Elliptic curve data - 47040.dn5

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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': '47040bm', 'Clabel': '47040bm3', 'Cnumber': 3, 'abc_quality': 0.9617149979611352, 'absD': 63248102400000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, -1, 0, 46975, -11463423], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 47040, 'degree': 393216, 'elladic_images': ['8.24.0.93'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9058701483063326973739127252', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 91, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [1486779836, 8203125], 'lmfdb_iso': '47040.dn', 'lmfdb_label': '47040.dn5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 240, 4092], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.5', '24.48.0-24.bz.2.12', '56.48.0-56.bu.1.10', '80.48.0.?', '84.12.0.?', '168.96.0.?', '240.96.0.?', '560.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.0249625494764726103401526352', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.0087188330320822989315935248672', 'prec': 110}, 'szpiro_ratio': 4.278353926767511, '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, 0, 0, 1, 0, 4, 0, -2, 0, -1, 0, -2, 0, -4, 0], 'aplist': [0, -1, 1, 0, 4, -2, -2, -4, 0, 10, 0, -6, 6, 4, 8, -6, -4, -10, -4, -16, 14, 8, -4, -10, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 47040, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '47040.dn', 'trace_hash': 2101520482659475810}
• 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': '0.022109668076119090750702690924', 'prec': 107}, 'conductor': 47040, 'gens': [[208, 2695, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.0249625494764726103401526352', 'prec': 100}], 'lmfdb_label': '47040.dn5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17532336035486346859975741728', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6453596758135487222732008091714102631', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[159, 0, 1]], 'xcoord_integral_points': [159, 208, 2659]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [2, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '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': '47040.dn5'}
• ec_torsion_growth •

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

  
  
  • id: 2292761
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [4]}
  • id: 2292762
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [4]}
  • id: 2292760
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [2, 2]}
  • id: 2292764
    {'degree': 4, 'field': [4, 0, 10, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [8]}
  • id: 2292763
    {'degree': 4, 'field': [25, 0, 4, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [2, 4]}
  • id: 2292765
    {'degree': 4, 'field': [49, 0, 0, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [8]}
  • id: 2292769
    {'degree': 8, 'field': [-115248, 0, 13888, 0, -1176, 0, 0, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [6]}
  • id: 2292768
    {'degree': 8, 'field': [1, 0, 0, 0, 23, 0, 0, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [2, 8]}
  • id: 2292767
    {'degree': 8, 'field': [25, 0, 46, 0, 54, 0, -26, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [8]}
  • id: 2292766
    {'degree': 8, 'field': [7000, 2800, 1400, 784, 64, 80, 20, -4, 1], 'lmfdb_label': '47040.dn5', 'torsion': [2, 4]}
  • id: 2292770
    {'degree': 16, 'field': [25, -1160, 26912, -53392, 54656, -39904, 29568, -21624, 12694, -6072, 2688, -976, 224, -64, 32, -8, 1], 'lmfdb_label': '47040.dn5', 'torsion': [4, 8]}
  • id: 2292771
    {'degree': 16, 'field': [1296, 0, 0, 0, 20736, 0, 0, 0, 7416, 0, 0, 0, 576, 0, 0, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [16]}
  • id: 2292774
    {'degree': 16, 'field': [81225, 0, 198900, 0, 84700, 0, -130116, 0, 18942, 0, -196, 0, -84, 0, -12, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [12]}
  • id: 2292772
    {'degree': 16, 'field': [194481, 0, 0, 0, 518616, 0, 0, 0, 72226, 0, 0, 0, 1176, 0, 0, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [16]}
  • id: 2292773
    {'degree': 16, 'field': [3515625, 0, -5128800, 0, 4918300, 0, 686400, 0, 22782, 0, 3488, 0, 204, 0, 0, 0, 1], 'lmfdb_label': '47040.dn5', 'torsion': [2, 6]}
  • id: 2292775
    {'degree': 16, 'field': [3841600, 0, 2195200, 0, 313600, 0, 263424, 0, 25872, 0, 3864, 0, 196, 0, 28, 0, 1], 'lmfdb_label': '47040.dn5', '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: 1122070
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '47040.dn5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1122071
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '47040.dn5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1122072
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '47040.dn5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 1122073
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '47040.dn5', '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: 1977448
    {'adelic_gens': [[5, 4, 1676, 1677], [1, 16, 0, 1], [1665, 16, 1664, 17], [1184, 1675, 765, 14], [15, 2, 1582, 1667], [1066, 1267, 863, 942], [568, 1, 1199, 10], [1, 0, 16, 1], [337, 16, 1016, 129], [1667, 1664, 996, 935]], 'adelic_image': '1680.192.1.?', 'conductor': 47040, 'lmfdb_label': '47040.dn5', 'prime': 0}
  • id: 203380
    {'conductor': 47040, 'elladic_image': '8.24.0.93', 'lmfdb_label': '47040.dn5', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2358252
    {'lmfdb_iso': '47040.dn', 'p': 11, 'prec': 20, 'unit': 1508477032590237374, 'val': 1}
  • id: 2358258
    {'lmfdb_iso': '47040.dn', 'p': 13, 'prec': 20, 'unit': 259931580049378919293, 'val': 1}
  • id: 2358260
    {'lmfdb_iso': '47040.dn', 'p': 17, 'prec': 20, 'unit': 84591741806669766997461, 'val': 1}
  • id: 2358261
    {'lmfdb_iso': '47040.dn', 'p': 19, 'prec': 20, 'unit': 1086989570023338935420785, 'val': 1}
  • id: 2358257
    {'lmfdb_iso': '47040.dn', 'p': 29, 'prec': 20, 'unit': 4080658220825922494946239572, 'val': 1}
  • id: 2358253
    {'lmfdb_iso': '47040.dn', 'p': 37, 'prec': 20, 'unit': 232449107620679778846122715940, 'val': 1}
  • id: 2358255
    {'lmfdb_iso': '47040.dn', 'p': 41, 'prec': 20, 'unit': 3678940388714991092577800440752, 'val': 1}
  • id: 2358256
    {'lmfdb_iso': '47040.dn', 'p': 43, 'prec': 20, 'unit': 7586579868356260734758159515060, 'val': 1}
  • id: 2358267
    {'lmfdb_iso': '47040.dn', 'p': 47, 'prec': 20, 'unit': 27538742629497498466771869632876, 'val': 1}
  • id: 2358262
    {'lmfdb_iso': '47040.dn', 'p': 53, 'prec': 20, 'unit': 542646187501937543248855448556508, 'val': 1}
  • id: 2358263
    {'lmfdb_iso': '47040.dn', 'p': 59, 'prec': 20, 'unit': 2704580464369885367301602474579828, 'val': 1}
  • id: 2358268
    {'lmfdb_iso': '47040.dn', 'p': 61, 'prec': 20, 'unit': 1386124893381444630913551168574706, 'val': 1}
  • id: 2358251
    {'lmfdb_iso': '47040.dn', 'p': 67, 'prec': 20, 'unit': 10856812629817188124715988882766533, 'val': 1}
  • id: 2358254
    {'lmfdb_iso': '47040.dn', 'p': 71, 'prec': 20, 'unit': 29657714862145458852950432651375157, 'val': 1}
  • id: 2358264
    {'lmfdb_iso': '47040.dn', 'p': 73, 'prec': 20, 'unit': 88284925888892052874317107443743536, 'val': 1}
  • id: 2358259
    {'lmfdb_iso': '47040.dn', 'p': 79, 'prec': 20, 'unit': 246534818396358512115739497655589932, 'val': 1}
  • id: 2358265
    {'lmfdb_iso': '47040.dn', 'p': 83, 'prec': 20, 'unit': 2546375798631385803290879721700360338, 'val': 1}
  • id: 2358266
    {'lmfdb_iso': '47040.dn', 'p': 89, 'prec': 20, 'unit': 4907580113973666582226143542742750914, 'val': 1}
  • id: 2358250
    {'lmfdb_iso': '47040.dn', 'p': 97, 'prec': 20, 'unit': 50393725278776967997521742297607822122, 'val': 1}