Elliptic curve data - 162240.ei2

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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': '162240ba', 'Clabel': '162240ba8', 'Cnumber': 8, 'abc_quality': 1.1359972360691755, 'absD': 7413978624000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [0, 1, 0, -4905281, 567497919], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 162240, 'degree': 10616832, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8863614347870380124418342245', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'intrinsic_torsion': 2, 'iso_nlabel': 112, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [10316097499609, 5859375000], 'lmfdb_iso': '162240.ei', 'lmfdb_label': '162240.ei2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -454, -544], 'min_quad_twist_disc': -104, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.3', '24.96.1.da.1', '40.12.0.bb.1', '52.12.0-4.c.1.1', '78.24.0.?', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '17.656010919175212372127434221', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 507], [3, 4, 10816], [5, 6, 32448], [13, 86, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232153', 'prec': 103}, 'szpiro_ratio': 4.820528623974719, '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, 0, 0, -1, 0, 6, 0, 4, 0], 'aplist': [0, 1, -1, -4, 0, 0, 6, 4, 0, 6, 8, 2, 6, -4, 0, 6, 0, 10, 4, 0, -2, -8, -12, -18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 162240, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '162240.ei', 'trace_hash': 1202810033819423020}
• 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': '0.0031112743758319866914995994923', 'prec': 110}, 'conductor': 162240, 'gens': [[-35189339, 4649759232391, 510]], 'heights': [{'__RealLiteral__': 0, 'data': '17.656010919175212372127434221', 'prec': 100}], 'lmfdb_label': '162240.ei2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11358969192273942577710189130', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.0221633635745429011332347294603367252', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-2271, 0, 1]], 'xcoord_integral_points': [-2271]}
• lmfdb_label 162240.ei2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7246742
    {'degree': 2, 'field': [-78, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [6]}
  • id: 7246739
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 2]}
  • id: 7246741
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [4]}
  • id: 7246740
    {'degree': 2, 'field': [78, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [4]}
  • id: 7246744
    {'degree': 4, 'field': [3, 18, -17, -2, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 6]}
  • id: 7246746
    {'degree': 4, 'field': [49, 0, 38, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [12]}
  • id: 7246743
    {'degree': 4, 'field': [361, 0, 14, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 4]}
  • id: 7246745
    {'degree': 4, 'field': [1521, 0, 0, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [12]}
  • id: 7246747
    {'degree': 6, 'field': [17585, 468, 2028, -6, 78, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [6]}
  • id: 7246748
    {'degree': 8, 'field': [-69, 348, -306, -72, 7, 32, -6, -4, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 12]}
  • id: 7246751
    {'degree': 8, 'field': [441, 252, -180, 72, 85, -12, 14, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 12]}
  • id: 7246749
    {'degree': 8, 'field': [18496, 0, 1688, 0, 588, 0, -22, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [8]}
  • id: 7246750
    {'degree': 8, 'field': [62001, 0, -396, 0, 172, 0, 36, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [8]}
  • id: 7246755
    {'degree': 12, 'field': [117406, 42516, 103554, 31860, 27399, 4464, 5310, 0, 579, -12, 36, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [12]}
  • id: 7246753
    {'degree': 12, 'field': [243000, 0, 0, 27648, 0, 0, 1299, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 6]}
  • id: 7246752
    {'degree': 12, 'field': [308810329, 0, 71349096, 0, 6852300, 0, 351526, 0, 10140, 0, 156, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [3, 6]}
  • id: 7246754
    {'degree': 12, 'field': [309021241, 0, 71227416, 0, 6856980, 0, 351514, 0, 10140, 0, 156, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [12]}
  • id: 7246756
    {'degree': 16, 'field': [4761, 0, 78876, 0, 142782, 0, 30912, 0, 10975, 0, 2296, 0, 306, 0, 28, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [4, 12]}
  • id: 7246758
    {'degree': 16, 'field': [12996, 0, -20232, 0, -4152, 0, 42300, 0, 31621, 0, 8440, 0, 978, 0, 52, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 8]}
  • id: 7246759
    {'degree': 16, 'field': [1336336, 0, 0, 0, -295343, 0, 0, 0, 28563, 0, 0, 0, -173, 0, 0, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [24]}
  • id: 7246760
    {'degree': 16, 'field': [10797796, 0, -5678896, 0, 2205284, 0, -355824, 0, 23189, 0, 2124, 0, -256, 0, -4, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [24]}
  • id: 7246757
    {'degree': 16, 'field': [20711601, 0, 9923244, 0, 2986150, 0, 332016, 0, 28599, 0, -2344, 0, 690, 0, -36, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [2, 8]}
  • id: 7246761
    {'degree': 18, 'field': [-11202790427228, -25569094750680, 39621001366596, -712150248740, -4969432682370, 11750912220, 193729536497, -293204940, -5400423576, -34458920, 106169799, 251700, -1329142, 1620, 18051, -20, -84, 0, 1], 'lmfdb_label': '162240.ei2', 'torsion': [18]}
• 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: 4013412
    {'conductor': 162240, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '162240.ei2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4013413
    {'conductor': 162240, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '162240.ei2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4013414
    {'conductor': 162240, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '162240.ei2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4013415
    {'conductor': 162240, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '162240.ei2', 'prime': 13, 'reduction_type': 0, '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: 2712866
    {'adelic_gens': [[506, 117, 585, 1286], [1, 12, 12, 145], [1537, 24, 1536, 25], [479, 0, 0, 1559], [714, 1391, 325, 64], [15, 106, 254, 131], [1, 24, 0, 1], [937, 624, 1404, 1249], [456, 1313, 1391, 1314], [1, 0, 24, 1]], 'adelic_image': '1560.384.5.?', 'conductor': 162240, 'lmfdb_label': '162240.ei2', 'prime': 0}
  • id: 616908
    {'conductor': 162240, 'elladic_image': '4.6.0.1', 'lmfdb_label': '162240.ei2', 'modell_image': '2B', 'prime': 2}
  • id: 616909
    {'conductor': 162240, 'elladic_image': '3.4.0.1', 'lmfdb_label': '162240.ei2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 162240.ei does not appear in ec_padic