Elliptic curve data - 51714.r3

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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': '51714p', 'Clabel': '51714p5', 'Cnumber': 5, 'abc_quality': 1.036242441540377, 'absD': 441826253527825360818, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 10608, 'ainvs': [1, -1, 1, -2500556, 1827946865], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 51714, 'degree': 2359296, 'elladic_images': ['8.48.0.224'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6788591087062954679621933959', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-491411892194497, 125563633938], 'lmfdb_iso': '51714.r', 'lmfdb_label': '51714.r3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1644, -30942], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.m.2', '156.12.0.?', '272.96.1.?', '312.96.0.?', '10608.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.031416099670777945132040861', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1521], [3, 8, 5746], [13, 86, 306], [17, 18, 3042]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84707828564147225423782705665', 'prec': 103}, 'szpiro_ratio': 5.1757924804564, '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, -2, 0, 0, 1, 0, -2, -4, 0, 0, 0, 0, 1, -1, 0, -4, -2], 'aplist': [1, 0, -2, 0, -4, 0, -1, -4, 0, 10, -8, 2, 10, 12, 0, -6, 12, -10, 12, 0, -10, -8, 4, -6, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 51714, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '51714.r', 'trace_hash': 1098033349666279345}
• 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': '0.0047116448003063611830815845289', 'prec': 110}, 'conductor': 51714, 'gens': [[-157811, 421323297, 20]], 'heights': [{'__RealLiteral__': 0, 'data': '11.031416099670777945132040861', 'prec': 100}], 'lmfdb_label': '51714.r3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.15908441584141470233084280048', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0197055444788123831535493461959885558', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-7461, 7457, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 1], '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '51714.r3'}
• ec_torsion_growth •

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

  
  
  • id: 2504665
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [4]}
  • id: 2504664
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [2, 2]}
  • id: 2504666
    {'degree': 2, 'field': [78, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [4]}
  • id: 2504669
    {'degree': 4, 'field': [100, 0, -19, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [8]}
  • id: 2504668
    {'degree': 4, 'field': [361, 0, -40, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [8]}
  • id: 2504667
    {'degree': 4, 'field': [361, 0, 40, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [2, 4]}
  • id: 2504673
    {'degree': 8, 'field': [-976, 3288, -5276, 3388, 72, 113, 59, -3, 1], 'lmfdb_label': '51714.r3', 'torsion': [6]}
  • id: 2504670
    {'degree': 8, 'field': [1024, 0, 0, 0, -14, 0, 0, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [2, 4]}
  • id: 2504671
    {'degree': 8, 'field': [1024, 0, 0, 0, 14, 0, 0, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [8]}
  • id: 2504672
    {'degree': 8, 'field': [10000, 0, 0, 0, 161, 0, 0, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [2, 8]}
  • id: 2504676
    {'degree': 16, 'field': [38416, 0, 1204224, 0, -7573248, 0, -3791040, 0, -434479, 0, 15360, 0, 2112, 0, -96, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [16]}
  • id: 2504674
    {'degree': 16, 'field': [65536, 0, -81920, 0, 51200, 0, -33600, 0, 14129, 0, -2100, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [4, 8]}
  • id: 2504675
    {'degree': 16, 'field': [1015564, 288, 900048, 766272, 109064, 163584, 158208, 24576, 2280, 144, -600, -864, -28, 0, 0, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [2, 8]}
  • id: 2504677
    {'degree': 16, 'field': [35078992, -26017888, 42971864, -38887056, 32667946, -18112784, 9986730, -3815992, 1517873, -415700, 124258, -24144, 5480, -700, 120, -8, 1], 'lmfdb_label': '51714.r3', 'torsion': [16]}
  • id: 2504678
    {'degree': 16, 'field': [106654752, -157158144, 259323216, -181108800, 140636496, -47846928, 22923288, -1098744, 895478, 464460, 31609, 15830, 4365, -212, 143, -6, 1], 'lmfdb_label': '51714.r3', 'torsion': [2, 6]}
  • id: 2504679
    {'degree': 16, 'field': [113550336, 0, -64068096, 0, 18552496, 0, -4037367, 0, 575082, 0, -51223, 0, 2697, 0, -78, 0, 1], 'lmfdb_label': '51714.r3', 'torsion': [12]}
  • id: 2504680
    {'degree': 16, 'field': [18547171344, 0, 9006175464, 0, 1644633844, 0, 165530040, 0, 10348884, 0, 416852, 0, 10608, 0, 156, 0, 1], 'lmfdb_label': '51714.r3', '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: 1237740
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51714.r3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1237741
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '51714.r3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1237742
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '51714.r3', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1237743
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '51714.r3', 'prime': 17, 'reduction_type': -1, '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: 2007704
    {'adelic_gens': [[10593, 16, 10592, 17], [1, 16, 0, 1], [7343, 0, 0, 10607], [3535, 0, 0, 10607], [1444, 8229, 6279, 7762], [1873, 4368, 6552, 3121], [1, 0, 16, 1], [5, 4, 10604, 10605], [8542, 8229, 4329, 7762], [15, 2, 10510, 10595]], 'adelic_image': '10608.192.1.?', 'conductor': 51714, 'lmfdb_label': '51714.r3', 'prime': 0}
  • id: 221301
    {'conductor': 51714, 'elladic_image': '8.48.0.224', 'lmfdb_label': '51714.r3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2602566
    {'lmfdb_iso': '51714.r', 'p': 5, 'prec': 20, 'unit': 12300314408908, 'val': 1}
  • id: 2602559
    {'lmfdb_iso': '51714.r', 'p': 11, 'prec': 20, 'unit': 31069457313411507776, 'val': 1}
  • id: 2602560
    {'lmfdb_iso': '51714.r', 'p': 19, 'prec': 20, 'unit': 255030065696486648465037, 'val': 1}
  • id: 2602557
    {'lmfdb_iso': '51714.r', 'p': 29, 'prec': 20, 'unit': 4463392126217334329796033779, 'val': 1}
  • id: 2602554
    {'lmfdb_iso': '51714.r', 'p': 31, 'prec': 20, 'unit': 5456091671341686601848796730, 'val': 1}
  • id: 2602553
    {'lmfdb_iso': '51714.r', 'p': 37, 'prec': 20, 'unit': 584186826094041325090361214401, 'val': 1}
  • id: 2602555
    {'lmfdb_iso': '51714.r', 'p': 41, 'prec': 20, 'unit': 3671672380521893778146034361364, 'val': 1}
  • id: 2602556
    {'lmfdb_iso': '51714.r', 'p': 43, 'prec': 20, 'unit': 8845376164281980623336293712572, 'val': 1}
  • id: 2602561
    {'lmfdb_iso': '51714.r', 'p': 53, 'prec': 20, 'unit': 224510403896887081291830254373806, 'val': 1}
  • id: 2602564
    {'lmfdb_iso': '51714.r', 'p': 59, 'prec': 20, 'unit': 2054746578245957721171306085088530, 'val': 1}
  • id: 2602565
    {'lmfdb_iso': '51714.r', 'p': 61, 'prec': 20, 'unit': 4477188547868777301894734523265857, 'val': 1}
  • id: 2602552
    {'lmfdb_iso': '51714.r', 'p': 67, 'prec': 20, 'unit': 20954183337915697929368436407811094, 'val': 1}
  • id: 2602562
    {'lmfdb_iso': '51714.r', 'p': 73, 'prec': 20, 'unit': 76814841240930742514933114713412927, 'val': 1}
  • id: 2602558
    {'lmfdb_iso': '51714.r', 'p': 79, 'prec': 20, 'unit': 1114114630320119143391605272006439809, 'val': 1}
  • id: 2602551
    {'lmfdb_iso': '51714.r', 'p': 83, 'prec': 20, 'unit': 1034998292838638025153262177917779785, 'val': 1}
  • id: 2602563
    {'lmfdb_iso': '51714.r', 'p': 89, 'prec': 20, 'unit': 9439951435410827574211656249800175059, 'val': 1}
  • id: 2602550
    {'lmfdb_iso': '51714.r', 'p': 97, 'prec': 20, 'unit': 31383608604234088447957631131258199338, 'val': 1}