Elliptic curve data - 8400.ce8

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

  
  {'Ciso': '8400cc', 'Clabel': '8400cc6', 'Cnumber': 6, 'abc_quality': 1.1083142308531486, 'absD': 17226562500000000000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [0, 1, 0, 507992, 6313399988], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8400, 'degree': 589824, 'elladic_images': ['32.96.0.23'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9457219633925858889620339747', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 56, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [226523624554079, 269165039062500], 'lmfdb_iso': '8400.ce', 'lmfdb_label': '8400.ce8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1270, -789048], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0.q.1', '16.48.0.j.1', '20.24.0-4.d.1.1', '24.48.0.be.1', '32.96.0-16.j.1.2', '40.48.0-8.q.1.2', '48.96.1.bf.2', '56.48.0.bd.1', '80.96.0.?', '84.24.0.?', '96.192.1.?', '112.96.1.?', '120.96.0.?', '160.192.2.?', '168.96.1.?', '224.192.1.?', '240.192.1.?', '280.96.0.?', '336.192.5.?', '420.48.0.?', '480.384.5.?', '560.192.1.?', '672.384.5.?', '840.192.1.?', '1120.384.5.?', '1680.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.7742257770575451022929518281', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 2800], [5, 18, 336], [7, 8, 1200]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4478558266155903922444221866', 'prec': 100}, 'szpiro_ratio': 6.491263475831356, '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, 0, 0, -1, 0, 1, 0, 4, 0, 2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 1, 0, -1, 4, 2, -2, -4, -8, -2, 0, -6, -6, -4, 0, 10, -12, 14, -12, 8, -10, -16, -12, 10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 8400, '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': '8400.ce', 'trace_hash': 2049824808251832654}
• 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': '0.0027629842682292462198446106698', 'prec': 110}, 'conductor': 8400, 'gens': [[-1228, 61962, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.7742257770575451022929518281', 'prec': 100}], 'lmfdb_label': '8400.ce8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.096352811876564560232813994683', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2217256152496001483955850835513197228', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-1757, 0, 1]], 'xcoord_integral_points': [-1757, -1228]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '8400.ce8'}
• ec_torsion_growth •

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

  
  
  • id: 439520
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '8400.ce8', 'torsion': [4]}
  • id: 439519
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [2, 2]}
  • id: 439521
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [4]}
  • id: 439522
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [2, 4]}
  • id: 439525
    {'degree': 4, 'field': [81, 0, -12, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [8]}
  • id: 439526
    {'degree': 4, 'field': [81, 0, 12, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [8]}
  • id: 439523
    {'degree': 4, 'field': [155, 30, -29, -2, 1], 'lmfdb_label': '8400.ce8', 'torsion': [8]}
  • id: 439524
    {'degree': 4, 'field': [239, -26, 27, -2, 1], 'lmfdb_label': '8400.ce8', 'torsion': [8]}
  • id: 439532
    {'degree': 8, 'field': [-75, 0, 20, 0, 30, 0, 0, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [6]}
  • id: 439529
    {'degree': 8, 'field': [145, -140, 164, -44, 13, 8, 2, -4, 1], 'lmfdb_label': '8400.ce8', 'torsion': [2, 8]}
  • id: 439527
    {'degree': 8, 'field': [1780, 700, -566, -254, 93, 38, -8, -4, 1], 'lmfdb_label': '8400.ce8', 'torsion': [4, 4]}
  • id: 439528
    {'degree': 8, 'field': [2745, -1260, -484, 56, 109, -28, 6, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [2, 8]}
  • id: 439530
    {'degree': 8, 'field': [2916, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [16]}
  • id: 439531
    {'degree': 8, 'field': [1324801, 0, 71060, 0, -2202, 0, 20, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [16]}
  • id: 439534
    {'degree': 16, 'field': [-61151, 245176, -180748, -109648, 18102, 13160, 44800, -37064, 1863, 6600, -3080, 1064, -238, 0, 20, -8, 1], 'lmfdb_label': '8400.ce8', 'torsion': [16]}
  • id: 439539
    {'degree': 16, 'field': [-14479, 62968, -84740, 49800, -40370, 17864, -4028, -3440, 3675, -2720, 1292, -304, -10, 0, 20, -8, 1], 'lmfdb_label': '8400.ce8', 'torsion': [12]}
  • id: 439533
    {'degree': 16, 'field': [1, 0, 0, 0, 161, 0, 0, 0, 576, 0, 0, 0, 161, 0, 0, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [4, 8]}
  • id: 439536
    {'degree': 16, 'field': [25, 0, 8940, 0, 8206, 0, -1728, 0, 399, 0, 216, 0, 34, 0, 12, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [2, 16]}
  • id: 439538
    {'degree': 16, 'field': [576, 0, 39168, 0, -11952, 0, 5536, 0, 320, 0, -104, 0, 88, 0, 8, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [2, 6]}
  • id: 439540
    {'degree': 16, 'field': [1440000, 0, 1656000, 0, -255600, 0, -8800, 0, 16400, 0, 6440, 0, 760, 0, 40, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [12]}
  • id: 439535
    {'degree': 16, 'field': [337386169, -193424104, 225161012, -62376048, 29012942, 1009960, 2349760, -2346504, 652303, -60600, 28840, -9016, 1442, 0, 20, -8, 1], 'lmfdb_label': '8400.ce8', 'torsion': [16]}
  • id: 439537
    {'degree': 16, 'field': [7831365025, 0, -914895060, 0, 120082006, 0, -5200128, 0, 519399, 0, -3384, 0, 1234, 0, 12, 0, 1], 'lmfdb_label': '8400.ce8', 'torsion': [2, 16]}
• 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: 175114
    {'conductor': 8400, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '8400.ce8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 175115
    {'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8400.ce8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 175116
    {'conductor': 8400, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '8400.ce8', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 175117
    {'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8400.ce8', 'prime': 7, '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: 1719508
    {'adelic_gens': [[1, 8, 0, 421], [1, 0, 32, 1], [25, 16, 1624, 2249], [2269, 24, 126, 2885], [1, 32, 0, 1], [3353, 3344, 585, 2567], [1343, 3344, 0, 3359], [985, 16, 1974, 2473], [3329, 32, 3328, 33], [1, 32, 4, 129]], 'adelic_image': '3360.768.13.?', 'conductor': 8400, 'lmfdb_label': '8400.ce8', 'prime': 0}
  • id: 41094
    {'conductor': 8400, 'elladic_image': '32.96.0.23', 'lmfdb_label': '8400.ce8', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 347796
    {'lmfdb_iso': '8400.ce', 'p': 11, 'prec': 20, 'unit': 628422117349648279, 'val': 1}
  • id: 347794
    {'lmfdb_iso': '8400.ce', 'p': 13, 'prec': 20, 'unit': 349271495255547364217, 'val': 1}
  • id: 347797
    {'lmfdb_iso': '8400.ce', 'p': 17, 'prec': 20, 'unit': 196241018784507202332868, 'val': 1}
  • id: 347798
    {'lmfdb_iso': '8400.ce', 'p': 19, 'prec': 20, 'unit': 1246898000664958584016455, 'val': 1}
  • id: 347801
    {'lmfdb_iso': '8400.ce', 'p': 23, 'prec': 20, 'unit': 6093622876150035598164389, 'val': 1}
  • id: 347793
    {'lmfdb_iso': '8400.ce', 'p': 29, 'prec': 20, 'unit': 4712638108296897260845437258, 'val': 1}
  • id: 347789
    {'lmfdb_iso': '8400.ce', 'p': 37, 'prec': 20, 'unit': 234386054469989696782136548083, 'val': 1}
  • id: 347791
    {'lmfdb_iso': '8400.ce', 'p': 41, 'prec': 20, 'unit': 1700010225766273015545826677283, 'val': 1}
  • id: 347792
    {'lmfdb_iso': '8400.ce', 'p': 43, 'prec': 20, 'unit': 5120718024680019599748665981574, 'val': 1}
  • id: 347799
    {'lmfdb_iso': '8400.ce', 'p': 53, 'prec': 20, 'unit': 14595952175553569184220646864138, 'val': 1}
  • id: 347803
    {'lmfdb_iso': '8400.ce', 'p': 59, 'prec': 20, 'unit': 86145348368628902279904544137704, 'val': 1}
  • id: 347804
    {'lmfdb_iso': '8400.ce', 'p': 61, 'prec': 20, 'unit': 7810123348449195284568608536089833, 'val': 1}
  • id: 347788
    {'lmfdb_iso': '8400.ce', 'p': 67, 'prec': 20, 'unit': 25186306093440199769002271556790506, 'val': 1}
  • id: 347790
    {'lmfdb_iso': '8400.ce', 'p': 71, 'prec': 20, 'unit': 27341288489721570511065676100476686, 'val': 1}
  • id: 347800
    {'lmfdb_iso': '8400.ce', 'p': 73, 'prec': 20, 'unit': 232523788047830903147639517459549802, 'val': 1}
  • id: 347795
    {'lmfdb_iso': '8400.ce', 'p': 79, 'prec': 20, 'unit': 614564455776874608022544985160469857, 'val': 1}
  • id: 347787
    {'lmfdb_iso': '8400.ce', 'p': 83, 'prec': 20, 'unit': 40605980271611025687316117204762689, 'val': 1}
  • id: 347802
    {'lmfdb_iso': '8400.ce', 'p': 89, 'prec': 20, 'unit': 2779095970682563613765555789143460668, 'val': 1}
  • id: 347786
    {'lmfdb_iso': '8400.ce', 'p': 97, 'prec': 20, 'unit': 46364668870772035884595722507163582088, 'val': 1}