Elliptic curve data - 54978.q3

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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': '54978bh', 'Clabel': '54978bh1', 'Cnumber': 1, 'abc_quality': 0.9879715979533532, 'absD': 813594904542427392, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 31416, 'ainvs': [1, 0, 1, -405697, 89459444], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 54978, 'degree': 1105920, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1700738831084011630414874064', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 4], 'jinv': [62768149033310713, 6915442583808], 'lmfdb_iso': '54978.q', 'lmfdb_label': '54978.q3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -8279, -264363], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '66.6.0.a.1', '84.12.0.?', '132.12.0.?', '308.12.0.?', '408.12.0.?', '924.24.0.?', '952.12.0.?', '1496.12.0.?', '2856.24.0.?', '4488.24.0.?', '10472.24.0.?', '31416.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 13, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.23433016914773489728164384899', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 1617], [3, 4, 1666], [5, 2, 18326], [7, 26, 1122], [11, 12, 4998], [17, 18, 3234]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1971188085807445104888110347', 'prec': 100}, 'szpiro_ratio': 4.613387325466961, '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, -2, -1, 0, -1, 1, 2, 1, 1, -6, 0, -2, 1, 1, -1, -4, -2], 'aplist': [-1, 1, -2, 0, 1, -6, 1, -4, 0, 2, 0, -10, 10, -4, -4, -2, 0, -2, 12, 0, 10, 4, 12, 14, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 54978, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '54978.q', 'trace_hash': 1463276707417532448}
• 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': '0.013034601987303215373948680165', 'prec': 107}, 'conductor': 54978, 'gens': [[187, 4394, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.23433016914773489728164384899', 'prec': 103}], 'lmfdb_label': '54978.q3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27366131502537328019864622645', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8476261343452371781359734301057483647', 'prec': 130}, 'tamagawa_product': 240, 'torsion_generators': [[459, -230, 1]], 'xcoord_integral_points': [-629, -374, 187, 459, 484, 748, 1243]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 0], '3': [2, 0], '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 0], '17': [2, 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': '54978.q3'}
• ec_torsion_growth •

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

  
  
  • id: 2656352
    {'degree': 2, 'field': [-19, -1, 1], 'lmfdb_label': '54978.q3', 'torsion': [4]}
  • id: 2656351
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '54978.q3', 'torsion': [2, 2]}
  • id: 2656353
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '54978.q3', 'torsion': [4]}
  • id: 2656354
    {'degree': 4, 'field': [-17, 37, -16, -1, 1], 'lmfdb_label': '54978.q3', 'torsion': [2, 4]}
  • id: 2656358
    {'degree': 8, 'field': [-3972, 7260, 4092, -724, -154, 122, 1, -2, 1], 'lmfdb_label': '54978.q3', 'torsion': [6]}
  • id: 2656355
    {'degree': 8, 'field': [2046, 3366, 1749, 528, 196, 16, 18, -2, 1], 'lmfdb_label': '54978.q3', 'torsion': [2, 4]}
  • id: 2656356
    {'degree': 8, 'field': [4761, 0, -101018, 0, 7707, 0, -174, 0, 1], 'lmfdb_label': '54978.q3', 'torsion': [8]}
  • id: 2656357
    {'degree': 8, 'field': [5380, 2206, -1145, -410, 172, -8, -2, -2, 1], 'lmfdb_label': '54978.q3', 'torsion': [8]}
  • id: 2656362
    {'degree': 16, 'field': [-41798336, 300812552, -598361676, 438933956, -88356416, 1850004, 22095874, -9067672, -105909, 187856, -17618, -900, 2380, -16, -60, -4, 1], 'lmfdb_label': '54978.q3', 'torsion': [2, 6]}
  • id: 2656360
    {'degree': 16, 'field': [-36931751, 123852734, 40031526, -267406838, -8749428, 147807720, -12278300, -28618742, 3405261, 2329736, -299108, -87150, 11340, 1442, -186, -8, 1], 'lmfdb_label': '54978.q3', 'torsion': [2, 8]}
  • id: 2656364
    {'degree': 16, 'field': [324, 0, -2823957, 0, 1177506, 0, -271755, 0, 54819, 0, -8511, 0, 747, 0, -42, 0, 1], 'lmfdb_label': '54978.q3', 'torsion': [12]}
  • id: 2656363
    {'degree': 16, 'field': [36864, 0, -138240, 0, -721664, 0, 34560, 0, -1195584, 0, 56160, 0, 3792, 0, 0, 0, 1], 'lmfdb_label': '54978.q3', 'torsion': [12]}
  • id: 2656359
    {'degree': 16, 'field': [1713481, 0, -897820, 0, 688930, 0, -63580, 0, 32803, 0, -7300, 0, 754, 0, -40, 0, 1], 'lmfdb_label': '54978.q3', 'torsion': [4, 4]}
  • id: 2656361
    {'degree': 16, 'field': [13307904, 4771584, 3852432, -1351872, -1733340, -115896, -174639, 87822, 38935, 22120, 15625, 382, 1861, -80, 79, -2, 1], 'lmfdb_label': '54978.q3', 'torsion': [2, 8]}
• 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: 1320633
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '54978.q3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1320634
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '54978.q3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 1320635
    {'conductor': 54978, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '54978.q3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1320636
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54978.q3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1320637
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '54978.q3', 'prime': 17, 'reduction_type': 1, '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: 2029475
    {'adelic_gens': [[29737, 29736, 574, 2815], [1, 0, 8, 1], [1, 8, 0, 1], [31409, 8, 31408, 9], [1, 4, 4, 17], [21883, 21882, 16282, 18523], [7484, 26929, 1519, 8982], [7, 6, 31410, 31411], [25712, 17955, 28973, 26930], [5545, 26936, 4228, 13497], [22439, 0, 0, 31415]], 'adelic_image': '31416.48.0.?', 'conductor': 54978, 'lmfdb_label': '54978.q3', 'prime': 0}
  • id: 234422
    {'conductor': 54978, 'elladic_image': '4.6.0.1', 'lmfdb_label': '54978.q3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2781373
    {'lmfdb_iso': '54978.q', 'p': 5, 'prec': 20, 'unit': 52131624246949, 'val': 0}
  • id: 2781365
    {'lmfdb_iso': '54978.q', 'p': 13, 'prec': 20, 'unit': 362640964181381122058, 'val': 1}
  • id: 2781367
    {'lmfdb_iso': '54978.q', 'p': 19, 'prec': 20, 'unit': 1968122064965877562367552, 'val': 1}
  • id: 2781364
    {'lmfdb_iso': '54978.q', 'p': 29, 'prec': 20, 'unit': 501009960785740103877490355, 'val': 1}
  • id: 2781361
    {'lmfdb_iso': '54978.q', 'p': 37, 'prec': 20, 'unit': 74267035403710088968375656223, 'val': 1}
  • id: 2781362
    {'lmfdb_iso': '54978.q', 'p': 41, 'prec': 20, 'unit': 3206335911250894807892140788044, 'val': 1}
  • id: 2781363
    {'lmfdb_iso': '54978.q', 'p': 43, 'prec': 20, 'unit': 6865612862995949297444106017890, 'val': 1}
  • id: 2781366
    {'lmfdb_iso': '54978.q', 'p': 47, 'prec': 20, 'unit': 12803840118979757564421852300164, 'val': 1}
  • id: 2781368
    {'lmfdb_iso': '54978.q', 'p': 53, 'prec': 20, 'unit': 504106174462780363673948492425020, 'val': 1}
  • id: 2781372
    {'lmfdb_iso': '54978.q', 'p': 61, 'prec': 20, 'unit': 3839910875867189240012206112013193, 'val': 1}
  • id: 2781360
    {'lmfdb_iso': '54978.q', 'p': 67, 'prec': 20, 'unit': 31117502199036087521725386535931572, 'val': 1}
  • id: 2781369
    {'lmfdb_iso': '54978.q', 'p': 73, 'prec': 20, 'unit': 172470584874400379449911637663194262, 'val': 1}
  • id: 2781371
    {'lmfdb_iso': '54978.q', 'p': 79, 'prec': 20, 'unit': 248838318596835015570242382414261983, 'val': 1}
  • id: 2781359
    {'lmfdb_iso': '54978.q', 'p': 83, 'prec': 20, 'unit': 925851333135950493057521936974489209, 'val': 1}
  • id: 2781370
    {'lmfdb_iso': '54978.q', 'p': 89, 'prec': 20, 'unit': 3374422626527543947703115026744395610, 'val': 1}
  • id: 2781358
    {'lmfdb_iso': '54978.q', 'p': 97, 'prec': 20, 'unit': 6040563919215096191944883446735373989, 'val': 1}