Elliptic curve data - 17745.j3

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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': '17745w', 'Clabel': '17745w4', 'Cnumber': 4, 'abc_quality': 0.9573510240464985, 'absD': 31657134775745115, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3640, 'ainvs': [1, 0, 0, -16650, -8601633], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 17745, 'degree': 172032, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8459549640224023211195048858', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4], 'jinv': [-105756712489, 6558605235], 'lmfdb_iso': '17745.j', 'lmfdb_label': '17745.j3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -99, -3923], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '70.6.0.a.1', '140.12.0.?', '260.12.0.?', '280.24.0.?', '364.12.0.?', '520.24.0.?', '728.24.0.?', '1820.24.0.?', '3640.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 5915], [3, 4, 5915], [5, 6, 3549], [7, 8, 2535], [13, 98, 105]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56348028529163395309276116502', 'prec': 103}, 'szpiro_ratio': 4.646198176978782, '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, 1, -1, 1, 3, 1, -1, -4, -1, 0, -1, 1, -1, 6, -1, -8, -1], 'aplist': [-1, 1, 1, 1, -4, 0, 6, -8, -4, -2, 4, -10, 2, 8, -8, 6, -8, -10, 12, 8, -6, 8, 4, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 17745, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '17745.j', 'trace_hash': 2022058243476571307}
• 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': '0.024924352833005905203361172372', 'prec': 107}, 'conductor': 17745, 'gens': [], 'heights': [], 'lmfdb_label': '17745.j3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16287119287403643277683433052', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3029695429922914622146746441919906383', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[927, -927, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 2], '3': [1, 0], '5': [5, 0], '7': [1, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '17745.j3'}
• ec_torsion_growth •

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

  
  
  • id: 908281
    {'degree': 2, 'field': [-91, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [4]}
  • id: 908280
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '17745.j3', 'torsion': [2, 2]}
  • id: 908282
    {'degree': 2, 'field': [65, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [4]}
  • id: 908284
    {'degree': 4, 'field': [-1260, 0, -28, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [8]}
  • id: 908283
    {'degree': 4, 'field': [1521, 0, -13, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [2, 4]}
  • id: 908288
    {'degree': 8, 'field': [-1990401, 88404, -93264, 9719, -4856, -7, 7, -4, 1], 'lmfdb_label': '17745.j3', 'torsion': [6]}
  • id: 908286
    {'degree': 8, 'field': [1225, 0, 0, 0, 970, 0, 0, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [8]}
  • id: 908285
    {'degree': 8, 'field': [19600, 0, 0, 0, 2555, 0, 0, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [2, 4]}
  • id: 908287
    {'degree': 8, 'field': [936441, -222660, 220878, 3584, -1841, 56, -14, -4, 1], 'lmfdb_label': '17745.j3', 'torsion': [2, 8]}
  • id: 908289
    {'degree': 16, 'field': [900492100, 2443354200, 2538419600, 1215093600, 259921230, 41130180, 17353240, 1500030, -832589, 17010, -3524, -11970, 561, 0, -4, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [4, 4]}
  • id: 908292
    {'degree': 16, 'field': [2184128961, 407639379, 330583031, -45629930, 141877520, -26233907, 14947046, 1184146, -208755, -124230, 28740, -5956, 1318, -70, 25, -4, 1], 'lmfdb_label': '17745.j3', 'torsion': [2, 6]}
  • id: 908290
    {'degree': 16, 'field': [2503601296, 0, 356984768, 0, -50541312, 0, -1409504, 0, 469480, 0, 2416, 0, -1152, 0, 8, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [2, 8]}
  • id: 908294
    {'degree': 16, 'field': [50254430625, 0, 18254202750, 0, 3726549225, 0, 246973475, 0, -9765700, 0, -294070, 0, 2965, 0, 130, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [12]}
  • id: 908293
    {'degree': 16, 'field': [567869252041, 0, -151503188837, 0, 2825595241, 0, -1088190824, 0, 41432146, 0, -145061, 0, -7889, 0, 7, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [12]}
  • id: 908291
    {'degree': 16, 'field': [2206933080625, 0, 541908640000, 0, 60376197700, 0, 1009645000, 0, 86690275, 0, 1680280, 0, -39788, 0, -224, 0, 1], 'lmfdb_label': '17745.j3', 'torsion': [16]}
• 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: 397305
    {'conductor': 17745, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '17745.j3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 397306
    {'conductor': 17745, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '17745.j3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 397307
    {'conductor': 17745, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '17745.j3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 397308
    {'conductor': 17745, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '17745.j3', 'prime': 13, '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: 1782309
    {'adelic_gens': [[3079, 3632, 1396, 3607], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [736, 3, 5, 2], [2283, 2276, 2322, 461], [7, 6, 3634, 3635], [459, 458, 1378, 3195], [3633, 8, 3632, 9], [2084, 1, 1063, 6]], 'adelic_image': '3640.48.0.?', 'conductor': 17745, 'lmfdb_label': '17745.j3', 'prime': 0}
  • id: 83102
    {'conductor': 17745, 'elladic_image': '8.12.0.6', 'lmfdb_label': '17745.j3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 17745.j does not appear in ec_padic