Elliptic curve data - 340704.ex1

Formats: - HTML - YAML - JSON - 2026-04-20T22:13:28.176031

• 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': '340704ex', 'Clabel': '340704ex1', 'Cnumber': 1, 'abc_quality': 0.9298969596640071, 'absD': 2250150948864, 'adelic_genus': 1, 'adelic_index': 12, 'adelic_level': 1092, 'ainvs': [0, 0, 0, -936, 73008], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 340704, 'degree': 442368, 'elladic_images': ['3.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0508173660561446151088777654', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 127, 'isogeny_degrees': [1], 'jinv': [-13824, 343], 'lmfdb_iso': '340704.ex', 'lmfdb_label': '340704.ex1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -104, 2704], 'min_quad_twist_disc': 12, 'modell_images': ['3Nn'], 'modm_images': ['3.3.0.a.1', '84.6.0.?', '156.6.0.?', '182.2.0.?', '546.6.1.?', '1092.12.1.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.74326919208419739408597577674', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 819], [3, 6, 5408], [7, 8, 48672], [13, 50, 2016]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.83287329820323972401934883491', 'prec': 107}, 'szpiro_ratio': 2.8197224687593883, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 3, 0], 'aplist': [0, 0, 3, 1, 2, 0, -2, 3, 3, 1, -9, -6, -6, 9, -1, 5, -4, -6, 4, -10, 3, -3, -1, 9, 15], 'class_deg': 1, 'class_size': 1, 'conductor': 340704, 'isogeny_matrix': [[1]], 'lmfdb_iso': '340704.ex', 'trace_hash': 1434520721104740329}
• 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': '0.12225640833139855925357493483', 'prec': 103}, 'conductor': 340704, 'gens': [[12, 252, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.74326919208419739408597577674', 'prec': 103}], 'lmfdb_label': '340704.ex1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.68774348334257543422239900761', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.268285037404985070974116792256188206', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [-23, 12]}
• lmfdb_label 340704.ex1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14246055
    {'degree': 3, 'field': [-2, 4, 0, 1], 'lmfdb_label': '340704.ex1', 'torsion': [2]}
  • id: 14246056
    {'degree': 6, 'field': [9, -33, 44, -23, 14, -3, 1], 'lmfdb_label': '340704.ex1', 'torsion': [2, 2]}
  • id: 14246057
    {'degree': 8, 'field': [-350, -940, -1316, -952, -332, -16, 10, -4, 1], 'lmfdb_label': '340704.ex1', 'torsion': [3]}
  • id: 14246058
    {'degree': 12, 'field': [104424619, -164918052, 90376494, -32705712, 11828079, -3057912, 267052, 16848, 453, -468, -18, 0, 1], 'lmfdb_label': '340704.ex1', 'torsion': [4]}
  • id: 14246059
    {'degree': 16, 'field': [122500, 329000, 423000, 570640, 720776, 634272, 447352, 265952, 116022, 28676, -2864, -3768, 368, -8, 6, -4, 1], 'lmfdb_label': '340704.ex1', 'torsion': [3, 3]}
• 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: 8430030
    {'conductor': 340704, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '340704.ex1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8430031
    {'conductor': 340704, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '340704.ex1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8430032
    {'conductor': 340704, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '340704.ex1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 8430033
    {'conductor': 340704, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '340704.ex1', 'prime': 13, 'reduction_type': 0, '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: 3792884
    {'adelic_gens': [[6, 5, 1081, 1083], [628, 3, 621, 1090], [424, 1, 1015, 2], [547, 4, 4, 17], [1087, 6, 1086, 7], [1, 6, 0, 1], [1, 368, 4, 745], [1, 0, 6, 1]], 'adelic_image': '1092.12.1.?', 'conductor': 340704, 'lmfdb_label': '340704.ex1', 'prime': 0}
  • id: 1181651
    {'conductor': 340704, 'elladic_image': '3.3.0.1', 'lmfdb_label': '340704.ex1', 'modell_image': '3Nn', 'prime': 3}
• lmfdb_iso 340704.ex does not appear in ec_padic