Elliptic curve data - 21675.s8

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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': '21675c', 'Clabel': '21675c5', 'Cnumber': 5, 'abc_quality': 1.0558519748642754, 'absD': 1325916265869140625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [1, 1, 0, 252725, -25931750], 'analytic_rank': 1, 'bad_primes': [3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 21675, 'degree': 245760, 'elladic_images': ['8.48.0.197'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1656216464422870946901665391', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4733169839, 3515625], 'lmfdb_iso': '21675.s', 'lmfdb_label': '21675.s8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 35, -28], 'min_quad_twist_disc': 85, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0.n.2', '24.96.1.cv.2', '80.96.1.?', '160.192.5.?', '240.192.5.?', '272.96.0.?', '340.24.0.?', '480.384.13.?', '680.96.0.?', '816.192.1.?', '1360.192.1.?', '2040.192.1.?', '2720.384.5.?', '4080.384.5.?', '8160.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.5457166100285265513110893318', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436450', 'prec': 110}, 'szpiro_ratio': 4.901260625951416, '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, -3, 1, 0, 4, 1, 2, 0, 0, -1, 0, 1, 4, 0], 'aplist': [1, -1, 0, 0, 4, 2, 0, 4, 0, 2, 0, -10, -10, -4, -8, 10, -4, 2, -12, 8, 10, 0, -12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 21675, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '21675.s', 'trace_hash': 1613917019537411626}
• 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': '0.013151186544808994716274957542', 'prec': 107}, 'conductor': 21675, 'gens': [[7770, 682490, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.5457166100285265513110893318', 'prec': 100}], 'lmfdb_label': '21675.s8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.15191672959770701400761904758', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5245632085880724149585475491176958986', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[395, -395, 2]], 'xcoord_integral_points': [7770]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 2], '3': [1, 0], '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '21675.s8'}
• ec_torsion_growth •

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

  
  
  • id: 1101614
    {'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '21675.s8', 'torsion': [8]}
  • id: 1101613
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [2, 2]}
  • id: 1101615
    {'degree': 2, 'field': [85, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [4]}
  • id: 1101616
    {'degree': 4, 'field': [441, 0, 43, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [2, 8]}
  • id: 1101617
    {'degree': 4, 'field': [6241, 0, 182, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [8]}
  • id: 1101618
    {'degree': 4, 'field': [8281, 0, 158, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [8]}
  • id: 1101621
    {'degree': 8, 'field': [-2031, -56949, 24905, 3663, 735, -62, -3, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [6]}
  • id: 1101620
    {'degree': 8, 'field': [-149, 622, -514, -194, 43, 62, -16, -4, 1], 'lmfdb_label': '21675.s8', 'torsion': [16]}
  • id: 1101619
    {'degree': 8, 'field': [203265, 16020, 35676, 504, 2749, -12, 86, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [4, 8]}
  • id: 1101622
    {'degree': 16, 'field': [65536, 0, 0, 0, 37632, 0, 0, 0, 4193, 0, 0, 0, 147, 0, 0, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [2, 16]}
  • id: 1101623
    {'degree': 16, 'field': [372196, -118712, 348624, 117048, -65650, 171688, -36168, 13778, 20109, -10826, 7338, -2182, 824, -150, 42, -4, 1], 'lmfdb_label': '21675.s8', 'torsion': [2, 16]}
  • id: 1101626
    {'degree': 16, 'field': [4124961, 0, 3344352711, 0, 1034481829, 0, -16143291, 0, 840945, 0, -41556, 0, 1479, 0, 6, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [2, 6]}
  • id: 1101627
    {'degree': 16, 'field': [58660281, -61746858, -14563667, 10094821, 1461772, -793488, -2387511, -411885, 99795, -21915, -17331, -2952, 72, -21, -47, -2, 1], 'lmfdb_label': '21675.s8', 'torsion': [24]}
  • id: 1101624
    {'degree': 16, 'field': [68254465, 22662360, 91955144, 37645776, 29566888, 17075880, 544472, 2083104, 575566, 17928, 78200, -3888, 4072, -72, 104, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [16]}
  • id: 1101625
    {'degree': 16, 'field': [396863041, -91085400, 160727024, -32496960, 55192264, -1525560, 10823336, -229440, 1110850, -59160, 76976, -3840, 3784, -120, 104, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [16]}
  • id: 1101628
    {'degree': 16, 'field': [41476173649, 0, 15680235173, 0, 2581811080, 0, 242803881, 0, 14277225, 0, 537399, 0, 12643, 0, 170, 0, 1], 'lmfdb_label': '21675.s8', 'torsion': [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: 494003
    {'conductor': 21675, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21675.s8', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 494004
    {'conductor': 21675, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '21675.s8', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 494005
    {'conductor': 21675, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21675.s8', 'prime': 17, '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: 1808978
    {'adelic_gens': [[1, 0, 32, 1], [1, 32, 0, 1], [6733, 6256, 6494, 8025], [3367, 6256, 2295, 3673], [8129, 32, 8128, 33], [3839, 0, 0, 8159], [2585, 4352, 6902, 7209], [3263, 952, 0, 8159], [1, 32, 4, 129], [25, 16, 6424, 7049]], 'adelic_image': '8160.768.13.?', 'conductor': 21675, 'lmfdb_label': '21675.s8', 'prime': 0}
  • id: 100377
    {'conductor': 21675, 'elladic_image': '8.48.0.197', 'lmfdb_label': '21675.s8', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1017777
    {'lmfdb_iso': '21675.s', 'p': 11, 'prec': 20, 'unit': 13467896696423701833, 'val': 1}
  • id: 1017783
    {'lmfdb_iso': '21675.s', 'p': 13, 'prec': 20, 'unit': 873745235657083841958, 'val': 1}
  • id: 1017785
    {'lmfdb_iso': '21675.s', 'p': 19, 'prec': 20, 'unit': 1786997467081226723591126, 'val': 1}
  • id: 1017782
    {'lmfdb_iso': '21675.s', 'p': 29, 'prec': 20, 'unit': 5728926769067599811607244674, 'val': 1}
  • id: 1017778
    {'lmfdb_iso': '21675.s', 'p': 37, 'prec': 20, 'unit': 325604035163841658787664846611, 'val': 1}
  • id: 1017780
    {'lmfdb_iso': '21675.s', 'p': 41, 'prec': 20, 'unit': 2335946351013533735080934282450, 'val': 1}
  • id: 1017781
    {'lmfdb_iso': '21675.s', 'p': 43, 'prec': 20, 'unit': 6222907997924789226746005107040, 'val': 1}
  • id: 1017784
    {'lmfdb_iso': '21675.s', 'p': 47, 'prec': 20, 'unit': 39907471382506937346550816696260, 'val': 1}
  • id: 1017786
    {'lmfdb_iso': '21675.s', 'p': 53, 'prec': 20, 'unit': 424357541189451579184730685357588, 'val': 1}
  • id: 1017790
    {'lmfdb_iso': '21675.s', 'p': 59, 'prec': 20, 'unit': 4041636160611928628954239719257161, 'val': 1}
  • id: 1017791
    {'lmfdb_iso': '21675.s', 'p': 61, 'prec': 20, 'unit': 6954756822031184756905048681627252, 'val': 1}
  • id: 1017776
    {'lmfdb_iso': '21675.s', 'p': 67, 'prec': 20, 'unit': 26535405373951341072606381452439983, 'val': 1}
  • id: 1017779
    {'lmfdb_iso': '21675.s', 'p': 71, 'prec': 20, 'unit': 98198907289403568084475322386884055, 'val': 1}
  • id: 1017787
    {'lmfdb_iso': '21675.s', 'p': 73, 'prec': 20, 'unit': 244135522648859087454542542971791195, 'val': 1}
  • id: 1017788
    {'lmfdb_iso': '21675.s', 'p': 83, 'prec': 20, 'unit': 1628457727739871329910446035115591472, 'val': 1}
  • id: 1017789
    {'lmfdb_iso': '21675.s', 'p': 89, 'prec': 20, 'unit': 3487714072107669045655391167430487101, 'val': 1}
  • id: 1017775
    {'lmfdb_iso': '21675.s', 'p': 97, 'prec': 20, 'unit': 12424474223728523914088093700010610273, 'val': 1}