Modular curve data - 168.192.1-168.oi.1.8

Formats: - HTML - YAML - JSON - 2024-06-01T13:27:14.341298

• gps_gl2zhat_fine •

  Column	Type
  CPlabel	text
  Glabel	text
  RSZBlabel	text
  RZBlabel	text
  SZlabel	text
  Slabel	text
  all_degree1_points_known	boolean
  bad_primes	integer[]
  canonical_conjugator	integer[]
  canonical_generators	integer[]
  cm_discriminants	integer[]
  coarse_class	text
  coarse_class_num	integer
  coarse_index	integer
  coarse_label	text
  coarse_level	integer
  coarse_num	integer
  conductor	integer[]
  contains_negative_one	boolean
  curve_label	text
  cusp_orbits	integer[]
  cusp_widths	integer[]
  cusps	integer
  determinant_label	text
  dims	integer[]
  factorization	text[]
  fine_num	integer
  generators	integer[]
  genus	integer
  genus_minus_rank	integer
  has_obstruction	smallint
  index	integer
  isogeny_orbits	integer[]
  kummer_orbits	integer[]
  label	text
  lattice_labels	text[]
  lattice_x	integer[]
  level	integer
  level_is_squarefree	boolean
  level_radical	integer
  log_conductor	numeric
  models	smallint
  mults	integer[]
  name	text
  newforms	text[]
  nu2	integer
  nu3	integer
  num_bad_primes	integer
  num_known_degree1_noncm_points	integer
  num_known_degree1_noncusp_points	integer
  num_known_degree1_points	integer
  obstructions	integer[]
  orbits	integer[]
  parents	text[]
  parents_conj	integer[]
  pointless	boolean
  power	boolean
  psl2index	integer
  psl2label	text
  psl2level	integer
  q_gonality	integer
  q_gonality_bounds	integer[]
  qbar_gonality	integer
  qbar_gonality_bounds	integer[]
  rank	integer
  rational_cusps	integer
  reductions	text[]
  scalar_label	text
  simple	boolean
  sl2label	text
  sl2level	integer
  squarefree	boolean
  trace_hash	bigint
  traces	integer[]

  
  {'CPlabel': '8K1', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 7], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 8, 1], [1, 0, 84, 1], [1, 4, 52, 147], [1, 4, 76, 75], [1, 8, 0, 1], [9, 8, 160, 161], [41, 0, 84, 41], [161, 164, 90, 139], [163, 164, 142, 67], [165, 164, 86, 107]], 'cm_discriminants': [], 'coarse_class': '168.96.1.oi', 'coarse_class_num': 373, 'coarse_index': 96, 'coarse_label': '168.96.1.oi.1', 'coarse_level': 168, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 2], [4, 3]], 'cusp_widths': [[4, 8], [8, 8]], 'cusps': 16, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 8, 'generators': [[17, 164, 72, 91], [51, 16, 38, 33], [87, 148, 34, 83], [151, 12, 68, 59]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 1, 'index': 192, 'isogeny_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [7, 8, 1], [8, 2, 2], [8, 4, 2], [12, 4, 2], [12, 8, 2], [14, 8, 3], [21, 32, 1], [24, 8, 2], [24, 16, 2], [28, 8, 2], [28, 16, 2], [42, 32, 3], [56, 16, 2], [56, 32, 2], [84, 32, 2], [84, 64, 2], [168, 64, 2], [168, 128, 2]], 'kummer_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [7, 24, 1], [8, 2, 2], [8, 4, 1], [8, 8, 2], [12, 8, 2], [12, 16, 2], [14, 24, 3], [21, 192, 1], [24, 16, 2], [24, 32, 1], [24, 64, 2], [28, 48, 2], [28, 96, 2], [42, 192, 3], [56, 96, 2], [56, 192, 1], [56, 384, 2], [84, 384, 2], [84, 768, 2], [168, 768, 2], [168, 1536, 1], [168, 3072, 2]], 'label': '168.192.1-168.oi.1.8', 'lattice_labels': None, 'lattice_x': None, 'level': 168, 'level_is_squarefree': False, 'level_radical': 42, 'log_conductor': None, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': None, 'num_known_degree1_noncusp_points': None, 'num_known_degree1_points': None, 'obstructions': None, 'orbits': [[2, 1, 3], [3, 8, 1], [4, 2, 2], [4, 4, 2], [6, 8, 3], [7, 48, 1], [8, 2, 4], [8, 8, 1], [8, 16, 2], [12, 16, 2], [12, 32, 2], [14, 48, 3], [21, 384, 1], [24, 16, 4], [24, 64, 1], [24, 128, 2], [28, 96, 2], [28, 192, 2], [42, 384, 3], [56, 96, 4], [56, 384, 1], [56, 768, 2], [84, 768, 2], [84, 1536, 2], [168, 768, 4], [168, 3072, 1], [168, 6144, 2]], 'parents': ['24.96.0-24.w.2.1', '56.96.1-56.bj.1.2', '168.96.0-24.w.2.9', '168.96.0-168.bk.1.16', '168.96.0-168.bk.1.20', '168.96.0-168.bl.2.6', '168.96.0-168.bl.2.20', '168.96.0-168.cr.2.2', '168.96.0-168.cr.2.27', '168.96.1-56.bj.1.1', '168.96.1-168.dq.1.15', '168.96.1-168.dq.1.29', '168.96.1-168.fe.1.7', '168.96.1-168.fe.1.22'], 'parents_conj': None, 'pointless': True, 'power': True, 'psl2index': 96, 'psl2label': '8.96.1.a.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [2, 96], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.12.0.b.1', '4.12.0.b.1', '8.48.0-8.e.2.6', '12.24.0-4.b.1.3', '12.24.0-4.b.1.3', '24.96.0-24.w.2.1', '56.96.1-56.bj.1.2'], 'scalar_label': '8.4.1', 'simple': True, 'sl2label': '8.96.1.a.1', 'sl2level': 8, 'squarefree': True, 'trace_hash': None, 'traces': None}
• gps_gl2zhat_fine •

  Column	Type
  CPlabel	text
  Glabel	text
  RSZBlabel	text
  RZBlabel	text
  SZlabel	text
  Slabel	text
  all_degree1_points_known	boolean
  bad_primes	integer[]
  canonical_conjugator	integer[]
  canonical_generators	integer[]
  cm_discriminants	integer[]
  coarse_class	text
  coarse_class_num	integer
  coarse_index	integer
  coarse_label	text
  coarse_level	integer
  coarse_num	integer
  conductor	integer[]
  contains_negative_one	boolean
  curve_label	text
  cusp_orbits	integer[]
  cusp_widths	integer[]
  cusps	integer
  determinant_label	text
  dims	integer[]
  factorization	text[]
  fine_num	integer
  generators	integer[]
  genus	integer
  genus_minus_rank	integer
  has_obstruction	smallint
  index	integer
  isogeny_orbits	integer[]
  kummer_orbits	integer[]
  label	text
  lattice_labels	text[]
  lattice_x	integer[]
  level	integer
  level_is_squarefree	boolean
  level_radical	integer
  log_conductor	numeric
  models	smallint
  mults	integer[]
  name	text
  newforms	text[]
  nu2	integer
  nu3	integer
  num_bad_primes	integer
  num_known_degree1_noncm_points	integer
  num_known_degree1_noncusp_points	integer
  num_known_degree1_points	integer
  obstructions	integer[]
  orbits	integer[]
  parents	text[]
  parents_conj	integer[]
  pointless	boolean
  power	boolean
  psl2index	integer
  psl2label	text
  psl2level	integer
  q_gonality	integer
  q_gonality_bounds	integer[]
  qbar_gonality	integer
  qbar_gonality_bounds	integer[]
  rank	integer
  rational_cusps	integer
  reductions	text[]
  scalar_label	text
  simple	boolean
  sl2label	text
  sl2level	integer
  squarefree	boolean
  trace_hash	bigint
  traces	integer[]

  
  {'CPlabel': '8K1', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 7], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 8, 1], [1, 0, 84, 1], [1, 4, 52, 147], [1, 4, 76, 75], [1, 8, 0, 1], [3, 4, 82, 61], [5, 4, 26, 101], [7, 4, 78, 29], [9, 8, 160, 161], [127, 0, 84, 127]], 'cm_discriminants': [], 'coarse_class': '168.96.1.oi', 'coarse_class_num': 373, 'coarse_index': 96, 'coarse_label': '168.96.1.oi.1', 'coarse_level': 168, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 2], [4, 3]], 'cusp_widths': [[4, 8], [8, 8]], 'cusps': 16, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[5, 44, 122, 147], [55, 92, 34, 163], [61, 4, 56, 163], [67, 148, 64, 147], [85, 32, 56, 143]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 1, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [7, 8, 1], [8, 2, 2], [8, 4, 2], [12, 4, 2], [12, 8, 2], [14, 8, 3], [21, 32, 1], [24, 8, 2], [24, 16, 2], [28, 8, 2], [28, 16, 2], [42, 32, 3], [56, 16, 2], [56, 32, 2], [84, 32, 2], [84, 64, 2], [168, 64, 2], [168, 128, 2]], 'kummer_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [7, 24, 1], [8, 2, 2], [8, 4, 1], [8, 8, 2], [12, 8, 2], [12, 16, 2], [14, 24, 3], [21, 192, 1], [24, 16, 2], [24, 32, 1], [24, 64, 2], [28, 48, 2], [28, 96, 2], [42, 192, 3], [56, 96, 2], [56, 192, 1], [56, 384, 2], [84, 384, 2], [84, 768, 2], [168, 768, 2], [168, 1536, 1], [168, 3072, 2]], 'label': '168.96.1.oi.1', 'lattice_labels': None, 'lattice_x': None, 'level': 168, 'level_is_squarefree': False, 'level_radical': 42, 'log_conductor': None, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': None, 'num_known_degree1_noncusp_points': None, 'num_known_degree1_points': None, 'obstructions': [0], 'orbits': [[2, 1, 3], [3, 8, 1], [4, 2, 2], [4, 4, 2], [6, 8, 3], [7, 48, 1], [8, 4, 2], [8, 8, 1], [8, 16, 2], [12, 16, 2], [12, 32, 2], [14, 48, 3], [21, 384, 1], [24, 32, 2], [24, 64, 1], [24, 128, 2], [28, 96, 2], [28, 192, 2], [42, 384, 3], [56, 192, 2], [56, 384, 1], [56, 768, 2], [84, 768, 2], [84, 1536, 2], [168, 1536, 2], [168, 3072, 1], [168, 6144, 2]], 'parents': ['24.48.0.w.2', '56.48.1.bj.1', '168.48.0.bk.1', '168.48.0.bl.2', '168.48.0.cr.2', '168.48.1.dq.1', '168.48.1.fe.1'], 'parents_conj': [[1, 0, 0, 1], [61, 61, 141, 100], [13, 13, 165, 148], [25, 42, 84, 67], [33, 82, 113, 135], [103, 103, 99, 58], [1, 0, 0, 1]], 'pointless': True, 'power': True, 'psl2index': 96, 'psl2label': '8.96.1.a.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [2, 96], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.12.0.b.1', '4.12.0.b.1', '4.12.0.b.1', '4.12.0.b.1', '8.24.0.e.2', '24.48.0.w.2', '56.48.1.bj.1'], 'scalar_label': '8.2.2', 'simple': True, 'sl2label': '8.96.1.a.1', 'sl2level': 8, 'squarefree': True, 'trace_hash': None, 'traces': None}
• modcurve 168.96.1.oi.1 does not appear in modcurve_models
• domain_label 168.96.1.oi.1 does not appear in modcurve_modelmaps
• curve_label 168.96.1.oi.1 does not appear in modcurve_points