Elliptic curve data - 1369.f2

Formats: - HTML - YAML - JSON - 2025-09-12T10:47:18.339104

• 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': '1369e', 'Clabel': '1369e1', 'Cnumber': 1, 'abc_quality': 0.7697818672856651, 'absD': 50653, 'adelic_genus': 9, 'adelic_index': 288, 'adelic_level': 1110, 'ainvs': [0, 1, 1, -12, -17], 'analytic_rank': 0, 'bad_primes': [37], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 1369, 'degree': 144, 'elladic_images': ['3.3.0.1', '5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.38656126612934378892157352570', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 5], 'jinv': [4096, 1], 'lmfdb_iso': '1369.f', 'lmfdb_label': '1369.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -12, -17], 'min_quad_twist_disc': 1, 'modell_images': ['3Nn', '5B'], 'modm_images': ['3.3.0.a.1', '5.6.0.a.1', '6.6.0.c.1', '10.12.0.a.1', '15.36.0.a.1', '30.72.1.r.2', '74.2.0.?', '111.6.0.?', '185.24.0.?', '222.12.1.?', '370.48.1.?', '555.144.3.?', '1110.288.9.?'], 'nonmax_primes': [3, 5], 'nonmax_rad': 15, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[37, 362, 1]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2892907442903999000135974435', 'prec': 103}, 'szpiro_ratio': 2.651752320039361, '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, 2, 1, 2, 2, 2, 3, 0, -2, 4, 3, 2, 6, 6, 2, -4, -2, -4, -6, 4], 'aplist': [2, 1, 2, 3, 3, 6, -2, -6, -4, -4, 0, 0, 3, 6, 3, 9, 4, 0, 12, -3, -9, -6, 9, -14, -12], 'class_deg': 5, 'class_size': 2, 'conductor': 1369, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '1369.f', 'trace_hash': 1327906458076464491}
• 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': '2.1665207336360652637964310822', 'prec': 100}, 'conductor': 1369, 'gens': [], 'heights': [], 'lmfdb_label': '1369.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.5929492242397520522139210050', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1858984484795041044278420100129502110', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': [4, 0], '5': [0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0, 0], '37': 'a', '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1369.f2'}
• ec_torsion_growth •

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

  
  
  • id: 69122
    {'degree': 3, 'field': [1, -3, -1, 1], 'lmfdb_label': '1369.f2', 'torsion': [2]}
  • id: 69123
    {'degree': 4, 'field': [49, -7, 5, -1, 1], 'lmfdb_label': '1369.f2', 'torsion': [5]}
  • id: 69124
    {'degree': 6, 'field': [1, -5, 0, 9, -2, -3, 1], 'lmfdb_label': '1369.f2', 'torsion': [2, 2]}
  • id: 69125
    {'degree': 8, 'field': [-27, 99, -126, 75, -33, 8, 2, -2, 1], 'lmfdb_label': '1369.f2', 'torsion': [3]}
  • id: 69126
    {'degree': 12, 'field': [-358, -4988, -13648, -11772, -4634, 1440, 1592, 484, -68, -38, -4, 0, 1], 'lmfdb_label': '1369.f2', 'torsion': [4]}
  • id: 69127
    {'degree': 12, 'field': [343, 931, 1463, 1475, 1161, 486, 179, 54, 39, -13, 14, -2, 1], 'lmfdb_label': '1369.f2', 'torsion': [2, 10]}
  • id: 69129
    {'degree': 16, 'field': [47, -39, -55, 366, -157, -389, 989, -444, -166, 271, 114, -68, 0, 9, 0, -2, 1], 'lmfdb_label': '1369.f2', 'torsion': [15]}
  • id: 69128
    {'degree': 16, 'field': [729, -2673, 6399, -8424, 7560, -3132, 567, -207, 372, -213, 28, -41, 53, -20, 2, -2, 1], 'lmfdb_label': '1369.f2', 'torsion': [3, 3]}
  • id: 69130
    {'degree': 20, 'field': [-14125, -300750, -768525, -229360, 651681, 127193, -273260, -14126, 85072, 36628, -38460, -1392, -1384, 6652, -1716, -739, 296, 27, -14, -3, 1], 'lmfdb_label': '1369.f2', 'torsion': [5]}
• 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

  
  {'conductor': 1369, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1369.f2', 'prime': 37, '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: 1673222
    {'adelic_gens': [[1018, 5, 275, 1052], [1081, 30, 1080, 31], [1, 0, 30, 1], [901, 30, 840, 487], [371, 30, 0, 1], [1, 30, 0, 1], [6, 11, 175, 321]], 'adelic_image': '1110.288.9.?', 'conductor': 1369, 'lmfdb_label': '1369.f2', 'prime': 0}
  • id: 6686
    {'conductor': 1369, 'elladic_image': '3.3.0.1', 'lmfdb_label': '1369.f2', 'modell_image': '3Nn', 'prime': 3}
  • id: 6687
    {'conductor': 1369, 'elladic_image': '5.6.0.1', 'lmfdb_label': '1369.f2', 'modell_image': '5B', 'prime': 5}
• lmfdb_iso 1369.f does not appear in ec_padic