Elliptic curve data - 47040.ce3

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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': '47040fl', 'Clabel': '47040fl7', 'Cnumber': 7, 'abc_quality': 1.0554678196515268, 'absD': 153740419343960822867558400, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [0, -1, 0, -374124865, -2848350713375], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 47040, 'degree': 18874368, 'elladic_images': ['32.96.0.58'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8071052622631376636315628013', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 56, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-187778242790732059201, 4984939585440150], 'lmfdb_iso': '47040.ce', 'lmfdb_label': '47040.ce3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -119300, -16229850], 'min_quad_twist_disc': 56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '16.48.0.v.2', '24.48.0.bp.2', '32.96.0-16.v.2.8', '48.96.1.eg.1', '56.48.0-8.bb.2.7', '80.96.2.?', '84.12.0.?', '96.192.1.?', '112.96.0.?', '160.192.2.?', '168.96.0.?', '224.192.1.?', '240.192.5.?', '336.192.1.?', '480.384.5.?', '560.192.2.?', '672.384.5.?', '1120.384.5.?', '1680.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 16, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7944294168955630469530382474', 'prec': 100}, 'szpiro_ratio': 6.588008085531551, '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, 8, 2, 0, -6, 6, -4, 0, 10, -12, 14, -12, 8, -10, -16, 12, -10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 47040, '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': '47040.ce', 'trace_hash': 1851703561843191490}
• 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': '0.00049339004789807968211510904817', 'prec': 113}, 'conductor': 47040, 'gens': [], 'heights': [], 'lmfdb_label': '47040.ce3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.017137008148548261846851693543', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0967685215070887581985083867217166351', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[22391, 0, 1]], 'xcoord_integral_points': [22391]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [1, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '47040.ce3'}
• ec_torsion_growth •

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

  
  
  • id: 2296459
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '47040.ce3', 'torsion': [4]}
  • id: 2296458
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 2]}
  • id: 2296460
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [4]}
  • id: 2296461
    {'degree': 4, 'field': [4, 0, 10, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 4]}
  • id: 2296463
    {'degree': 4, 'field': [16, 0, 6, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [8]}
  • id: 2296462
    {'degree': 4, 'field': [196, 0, -14, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [8]}
  • id: 2296469
    {'degree': 8, 'field': [-588, 0, -4382, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [6]}
  • id: 2296466
    {'degree': 8, 'field': [4, 24, 22, -104, 83, -40, 18, -4, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 8]}
  • id: 2296468
    {'degree': 8, 'field': [7406, 1288, -864, -816, 329, 92, -26, -4, 1], 'lmfdb_label': '47040.ce3', 'torsion': [16]}
  • id: 2296465
    {'degree': 8, 'field': [8716, 20880, -1880, -480, -192, -120, -20, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [8]}
  • id: 2296464
    {'degree': 8, 'field': [18025, -12600, 10600, -1200, 366, -120, -8, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 4]}
  • id: 2296467
    {'degree': 8, 'field': [135646, -59192, 64016, -9776, 5209, -388, 134, -4, 1], 'lmfdb_label': '47040.ce3', 'torsion': [16]}
  • id: 2296474
    {'degree': 16, 'field': [11908, -34288, 142752, -209648, 242208, -208896, 158104, -99008, 54888, -25720, 10840, -3768, 1176, -280, 60, -8, 1], 'lmfdb_label': '47040.ce3', 'torsion': [16]}
  • id: 2296478
    {'degree': 16, 'field': [55696, 0, 198616, 0, 131236, 0, 2576, 0, 11060, 0, -8764, 0, 616, 0, -44, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [12]}
  • id: 2296471
    {'degree': 16, 'field': [399025, 6000, 1091600, -1333200, 283900, 127200, 9200, 88800, 9106, -6960, -1456, -240, 196, 0, -16, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 8]}
  • id: 2296475
    {'degree': 16, 'field': [1565116, 5453168, 5802568, -6789360, 1764920, 3528672, -1471696, -865960, 331359, 113300, -38374, -8016, 2455, 280, -78, -4, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 16]}
  • id: 2296473
    {'degree': 16, 'field': [29160000, 0, 0, 0, 0, 0, 0, 0, -2845800, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [16]}
  • id: 2296477
    {'degree': 16, 'field': [66928761, 0, -37651392, 0, 2714796, 0, 741636, 0, 66906, 0, 3024, 0, -504, 0, 12, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 6]}
  • id: 2296479
    {'degree': 16, 'field': [144120025, 0, -48431600, 0, -406700, 0, 2632084, 0, 143962, 0, 7504, 0, -224, 0, 28, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [12]}
  • id: 2296470
    {'degree': 16, 'field': [362940601, -356634720, 175219200, 12462960, 11229946, -7615080, 2275200, -143520, 94431, -49080, 7200, -1440, 646, -120, 0, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [4, 4]}
  • id: 2296472
    {'degree': 16, 'field': [673454401, 448433280, 149299200, -9150960, -16179854, -8551080, -2044800, -144480, 176631, 58920, 7200, 1440, -554, -120, 0, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [2, 8]}
  • id: 2296476
    {'degree': 16, 'field': [26098402500, 0, -15892200000, 0, 1591650000, 0, 450684000, 0, 32915700, 0, 1188000, 0, 23400, 0, 240, 0, 1], 'lmfdb_label': '47040.ce3', 'torsion': [32]}
• 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: 1123282
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '47040.ce3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1123283
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '47040.ce3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1123284
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.ce3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1123285
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '47040.ce3', 'prime': 7, '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: 1977341
    {'adelic_gens': [[1889, 3328, 1034, 2847], [1244, 3331, 2689, 2590], [1, 0, 32, 1], [1439, 3328, 2864, 2847], [1, 32, 0, 1], [30, 31, 2089, 3204], [5, 28, 68, 381], [2711, 26, 2118, 875], [3329, 32, 3328, 33], [23, 18, 798, 1355]], 'adelic_image': '3360.768.13.?', 'conductor': 47040, 'lmfdb_label': '47040.ce3', 'prime': 0}
  • id: 203274
    {'conductor': 47040, 'elladic_image': '32.96.0.58', 'lmfdb_label': '47040.ce3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 47040.ce does not appear in ec_padic