Elliptic curve data - 47610.bu4

Formats: - HTML - YAML - JSON - 2026-07-26T18:21:53.425436

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '47610bz', 'Clabel': '47610bz5', 'Cnumber': 5, 'abc_quality': 1.0501740895315954, 'absD': 3642238003983750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 2760, 'ainvs': [1, -1, 1, -1373648, 620007581], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 23], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 47610, 'degree': 811008, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1319130931809265256926187375', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 46, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [2656166199049, 33750], 'lmfdb_iso': '47610.bu', 'lmfdb_label': '47610.bu4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -289, 1862], 'min_quad_twist_disc': 69, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.4', '24.96.1.da.3', '40.12.0.bb.1', '69.8.0-3.a.1.1', '92.12.0.?', '120.192.5.?', '138.24.0.?', '276.96.0.?', '552.192.1.?', '920.24.0.?', '2760.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 4761], [3, 2, 5290], [5, 6, 9522], [23, 266, 90]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703132', 'prec': 107}, 'szpiro_ratio': 5.014720676746942, '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, 0, 1, -1, 0, 4, 1, 0, -1, 0, 0, 2, 4, 0, 1, 6, 0, 4, -1], 'aplist': [1, 0, -1, 4, 0, 2, 6, 4, 0, 6, 8, -2, 6, 4, 0, -6, 0, 10, 4, 0, 2, -8, 12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 47610, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '47610.bu', 'trace_hash': 165428160184926014}
• 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': '0.014068371090718548518085145531', 'prec': 107}, 'conductor': 47610, 'gens': [], 'heights': [], 'lmfdb_label': '47610.bu4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.40352715068814660625432089169', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.4564344110103457000691342670967880936', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[2715, -2719, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': 'a', '5': [0, 0], '23': 'a'}, 'iwp0': 5, 'lmfdb_label': '47610.bu4'}
• ec_torsion_growth •

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

  
  
  • id: 2322550
    {'degree': 2, 'field': [-138, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [4]}
  • id: 2322551
    {'degree': 2, 'field': [-23, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [4]}
  • id: 2322552
    {'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '47610.bu4', 'torsion': [6]}
  • id: 2322549
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 2]}
  • id: 2322556
    {'degree': 4, 'field': [25, 0, -13, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [12]}
  • id: 2322554
    {'degree': 4, 'field': [100, 0, -26, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 6]}
  • id: 2322555
    {'degree': 4, 'field': [223, 38, -37, -2, 1], 'lmfdb_label': '47610.bu4', 'torsion': [12]}
  • id: 2322553
    {'degree': 4, 'field': [289, 0, -58, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 4]}
  • id: 2322557
    {'degree': 6, 'field': [522, -204, 108, 1, 11, -1, 1], 'lmfdb_label': '47610.bu4', 'torsion': [6]}
  • id: 2322561
    {'degree': 8, 'field': [-207, 828, -792, -72, 289, -12, -34, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 12]}
  • id: 2322558
    {'degree': 8, 'field': [1038, -1272, 1476, -432, 277, -76, 30, -4, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 4]}
  • id: 2322559
    {'degree': 8, 'field': [15376, 0, -22944, 0, 2782, 0, -96, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [8]}
  • id: 2322560
    {'degree': 8, 'field': [58501, 8074, 9919, 1678, 478, 34, 31, -2, 1], 'lmfdb_label': '47610.bu4', 'torsion': [8]}
  • id: 2322562
    {'degree': 12, 'field': [25281, 0, 45015, 0, 17758, 0, 3995, 0, 498, 0, 35, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [3, 6]}
  • id: 2322565
    {'degree': 12, 'field': [67978, 1232, -20730, -5746, 5076, 4948, -1767, -1208, 339, 110, -27, -4, 1], 'lmfdb_label': '47610.bu4', 'torsion': [12]}
  • id: 2322564
    {'degree': 12, 'field': [70872, -10080, 7132, 2216, 8766, -13776, 7925, -3102, 1089, -220, 55, -6, 1], 'lmfdb_label': '47610.bu4', 'torsion': [12]}
  • id: 2322563
    {'degree': 12, 'field': [193896, 1728, 4668, -15480, 14986, -10200, 6005, -2430, 861, -180, 47, -6, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 6]}
  • id: 2322567
    {'degree': 16, 'field': [820836, 0, -5084112, 0, 5877940, 0, -2757792, 0, 623229, 0, -71428, 0, 4110, 0, -108, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 8]}
  • id: 2322566
    {'degree': 16, 'field': [1077444, 0, -1446192, 0, 1654620, 0, -500016, 0, 91525, 0, -10340, 0, 846, 0, -44, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [4, 4]}
  • id: 2322569
    {'degree': 16, 'field': [2112300, -1679040, 2878128, -2752272, 2345298, -1409952, 918528, -461616, 219319, -81296, 28984, -7856, 2098, -392, 76, -8, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 12]}
  • id: 2322571
    {'degree': 16, 'field': [4045621, 2940708, -3594666, -1793136, 1889464, 393936, -489798, -43032, 79581, 2352, -8466, 48, 664, -12, -36, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [24]}
  • id: 2322568
    {'degree': 16, 'field': [30569841, 0, -13407264, 0, 3288066, 0, -641124, 0, 80419, 0, -6356, 0, 438, 0, -20, 0, 1], 'lmfdb_label': '47610.bu4', 'torsion': [2, 8]}
  • id: 2322570
    {'degree': 16, 'field': [594854551, 752439408, -420977812, -595519624, 136180436, 174872376, -27714328, -23986824, 3298129, 1678440, -217460, -61472, 7758, 1120, -140, -8, 1], 'lmfdb_label': '47610.bu4', 'torsion': [24]}
  • id: 2322572
    {'degree': 18, 'field': [-52558421, 187111749, 47194038, -65398472, 44781339, -28568055, 7727381, -1754739, 275235, -70166, 37041, -9819, -3409, 2418, -789, 130, 0, -6, 1], 'lmfdb_label': '47610.bu4', 'torsion': [18]}
• 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: 1137502
    {'conductor': 47610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '47610.bu4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1137503
    {'conductor': 47610, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '47610.bu4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1137504
    {'conductor': 47610, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '47610.bu4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1137505
    {'conductor': 47610, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '47610.bu4', 'prime': 23, '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: 1981344
    {'adelic_gens': [[1657, 1104, 2484, 2209], [2737, 24, 2736, 25], [1, 12, 12, 145], [15, 106, 1454, 1811], [2646, 529, 1955, 1496], [1559, 0, 0, 2759], [1, 24, 0, 1], [344, 759, 2185, 574], [1174, 483, 2415, 2554], [1, 0, 24, 1]], 'adelic_image': '2760.384.5.?', 'conductor': 47610, 'lmfdb_label': '47610.bu4', 'prime': 0}
  • id: 205740
    {'conductor': 47610, 'elladic_image': '4.6.0.1', 'lmfdb_label': '47610.bu4', 'modell_image': '2B', 'prime': 2}
  • id: 205741
    {'conductor': 47610, 'elladic_image': '3.4.0.1', 'lmfdb_label': '47610.bu4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 47610.bu does not appear in ec_padic