Elliptic curve data - 4998.b1

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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': '4998i', 'Clabel': '4998i2', 'Cnumber': 2, 'abc_quality': 1.0039262932249595, 'absD': 374030581770771072, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2856, 'ainvs': [1, 1, 0, -667356, -208043184], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4998, 'degree': 112896, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1852261462469088674030174349', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [814544990575471, 9268826496], 'lmfdb_iso': '4998.b', 'lmfdb_label': '4998.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -13620, 604594], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '168.6.0.?', '408.6.0.?', '476.6.0.?', '2856.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.7421224499944928401386349309', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.72579353445542388857400287732', 'prec': 103}, 'szpiro_ratio': 6.087601453136535, '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, -4, -1, -2, 0, 2, 1, 1, -1, 4, -2], 'aplist': [-1, -1, -2, 0, -4, -2, 1, 4, 6, -10, 8, 0, 6, -8, 4, 14, -14, 14, 4, -10, 14, 4, -6, 2, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 4998, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4998.b', 'trace_hash': 263738495998481692}
• 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': '0.012645519800686497798819729711', 'prec': 107}, 'conductor': 4998, 'gens': [[1373, 37606, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.7421224499944928401386349309', 'prec': 100}], 'lmfdb_label': '4998.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16715091212108225967496464480', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8764975423560755462971733481015828356', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[-1733, 1733, 2]], 'xcoord_integral_points': [1373]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [7, 0], '3': [3, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [4, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4998.b1'}
• ec_torsion_growth •

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

  
  
  • id: 261146
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '4998.b1', 'torsion': [2, 2]}
  • id: 261147
    {'degree': 4, 'field': [1512, 0, 77, 0, 1], 'lmfdb_label': '4998.b1', 'torsion': [4]}
  • id: 261150
    {'degree': 8, 'field': [8, 26, 65, -38, -29, -38, -5, -2, 1], 'lmfdb_label': '4998.b1', 'torsion': [6]}
  • id: 261148
    {'degree': 8, 'field': [6561, 0, -486, 0, 1242, 0, -6, 0, 1], 'lmfdb_label': '4998.b1', 'torsion': [2, 4]}
  • id: 261149
    {'degree': 8, 'field': [736164, 0, -87840, 0, 4434, 0, -120, 0, 1], 'lmfdb_label': '4998.b1', 'torsion': [2, 4]}
  • id: 261152
    {'degree': 16, 'field': [186624, 0, -4839912, 0, 717588, 0, 3024, 0, 19332, 0, -588, 0, -180, 0, 0, 0, 1], 'lmfdb_label': '4998.b1', 'torsion': [2, 6]}
  • id: 261151
    {'degree': 16, 'field': [262440000, 0, 138272832, 0, 258602112, 0, -28732176, 0, 18660996, 0, 175848, 0, -5898, 0, -68, 0, 1], 'lmfdb_label': '4998.b1', 'torsion': [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: 96784
    {'conductor': 4998, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '4998.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 96785
    {'conductor': 4998, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4998.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 96786
    {'conductor': 4998, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4998.b1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 96787
    {'conductor': 4998, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '4998.b1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1696596
    {'adelic_gens': [[1, 0, 4, 1], [1636, 1, 2447, 0], [3, 4, 8, 11], [2, 1, 1427, 0], [1, 2, 2, 5], [1, 4, 0, 1], [2689, 4, 2522, 9], [2853, 4, 2852, 5], [1906, 1, 1903, 0], [1073, 1786, 1784, 1071]], 'adelic_image': '2856.12.0.?', 'conductor': 4998, 'lmfdb_label': '4998.b1', 'prime': 0}
  • id: 24788
    {'conductor': 4998, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4998.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 183772
    {'lmfdb_iso': '4998.b', 'p': 5, 'prec': 20, 'unit': 4985472190226, 'val': 1}
  • id: 183771
    {'lmfdb_iso': '4998.b', 'p': 11, 'prec': 20, 'unit': 54510469102607619839, 'val': 1}
  • id: 183777
    {'lmfdb_iso': '4998.b', 'p': 13, 'prec': 20, 'unit': 225223003253490534934, 'val': 1}
  • id: 183780
    {'lmfdb_iso': '4998.b', 'p': 19, 'prec': 20, 'unit': 335258072560496325466386, 'val': 1}
  • id: 183783
    {'lmfdb_iso': '4998.b', 'p': 23, 'prec': 20, 'unit': 66659603998351900995224410, 'val': 1}
  • id: 183776
    {'lmfdb_iso': '4998.b', 'p': 29, 'prec': 20, 'unit': 8469594703905868076987131, 'val': 1}
  • id: 183788
    {'lmfdb_iso': '4998.b', 'p': 31, 'prec': 20, 'unit': 7127360894496506890012221260, 'val': 1}
  • id: 183774
    {'lmfdb_iso': '4998.b', 'p': 41, 'prec': 20, 'unit': 109588419374411583655500711263, 'val': 1}
  • id: 183775
    {'lmfdb_iso': '4998.b', 'p': 43, 'prec': 20, 'unit': 4102195733997865375733975898142, 'val': 1}
  • id: 183785
    {'lmfdb_iso': '4998.b', 'p': 47, 'prec': 20, 'unit': 55892861994886301419387061177970, 'val': 1}
  • id: 183781
    {'lmfdb_iso': '4998.b', 'p': 53, 'prec': 20, 'unit': 110245940433980898424584568730014, 'val': 1}
  • id: 183779
    {'lmfdb_iso': '4998.b', 'p': 59, 'prec': 20, 'unit': 4044238950249066339166992336333088, 'val': 1}
  • id: 183786
    {'lmfdb_iso': '4998.b', 'p': 61, 'prec': 20, 'unit': 6371701195947135129066119010596825, 'val': 1}
  • id: 183770
    {'lmfdb_iso': '4998.b', 'p': 67, 'prec': 20, 'unit': 24322663423424536114223176516128029, 'val': 1}
  • id: 183773
    {'lmfdb_iso': '4998.b', 'p': 71, 'prec': 20, 'unit': 12597342369559862366335775678360296, 'val': 1}
  • id: 183782
    {'lmfdb_iso': '4998.b', 'p': 73, 'prec': 20, 'unit': 56854287537718457577369714565362433, 'val': 1}
  • id: 183778
    {'lmfdb_iso': '4998.b', 'p': 79, 'prec': 20, 'unit': 816041667994890583246623382297239690, 'val': 1}
  • id: 183787
    {'lmfdb_iso': '4998.b', 'p': 83, 'prec': 20, 'unit': 242149605138834860835429895616187057, 'val': 1}
  • id: 183784
    {'lmfdb_iso': '4998.b', 'p': 89, 'prec': 20, 'unit': 10033545212497887581183582053319592808, 'val': 1}
  • id: 183769
    {'lmfdb_iso': '4998.b', 'p': 97, 'prec': 20, 'unit': 33593777568446029747946014790871939452, 'val': 1}