Elliptic curve data - 1734.j3

Formats: - HTML - YAML - JSON - 2025-11-12T19:25:50.607723

• 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': '1734i', 'Clabel': '1734i6', 'Cnumber': 6, 'abc_quality': 1.036242441540377, 'absD': 3030800878069216722, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 272, 'ainvs': [1, 1, 1, -475122, -151542927], 'analytic_rank': 0, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 1734, 'degree': 36864, 'elladic_images': ['16.96.0.275'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2636849576695802943625943656', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-491411892194497, 125563633938], 'lmfdb_iso': '1734.j', 'lmfdb_label': '1734.j3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1644, -30942], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.m.2', '16.96.0-8.m.2.2', '68.12.0-4.c.1.1', '136.96.0.?', '272.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 578], [17, 162, 6]], 'sha': 16, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84707828564147225423782705666', 'prec': 103}, 'szpiro_ratio': 6.864040268465708, '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, 2, -1, 0, 1, 1, 2, 4, -1, -2, 0, -2, 1, 0, 1, 4, 2], 'aplist': [1, -1, 2, 0, 4, -2, 0, 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': 1734, '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': '1734.j', 'trace_hash': 1721197873408140957}
• 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': '0.010809067483055769772951870390', 'prec': 107}, 'conductor': 1734, 'gens': [], 'heights': [], 'lmfdb_label': '1734.j3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.089718652767524935890435144755', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8709968885607979484939246321705581062', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[3251, -3255, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 3], '3': [0, 0], '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '1734.j3'}
• ec_torsion_growth •

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

  
  
  • id: 88388
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [4]}
  • id: 88387
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 2]}
  • id: 88389
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [4]}
  • id: 88391
    {'degree': 4, 'field': [16, 0, 9, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [8]}
  • id: 88390
    {'degree': 4, 'field': [81, 0, -16, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 4]}
  • id: 88392
    {'degree': 4, 'field': [81, 0, 16, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [8]}
  • id: 88397
    {'degree': 8, 'field': [-1138, 664, -772, 215, -104, -7, 7, -4, 1], 'lmfdb_label': '1734.j3', 'torsion': [6]}
  • id: 88394
    {'degree': 8, 'field': [-302, 1192, -1132, -104, 13, 44, -10, -4, 1], 'lmfdb_label': '1734.j3', 'torsion': [8]}
  • id: 88396
    {'degree': 8, 'field': [16, 0, 24, 0, 18, 0, -6, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [16]}
  • id: 88395
    {'degree': 8, 'field': [256, 0, 0, 0, 49, 0, 0, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 8]}
  • id: 88393
    {'degree': 8, 'field': [1462, -680, 812, -248, 85, 44, -10, -4, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 4]}
  • id: 88402
    {'degree': 16, 'field': [16, 0, 0, 0, 312, 0, 0, 0, 305, 0, 0, 0, 78, 0, 0, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 16]}
  • id: 88404
    {'degree': 16, 'field': [3986, -36844, 188406, -170272, -356758, 855132, -879911, 619504, -298074, 105050, -30547, 5124, -763, -70, 30, -8, 1], 'lmfdb_label': '1734.j3', 'torsion': [12]}
  • id: 88400
    {'degree': 16, 'field': [82944, 0, 0, 0, 0, 0, 0, 0, -11592, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [16]}
  • id: 88399
    {'degree': 16, 'field': [99862, 30128, 133304, -273840, 22316, 90832, 37240, -38640, -11387, 9624, 2044, -1624, -154, 168, -4, -8, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 8]}
  • id: 88398
    {'degree': 16, 'field': [100258, 25688, -8524, -71592, 159290, -222416, 166912, -21384, -59117, 30648, 5416, -5320, 98, 336, -28, -8, 1], 'lmfdb_label': '1734.j3', 'torsion': [4, 8]}
  • id: 88401
    {'degree': 16, 'field': [104976, 0, 0, 0, 0, 0, 0, 0, 13041, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 16]}
  • id: 88403
    {'degree': 16, 'field': [115788, -524616, 1393340, -2249260, 2461550, -1764956, 855877, -228728, 55992, 1314, -507, -236, 373, -182, 46, -8, 1], 'lmfdb_label': '1734.j3', 'torsion': [2, 6]}
  • id: 88405
    {'degree': 16, 'field': [399424, 0, 308272, 0, -70388, 0, 14793, 0, 12618, 0, 3993, 0, 541, 0, 34, 0, 1], 'lmfdb_label': '1734.j3', '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: 27842
    {'conductor': 1734, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1734.j3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 27843
    {'conductor': 1734, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1734.j3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 27844
    {'conductor': 1734, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '1734.j3', 'prime': 17, '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: 1675412
    {'adelic_gens': [[257, 16, 256, 17], [1, 16, 0, 1], [110, 69, 249, 146], [84, 69, 23, 146], [31, 256, 248, 143], [1, 0, 16, 1], [5, 4, 268, 269], [15, 2, 174, 259]], 'adelic_image': '272.192.1.?', 'conductor': 1734, 'lmfdb_label': '1734.j3', 'prime': 0}
  • id: 8548
    {'conductor': 1734, 'elladic_image': '16.96.0.275', 'lmfdb_label': '1734.j3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1734.j does not appear in ec_padic