?', '2760.48.0.?', '3864.48.0.?', '5520.96.0.?', '6440.48.0.?', '7728.96.0.?', '12880.96.0.?', '19320.96.0.?', '38640.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3774297772099587867574549084', 'prec': 100}, 'szpiro_ratio': 5.564564700553836, '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, -1, 1, 1, 0, -1, 0, -1, 1, 0, 4, 1, -2, 0, 0, 1, 2, -1, 4, 0], 'aplist': [-1, 1, 0, 0, 4, -2, 2, 4, 1, -2, -8, -6, -2, -4, 8, 2, 4, -14, 4, 0, 2, 0, 12, 6, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 169050, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 2, 4, 2], [8, 4, 2, 1, 8, 4], [4, 2, 4, 8, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '169050.ee', 'trace_hash': 225140964451054526}
• 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': '0.0018176558257659926241496328686', 'prec': 110}, 'conductor': 169050, 'gens': [], 'heights': [], 'lmfdb_label': '169050.ee1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15369655599277103316905018560', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4591448958843365307048029695774328337', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[23543, -23547, 2]], 'xcoord_integral_points': []}
• lmfdb_label 169050.ee1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7521834
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [4]}
  • id: 7521833
    {'degree': 2, 'field': [-35, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [4]}
  • id: 7521832
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [2, 2]}
  • id: 7521835
    {'degree': 4, 'field': [9, 0, -36, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [2, 4]}
  • id: 7521837
    {'degree': 4, 'field': [9, 0, -29, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [8]}
  • id: 7521836
    {'degree': 4, 'field': [4761, 0, -828, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [8]}
  • id: 7521841
    {'degree': 8, 'field': [-45204, 110589, -111048, 917, -455, -7, 7, -4, 1], 'lmfdb_label': '169050.ee1', 'torsion': [6]}
  • id: 7521840
    {'degree': 8, 'field': [441, 8820, 22680, 17640, 3217, -420, -130, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [2, 8]}
  • id: 7521839
    {'degree': 8, 'field': [36201, 9564, -8838, -1488, 835, -112, 42, -4, 1], 'lmfdb_label': '169050.ee1', 'torsion': [8]}
  • id: 7521838
    {'degree': 8, 'field': [249847971, -1653396, 1622142, 62472, -31145, -112, 42, -4, 1], 'lmfdb_label': '169050.ee1', 'torsion': [2, 4]}
  • id: 7521843
    {'degree': 16, 'field': [8242641, -26872560, 43804800, -40402800, 12025314, 9710280, 3456000, 4320, 102951, 31320, 7200, -2880, -426, -120, 0, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [2, 8]}
  • id: 7521848
    {'degree': 16, 'field': [2482430976, 0, -1608944256, 0, 151212672, 0, -33918048, 0, 1813680, 0, -81912, 0, 2412, 0, -84, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [12]}
  • id: 7521847
    {'degree': 16, 'field': [2221104373569, 0, -417740088888, 0, 52628793660, 0, -3281027816, 0, 111859910, 0, -2408264, 0, 34108, 0, -280, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [12]}
  • id: 7521846
    {'degree': 16, 'field': [2252304589824, 0, -560977467264, 0, 36712206720, 0, 507251808, 0, -35335440, 0, -424872, 0, 252, 0, -60, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [2, 6]}
  • id: 7521845
    {'degree': 16, 'field': [839024753173776, 0, -126874223030880, 0, 8052749001216, 0, -269403660720, 0, 5143079772, 0, -56179800, 0, 333224, 0, -920, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [16]}
  • id: 7521844
    {'degree': 16, 'field': [19063048761000000, 0, -11079688744800000, 0, 950065767486000, 0, -28124312508000, 0, 309503207025, 0, -1378785600, 0, 2860740, 0, -2760, 0, 1], 'lmfdb_label': '169050.ee1', 'torsion': [16]}
  • id: 7521842
    {'degree': 16, 'field': [62217994328493201, 10851216006795120, 946260724867200, 82861352233200, -11125228670046, -1967891594760, -118834560000, -4196867040, 1543457511, 131875560, 3808800, -66240, -63786, -2760, 0, 0, 1], 'lmfdb_label': '169050.ee1', '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: 4183248
    {'conductor': 169050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '169050.ee1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4183249
    {'conductor': 169050, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '169050.ee1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4183250
    {'conductor': 169050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '169050.ee1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4183251
    {'conductor': 169050, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '169050.ee1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4183252
    {'conductor': 169050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '169050.ee1', 'prime': 23, '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: 2754957
    {'adelic_gens': [[1, 16, 0, 1], [25768, 1, 12959, 10], [28996, 28981, 19479, 19330], [24158, 28981, 14569, 19330], [15, 2, 38542, 38627], [16559, 38624, 16552, 38511], [1, 0, 16, 1], [30904, 38639, 15377, 38630], [5, 4, 38636, 38637], [38625, 16, 38624, 17], [10093, 16, 18224, 38325]], 'adelic_image': '38640.192.1.?', 'conductor': 169050, 'lmfdb_label': '169050.ee1', 'prime': 0}
  • id: 638927
    {'conductor': 169050, 'elladic_image': '8.12.0.5', 'lmfdb_label': '169050.ee1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 169050.ee does not appear in ec_padic