Elliptic curve data - 162624.hy5

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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': '162624gh', 'Clabel': '162624gh6', 'Cnumber': 6, 'abc_quality': 1.0676539350043504, 'absD': 6271595843615243108352, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 3696, 'ainvs': [0, 1, 0, 239903, 3810006143], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 162624, 'degree': 9830400, 'elladic_images': ['16.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8614583976258288729241184069', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 206, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [3288008303, 13504609503], 'lmfdb_iso': '162624.hy', 'lmfdb_label': '162624.hy5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 31, -5578], 'min_quad_twist_disc': -88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '14.6.0.b.1', '16.24.0-8.n.1.5', '24.24.0.bz.2', '28.12.0.g.1', '48.48.0-24.bz.2.11', '56.24.0.bf.1', '88.24.0.?', '112.48.0.?', '168.48.0.?', '176.48.0.?', '264.48.0.?', '336.96.0.?', '528.96.0.?', '616.48.0.?', '1232.96.0.?', '1848.96.0.?', '3696.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '13.742248174889596730615006488', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.62278999038672563676729843573', 'prec': 103}, 'szpiro_ratio': 4.8040632485711185, '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, 0, 0, 6, 0, 2, 0, -2, 0, 4, 0], 'aplist': [0, 1, 2, -1, 0, 6, -2, 4, 0, -2, 8, -6, -10, -4, -8, -6, -4, -10, 12, 0, -2, -16, 4, 18, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 162624, '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': '162624.hy', 'trace_hash': 1575058731695238843}
• 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': '0.0032701585949915115048289779501', 'prec': 110}, 'conductor': 162624, 'gens': [[3195029, 5711070108, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '13.742248174889596730615006488', 'prec': 100}], 'lmfdb_label': '162624.hy5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10536628407626476963237230688', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.583757000335586472418369148275945256', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-1511, 0, 1]], 'xcoord_integral_points': [-1511]}
• lmfdb_label 162624.hy5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7268557
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [4]}
  • id: 7268556
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '162624.hy5', 'torsion': [2, 2]}
  • id: 7268558
    {'degree': 2, 'field': [154, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [4]}
  • id: 7268560
    {'degree': 4, 'field': [25, 0, -32, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [8]}
  • id: 7268561
    {'degree': 4, 'field': [49, 0, -8, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [8]}
  • id: 7268559
    {'degree': 4, 'field': [554, 40, -39, -2, 1], 'lmfdb_label': '162624.hy5', 'torsion': [2, 4]}
  • id: 7268566
    {'degree': 8, 'field': [-702768, 0, 72512, 0, -2904, 0, 0, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [6]}
  • id: 7268563
    {'degree': 8, 'field': [576, 0, 1600, 0, 276, 0, 36, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [8]}
  • id: 7268565
    {'degree': 8, 'field': [3969, 0, -1512, 0, 744, 0, 24, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [16]}
  • id: 7268564
    {'degree': 8, 'field': [3994, 1444, -1298, -284, 123, 20, -2, -4, 1], 'lmfdb_label': '162624.hy5', 'torsion': [2, 8]}
  • id: 7268562
    {'degree': 8, 'field': [368272, -45792, 44368, -3544, 2822, -104, 81, -2, 1], 'lmfdb_label': '162624.hy5', 'torsion': [2, 4]}
  • id: 7268568
    {'degree': 16, 'field': [1296, 0, 0, 0, 35032, 0, 0, 0, -2367, 0, 0, 0, 186, 0, 0, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [2, 8]}
  • id: 7268572
    {'degree': 16, 'field': [1185921, 0, -431244, 0, 39204, 0, -4914052, 0, 440198, 0, -11044, 0, 484, 0, -44, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [12]}
  • id: 7268567
    {'degree': 16, 'field': [105390756, -20449872, 1984032, 20520504, 12583192, 4793296, 830792, 30284, -8427, 36656, 8752, -3440, 642, 16, 8, -4, 1], 'lmfdb_label': '162624.hy5', 'torsion': [4, 4]}
  • id: 7268570
    {'degree': 16, 'field': [582643044, 0, -56966976, 0, 24615900, 0, -379728, 0, 233829, 0, -5976, 0, 1236, 0, -24, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [2, 16]}
  • id: 7268569
    {'degree': 16, 'field': [654234084, 0, 6173604864, 0, 411447708, 0, -190702512, 0, -12765627, 0, 666792, 0, -924, 0, -168, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [16]}
  • id: 7268573
    {'degree': 16, 'field': [626128786089, 0, -305121381552, 0, 41924454532, 0, -1218049632, 0, 29113086, 0, -185712, 0, 4692, 0, 0, 0, 1], 'lmfdb_label': '162624.hy5', 'torsion': [12]}
  • id: 7268571
    {'degree': 16, 'field': [672519179984, 120495190144, -112249484864, -16196952384, 7366563880, 866284928, -268279664, -18469232, 5718681, -671864, 72236, 33560, -5290, -168, 44, -8, 1], 'lmfdb_label': '162624.hy5', '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: 4025552
    {'conductor': 162624, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '162624.hy5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4025553
    {'conductor': 162624, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '162624.hy5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4025554
    {'conductor': 162624, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '162624.hy5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4025555
    {'conductor': 162624, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '162624.hy5', 'prime': 11, 'reduction_type': 0, '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: 2715896
    {'adelic_gens': [[3683, 3680, 1180, 1239], [1, 16, 0, 1], [5, 4, 3692, 3693], [3681, 16, 3680, 17], [2477, 16, 976, 3381], [1592, 1, 3247, 10], [1399, 16, 726, 3097], [1, 0, 16, 1], [15, 2, 3598, 3683], [3023, 3680, 2008, 3567]], 'adelic_image': '3696.192.1.?', 'conductor': 162624, 'lmfdb_label': '162624.hy5', 'prime': 0}
  • id: 618685
    {'conductor': 162624, 'elladic_image': '16.24.0.3', 'lmfdb_label': '162624.hy5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 162624.hy does not appear in ec_padic