Elliptic curve data - 51714.h1

Formats: - HTML - YAML - JSON - 2024-06-04T10:40:00.145315

• 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': '51714f', 'Clabel': '51714f3', 'Cnumber': 3, 'abc_quality': 1.0866579960559595, 'absD': 40786537448770633728, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 5304, 'ainvs': [1, -1, 0, -1141542, 355203252], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 51714, 'degree': 1327104, 'elladic_images': ['8.6.0.4', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4732071437462428682725441971', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [46753267515625, 11591221248], 'lmfdb_iso': '51714.h', 'lmfdb_label': '51714.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -751, -6046], 'min_quad_twist_disc': -39, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.d.1', '24.24.0.bx.1', '34.6.0.a.1', '39.8.0-3.a.1.1', '78.24.0.?', '102.24.0.?', '136.12.0.?', '312.48.0.?', '408.48.1.?', '1326.48.0.?', '5304.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8312193635633232375011249712', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.64142632068141965454817785785', 'prec': 103}, 'szpiro_ratio': 4.92535632257206, '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, 0, 0, -2, -1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0, 4, 0], 'aplist': [-1, 0, 0, -2, 0, 0, 1, 4, 6, 0, 10, -8, 6, -4, 12, -6, -12, 8, 4, 6, -2, -10, 12, -18, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 51714, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '51714.h', 'trace_hash': 340975074092719720}
• 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': '0.0071088535883989602803971449592', 'prec': 110}, 'conductor': 51714, 'gens': [[1401, 38085, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8312193635633232375011249712', 'prec': 100}], 'lmfdb_label': '51714.h1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19121496452957093956732082156', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2018785477954918819428968955748346720', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[348, -174, 1]], 'xcoord_integral_points': [348, 1401]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': [1, 3, 0], '7': [1, 0], '11': [1, 1, 0], '13': 'a', '17': [2, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '51714.h1'}
• ec_torsion_growth •

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

  
  
  • id: 2504478
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '51714.h1', 'torsion': [2, 2]}
  • id: 2504479
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '51714.h1', 'torsion': [6]}
  • id: 2504481
    {'degree': 4, 'field': [1, 0, -15, 0, 1], 'lmfdb_label': '51714.h1', 'torsion': [2, 6]}
  • id: 2504480
    {'degree': 4, 'field': [1563, 18, 61, -2, 1], 'lmfdb_label': '51714.h1', 'torsion': [4]}
  • id: 2504482
    {'degree': 6, 'field': [192, 0, 0, -27, 0, 0, 1], 'lmfdb_label': '51714.h1', 'torsion': [6]}
  • id: 2504483
    {'degree': 8, 'field': [-42059, -55820, 27151, -1586, -3060, -418, -77, -4, 1], 'lmfdb_label': '51714.h1', 'torsion': [2, 4]}
  • id: 2504485
    {'degree': 8, 'field': [1179, 504, -36, -144, 73, -12, -2, 0, 1], 'lmfdb_label': '51714.h1', 'torsion': [12]}
  • id: 2504484
    {'degree': 8, 'field': [34732, 17920, 5666, -3972, 599, -270, 65, -2, 1], 'lmfdb_label': '51714.h1', 'torsion': [2, 4]}
  • id: 2504486
    {'degree': 12, 'field': [1200, 360, 1152, -2490, 45, 1080, 187, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '51714.h1', 'torsion': [3, 6]}
  • id: 2504487
    {'degree': 12, 'field': [96256, -255360, 223056, -68524, 5181, 4992, 1721, -1212, 258, 46, -9, -6, 1], 'lmfdb_label': '51714.h1', 'torsion': [2, 6]}
  • id: 2504489
    {'degree': 16, 'field': [-342143, -934142, -334710, 955914, 1249232, -102308, -558744, 89702, 28401, -1820, 5376, -3442, 104, 258, -42, -4, 1], 'lmfdb_label': '51714.h1', 'torsion': [2, 12]}
  • id: 2504490
    {'degree': 16, 'field': [237403, 602812, 215394, -139152, 476138, -162392, -101766, 53732, 23859, -9488, -726, -76, -64, 60, 0, -4, 1], 'lmfdb_label': '51714.h1', 'torsion': [2, 12]}
  • id: 2504488
    {'degree': 16, 'field': [6456290649, -2529133104, 1720154056, -80519040, -86696008, -44662576, -10176, 886144, 1354854, -77712, -936, -9344, 408, -16, 32, 0, 1], 'lmfdb_label': '51714.h1', 'torsion': [8]}
  • id: 2504491
    {'degree': 18, 'field': [-3828672, -873936, 4234428, 1407702, -1402857, -1096551, 52551, 461178, 67470, -111746, -23904, 19080, 5024, -2946, -402, 308, -15, -9, 1], 'lmfdb_label': '51714.h1', '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: 1237656
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '51714.h1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1237657
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '51714.h1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1237658
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '51714.h1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1237659
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '51714.h1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 2007682
    {'adelic_gens': [[2653, 3276, 1638, 3745], [11, 2, 5254, 5295], [5293, 12, 5292, 13], [2039, 0, 0, 5303], [1, 0, 12, 1], [3535, 2028, 884, 5303], [1, 6, 6, 37], [5266, 819, 429, 2848], [1, 12, 0, 1], [2367, 3250, 3302, 2549]], 'adelic_image': '5304.96.1.?', 'conductor': 51714, 'lmfdb_label': '51714.h1', 'prime': 0}
  • id: 221277
    {'conductor': 51714, 'elladic_image': '8.6.0.4', 'lmfdb_label': '51714.h1', 'modell_image': '2B', 'prime': 2}
  • id: 221278
    {'conductor': 51714, 'elladic_image': '3.4.0.1', 'lmfdb_label': '51714.h1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2602324
    {'lmfdb_iso': '51714.h', 'p': 7, 'prec': 20, 'unit': 7344406400822917, 'val': 1}
  • id: 2602320
    {'lmfdb_iso': '51714.h', 'p': 19, 'prec': 20, 'unit': 1739373941041840790009905, 'val': 1}
  • id: 2602332
    {'lmfdb_iso': '51714.h', 'p': 23, 'prec': 20, 'unit': 28661197292163034757505628, 'val': 1}
  • id: 2602337
    {'lmfdb_iso': '51714.h', 'p': 31, 'prec': 20, 'unit': 1451256415332662747789333286, 'val': 1}
  • id: 2602323
    {'lmfdb_iso': '51714.h', 'p': 37, 'prec': 20, 'unit': 433059638168631236990658313383, 'val': 1}
  • id: 2602325
    {'lmfdb_iso': '51714.h', 'p': 41, 'prec': 20, 'unit': 2925756497149595319848754119841, 'val': 1}
  • id: 2602326
    {'lmfdb_iso': '51714.h', 'p': 43, 'prec': 20, 'unit': 5322772232062170160427584922339, 'val': 1}
  • id: 2602335
    {'lmfdb_iso': '51714.h', 'p': 47, 'prec': 20, 'unit': 54530412290115166375253177807554, 'val': 1}
  • id: 2602330
    {'lmfdb_iso': '51714.h', 'p': 53, 'prec': 20, 'unit': 173592273869234875251003747032536, 'val': 1}
  • id: 2602328
    {'lmfdb_iso': '51714.h', 'p': 59, 'prec': 20, 'unit': 1494465785743832315831031858566515, 'val': 1}
  • id: 2602336
    {'lmfdb_iso': '51714.h', 'p': 61, 'prec': 20, 'unit': 7505967110704749063032545296480794, 'val': 1}
  • id: 2602322
    {'lmfdb_iso': '51714.h', 'p': 67, 'prec': 20, 'unit': 19832163747415238136853062899217358, 'val': 1}
  • id: 2602334
    {'lmfdb_iso': '51714.h', 'p': 71, 'prec': 20, 'unit': 15907334646451325444994849079983, 'val': 1}
  • id: 2602331
    {'lmfdb_iso': '51714.h', 'p': 73, 'prec': 20, 'unit': 219284912910169483091555412013144544, 'val': 1}
  • id: 2602327
    {'lmfdb_iso': '51714.h', 'p': 79, 'prec': 20, 'unit': 1020432314664556209842677497970615073, 'val': 1}
  • id: 2602329
    {'lmfdb_iso': '51714.h', 'p': 83, 'prec': 20, 'unit': 2443674292399179660513325223194495509, 'val': 1}
  • id: 2602333
    {'lmfdb_iso': '51714.h', 'p': 89, 'prec': 20, 'unit': 7933769721065347084578968838593043717, 'val': 1}
  • id: 2602321
    {'lmfdb_iso': '51714.h', 'p': 97, 'prec': 20, 'unit': 24824197802839943274689666758737964006, 'val': 1}