Elliptic curve data - 39.a3

Formats: - HTML - YAML - JSON - 2026-05-14T11:21:16.955231

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '39a', 'Clabel': '39a1', 'Cnumber': 1, 'abc_quality': 0.9140273049268122, 'absD': 1521, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 156, 'ainvs': [1, 1, 0, -4, -5], 'analytic_rank': 0, 'bad_primes': [3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 39, 'degree': 2, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.66494005240836010765739307790', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [10218313, 1521], 'lmfdb_iso': '39.a', 'lmfdb_label': '39.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -4, -5], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '12.24.0-12.a.1.1', '52.24.0-52.b.1.2', '156.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [3, 4, 13], [13, 14, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.66494005240836010765739307790', 'prec': 107}, 'szpiro_ratio': 4.4054648507613035, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -4, -3, 1, 2, 4, 1, 1, -4, -2, -1, 2, 1, 0, -2], 'aplist': [1, -1, 2, -4, 4, 1, 2, 0, 0, -10, 4, -2, 6, -12, 0, 6, 12, -2, -8, 0, 2, 8, 4, -2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 39, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '39.a', 'trace_hash': 1907566206816012334}
• 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': '3.7805900858537284847121588785', 'prec': 100}, 'conductor': 39, 'gens': [], 'heights': [], 'lmfdb_label': '39.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.3067514026935424178794279102', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.82668785067338560446985697753944979021', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-2, 1, 1], [2, -1, 1]], 'xcoord_integral_points': [-2, 2]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '3': [0, 0], '13': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '39.a3'}
• ec_torsion_growth •

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

  
  
  • id: 1156
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 4]}
  • id: 1158
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 4]}
  • id: 1157
    {'degree': 4, 'field': [16, 0, 5, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 4]}
  • id: 1161
    {'degree': 8, 'field': [-3, 0, -5, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 6]}
  • id: 1160
    {'degree': 8, 'field': [1, 0, -4, 0, -7, 0, -4, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 8]}
  • id: 1159
    {'degree': 8, 'field': [81, 0, -63, 0, 40, 0, -7, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [4, 4]}
  • id: 1163
    {'degree': 16, 'field': [1, 0, -4, 0, 13, 0, -4, 0, -8, 0, -4, 0, 13, 0, -4, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 8]}
  • id: 1164
    {'degree': 16, 'field': [169, 0, -650, 0, 1327, 0, -957, 0, -567, 0, 150, 0, 19, 0, -11, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 12]}
  • id: 1162
    {'degree': 16, 'field': [234256, 0, -119360, 0, 78472, 0, -44048, 0, 15649, 0, -3368, 0, 439, 0, -32, 0, 1], 'lmfdb_label': '39.a3', 'torsion': [2, 8]}
• 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: 156
    {'conductor': 39, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '39.a3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 157
    {'conductor': 39, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '39.a3', 'prime': 13, '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: 1665963
    {'adelic_gens': [[53, 4, 106, 9], [145, 2, 0, 1], [153, 4, 152, 5], [79, 4, 2, 9], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '156.48.0.?', 'conductor': 39, 'lmfdb_label': '39.a3', 'prime': 0}
  • id: 96
    {'conductor': 39, 'elladic_image': '4.12.0.1', 'lmfdb_label': '39.a3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 39.a does not appear in ec_padic