Elliptic curve data - 1734.l2

Formats: - HTML - YAML - JSON - 2025-10-18T08:10:15.804174

• 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': '1734l', 'Clabel': '1734l1', 'Cnumber': 1, 'abc_quality': 1.037140822363524, 'absD': 70299562860135936, 'adelic_genus': 2, 'adelic_index': 144, 'adelic_level': 72, 'ainvs': [1, 0, 0, -463562, -122187996], 'analytic_rank': 0, 'bad_primes': [2, 3, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 1734, 'degree': 38556, 'elladic_images': ['9.72.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0698456763578888448107207900', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 11, 'isogeny_degrees': [1, 3], 'jinv': [-1579268174113, 10077696], 'lmfdb_iso': '1734.l', 'lmfdb_label': '1734.l2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1604, -25531], 'min_quad_twist_disc': 17, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '9.72.0-9.f.2.2', '24.16.0-24.d.1.8', '72.144.2.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 867], [3, 4, 289], [17, 114, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18103678032041145797769771142', 'prec': 103}, 'szpiro_ratio': 6.806568620645966, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, -3, 1, -4, 1, 1, -3, 3, 1, 2, -4, -3, 1, 0, 1, 8, -3], 'aplist': [1, 1, -3, -4, 3, 2, 0, 8, 6, 3, -7, 8, 6, -4, -6, -9, 15, 14, 2, 0, -7, -1, 12, 0, -13], 'class_deg': 3, 'class_size': 2, 'conductor': 1734, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '1734.l', 'trace_hash': 543888392391500011}
• 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': '0.015927766807894133861015022468', 'prec': 107}, 'conductor': 1734, 'gens': [], 'heights': [], 'lmfdb_label': '1734.l2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.091448583834496025560690366973', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4691117635313926901386399082596146350', 'prec': 130}, 'tamagawa_product': 243, 'torsion_generators': [[1180, 30622, 1]], 'xcoord_integral_points': [1180]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [5, 0], '17': 'a'}, 'iwp0': 5, 'lmfdb_label': '1734.l2'}
• ec_torsion_growth •

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

  
  
  • id: 88433
    {'degree': 3, 'field': [-12, 6, -1, 1], 'lmfdb_label': '1734.l2', 'torsion': [9]}
  • id: 88432
    {'degree': 3, 'field': [39, -11, -1, 1], 'lmfdb_label': '1734.l2', 'torsion': [6]}
  • id: 88435
    {'degree': 6, 'field': [12, 0, -11, 0, 1, 0, 1], 'lmfdb_label': '1734.l2', 'torsion': [3, 9]}
  • id: 88434
    {'degree': 6, 'field': [24, -120, 142, 52, 15, -2, 1], 'lmfdb_label': '1734.l2', 'torsion': [2, 6]}
  • id: 88436
    {'degree': 9, 'field': [24, -42, 74, -57, 47, -26, 5, 4, -3, 1], 'lmfdb_label': '1734.l2', 'torsion': [18]}
  • id: 88437
    {'degree': 12, 'field': [-7776, 0, 729, 0, 621, 0, 126, 0, 54, 0, 13, 0, 1], 'lmfdb_label': '1734.l2', 'torsion': [12]}
  • id: 88439
    {'degree': 18, 'field': [24, 0, 2092, 0, 3042, 0, 3873, 0, 2040, 0, 880, 0, 126, 0, 48, 0, 6, 0, 1], 'lmfdb_label': '1734.l2', 'torsion': [2, 18]}
  • id: 88438
    {'degree': 18, 'field': [108, -234, 813, -537, 1639, 4, 1501, 673, 640, 581, 54, 197, -40, 7, -3, -14, 5, -3, 1], 'lmfdb_label': '1734.l2', 'torsion': [3, 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: 27854
    {'conductor': 1734, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '1734.l2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 27855
    {'conductor': 1734, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '1734.l2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 27856
    {'conductor': 1734, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '1734.l2', 'prime': 17, 'reduction_type': 0, '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: 1675419
    {'adelic_gens': [[55, 18, 0, 1], [1, 18, 0, 1], [37, 18, 45, 19], [1, 0, 18, 1], [55, 54, 0, 55], [65, 54, 63, 19], [13, 12, 8, 13], [10, 9, 9, 1], [55, 18, 54, 19], [1, 18, 12, 1]], 'adelic_image': '72.144.2.?', 'conductor': 1734, 'lmfdb_label': '1734.l2', 'prime': 0}
  • id: 8555
    {'conductor': 1734, 'elladic_image': '9.72.0.8', 'lmfdb_label': '1734.l2', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 1734.l does not appear in ec_padic