Elliptic curve data - 28224.dh5

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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': '28224bi', 'Clabel': '28224bi1', 'Cnumber': 1, 'abc_quality': 1.0171207213859017, 'absD': 629526072655872, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 504, 'ainvs': [0, 0, 0, -14700, 1388464], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 28224, 'degree': 73728, 'elladic_images': ['8.6.0.1', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5298970911766315738530682296', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 85, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [-15625, 28], 'lmfdb_iso': '28224.dh', 'lmfdb_label': '28224.dh5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1, 0], 'min_quad_twist_disc': 168, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.c.1', '9.12.0.a.1', '12.24.0-6.a.1.7', '14.6.0.b.1', '18.36.0.a.1', '24.48.0-24.bw.1.16', '36.72.0-18.a.1.5', '42.24.0.b.1', '56.12.0.n.1', '63.36.0.d.2', '72.144.1.?', '84.48.0.?', '126.216.7.?', '168.96.1.?', '252.432.7.?', '504.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9225766590733578940754514109', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0320848985249978885230789428', 'prec': 103}, 'szpiro_ratio': 4.0799040568922855, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, 2, 0], 'aplist': [0, 0, 0, 0, 0, -4, 6, 2, 0, -6, 4, -2, 6, -8, -12, 6, 6, 8, 4, 0, -2, 8, 6, -6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 28224, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '28224.dh', 'trace_hash': 2115507073587996266}
• 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': '0.046897346528250289044604553016', 'prec': 107}, 'conductor': 28224, 'gens': [[-90, 1408, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9225766590733578940754514109', 'prec': 100}], 'lmfdb_label': '28224.dh5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.45859155186234602762573600354', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3610758620844871672230403749565818147', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-154, 0, 1]], 'xcoord_integral_points': [-154, -90, 728]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 1, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.dh5'}
• ec_torsion_growth •

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

  
  
  • id: 1412709
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [6]}
  • id: 1412708
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 2]}
  • id: 1412710
    {'degree': 4, 'field': [-2, -4, -1, -2, 1], 'lmfdb_label': '28224.dh5', 'torsion': [4]}
  • id: 1412711
    {'degree': 4, 'field': [22, -16, 17, -2, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 6]}
  • id: 1412713
    {'degree': 6, 'field': [-1512, 0, 504, 0, -42, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [18]}
  • id: 1412712
    {'degree': 6, 'field': [126, 0, 84, 0, 14, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [6]}
  • id: 1412716
    {'degree': 8, 'field': [4, -8, -42, 0, 9, -2, -1, -2, 1], 'lmfdb_label': '28224.dh5', 'torsion': [12]}
  • id: 1412714
    {'degree': 8, 'field': [16, 96, 192, -88, 118, 12, 13, -2, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 4]}
  • id: 1412715
    {'degree': 8, 'field': [18, 0, 15, -18, 1, -4, 5, -2, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 4]}
  • id: 1412719
    {'degree': 12, 'field': [64, 0, 32, 0, 128, 0, -34, 0, 32, 0, 2, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 6]}
  • id: 1412718
    {'degree': 12, 'field': [9604, 0, 0, 0, 0, 0, -182, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [18]}
  • id: 1412717
    {'degree': 12, 'field': [15876, 0, -10584, 0, 5292, 0, -924, 0, 112, 0, -14, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [3, 6]}
  • id: 1412720
    {'degree': 12, 'field': [46656, 0, -7776, 0, 1296, 0, -216, 0, 36, 0, -6, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 18]}
  • id: 1412721
    {'degree': 16, 'field': [-878, 1752, -5068, 9960, -9719, 16532, -14122, 5820, -1863, 1072, -376, 32, 11, -28, 14, -4, 1], 'lmfdb_label': '28224.dh5', 'torsion': [8]}
  • id: 1412723
    {'degree': 16, 'field': [16, 0, 24, 0, 32, 0, 38, 0, 21, 0, -16, 0, 15, 0, -4, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 12]}
  • id: 1412722
    {'degree': 16, 'field': [2401, 0, 5488, 0, 4361, 0, 616, 0, 1264, 0, -88, 0, 89, 0, -16, 0, 1], 'lmfdb_label': '28224.dh5', 'torsion': [2, 12]}
• 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: 653546
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '28224.dh5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 653547
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '28224.dh5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 653548
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '28224.dh5', 'prime': 7, '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: 1852445
    {'adelic_gens': [[344, 495, 457, 482], [1, 0, 36, 1], [19, 36, 216, 91], [1, 36, 0, 1], [1, 18, 14, 253], [469, 36, 468, 37], [251, 468, 494, 143], [127, 36, 262, 361], [223, 468, 0, 503]], 'adelic_image': '504.864.21.?', 'conductor': 28224, 'lmfdb_label': '28224.dh5', 'prime': 0}
  • id: 127544
    {'conductor': 28224, 'elladic_image': '8.6.0.1', 'lmfdb_label': '28224.dh5', 'modell_image': '2B', 'prime': 2}
  • id: 127545
    {'conductor': 28224, 'elladic_image': '9.12.0.1', 'lmfdb_label': '28224.dh5', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1355751
    {'lmfdb_iso': '28224.dh', 'p': 13, 'prec': 20, 'unit': 1394334888159029171924, 'val': 1}
  • id: 1355753
    {'lmfdb_iso': '28224.dh', 'p': 17, 'prec': 20, 'unit': 53304240224446901995020, 'val': 1}
  • id: 1355754
    {'lmfdb_iso': '28224.dh', 'p': 19, 'prec': 20, 'unit': 343997297998841000138585, 'val': 1}
  • id: 1355750
    {'lmfdb_iso': '28224.dh', 'p': 29, 'prec': 20, 'unit': 1742096322562783100015446202, 'val': 1}
  • id: 1355761
    {'lmfdb_iso': '28224.dh', 'p': 31, 'prec': 20, 'unit': 3719318415917655183773069040, 'val': 1}
  • id: 1355747
    {'lmfdb_iso': '28224.dh', 'p': 37, 'prec': 20, 'unit': 428730877503497455810414693286, 'val': 1}
  • id: 1355748
    {'lmfdb_iso': '28224.dh', 'p': 41, 'prec': 20, 'unit': 3761869233613637927299511016890, 'val': 1}
  • id: 1355749
    {'lmfdb_iso': '28224.dh', 'p': 43, 'prec': 20, 'unit': 4637502129296616244133413892277, 'val': 1}
  • id: 1355759
    {'lmfdb_iso': '28224.dh', 'p': 47, 'prec': 20, 'unit': 43422908606429964204441997231206, 'val': 1}
  • id: 1355755
    {'lmfdb_iso': '28224.dh', 'p': 53, 'prec': 20, 'unit': 567436357464195375936146118670588, 'val': 1}
  • id: 1355756
    {'lmfdb_iso': '28224.dh', 'p': 59, 'prec': 20, 'unit': 3020016098492755233273755631825743, 'val': 1}
  • id: 1355760
    {'lmfdb_iso': '28224.dh', 'p': 61, 'prec': 20, 'unit': 4270785494520318259351587925355535, 'val': 1}
  • id: 1355746
    {'lmfdb_iso': '28224.dh', 'p': 67, 'prec': 20, 'unit': 10905715977478734497059012010808617, 'val': 1}
  • id: 1355757
    {'lmfdb_iso': '28224.dh', 'p': 73, 'prec': 20, 'unit': 101214603246672469322965920241932840, 'val': 1}
  • id: 1355752
    {'lmfdb_iso': '28224.dh', 'p': 79, 'prec': 20, 'unit': 901341566699740781751034750130192179, 'val': 1}
  • id: 1355745
    {'lmfdb_iso': '28224.dh', 'p': 83, 'prec': 20, 'unit': 184670388145349353078068131554612845, 'val': 1}
  • id: 1355758
    {'lmfdb_iso': '28224.dh', 'p': 89, 'prec': 20, 'unit': 5736228878370826867927269078018884924, 'val': 1}
  • id: 1355744
    {'lmfdb_iso': '28224.dh', 'p': 97, 'prec': 20, 'unit': 147417584032947644805921972931625626, 'val': 2}