Modular curve data - 168.48.0-168.cs.1.1

Formats: - HTML - YAML - JSON - 2024-06-05T20:34:42.514873

• 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': '8G0', '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, 42, 1], [1, 8, 0, 1], [1, 8, 5, 63], [1, 8, 5, 147], [1, 8, 17, 75], [1, 8, 39, 161], [3, 4, 82, 103], [9, 8, 160, 161], [85, 0, 42, 85], [125, 0, 126, 125]], 'cm_discriminants': [], 'coarse_class': '168.24.0.cs', 'coarse_class_num': 71, 'coarse_index': 24, 'coarse_label': '168.24.0.cs.1', 'coarse_level': 168, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[2, 4], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 1, 'generators': [[51, 76, 65, 17], [57, 160, 86, 155], [95, 28, 122, 95], [119, 68, 96, 97]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [7, 8, 1], [8, 2, 2], [8, 8, 1], [12, 4, 2], [12, 16, 1], [14, 8, 1], [14, 16, 1], [21, 32, 1], [24, 8, 2], [24, 32, 1], [28, 8, 2], [28, 32, 1], [42, 32, 1], [42, 64, 1], [56, 16, 2], [56, 64, 1], [84, 32, 2], [84, 128, 1], [168, 64, 2], [168, 256, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [7, 24, 1], [8, 4, 2], [8, 16, 1], [12, 8, 2], [12, 32, 1], [14, 24, 1], [14, 48, 1], [21, 192, 1], [24, 32, 2], [24, 128, 1], [28, 48, 2], [28, 192, 1], [42, 192, 1], [42, 384, 1], [56, 192, 2], [56, 768, 1], [84, 384, 2], [84, 1536, 1], [168, 1536, 2], [168, 6144, 1]], 'label': '168.48.0-168.cs.1.1', 'lattice_labels': None, 'lattice_x': None, 'level': 168, 'level_is_squarefree': False, 'level_radical': 42, 'log_conductor': None, 'models': None, 'mults': None, '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, 1], [2, 2, 1], [3, 8, 1], [4, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [7, 48, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [12, 16, 2], [12, 64, 1], [14, 48, 1], [14, 96, 1], [21, 384, 1], [24, 32, 2], [24, 64, 1], [24, 256, 1], [28, 96, 2], [28, 384, 1], [42, 384, 1], [42, 768, 1], [56, 192, 2], [56, 384, 1], [56, 1536, 1], [84, 768, 2], [84, 3072, 1], [168, 1536, 2], [168, 3072, 1], [168, 12288, 1]], 'parents': ['24.24.0-24.ba.1.12', '56.24.0-28.h.1.5', '84.24.0-28.h.1.1', '168.24.0-24.ba.1.6', '168.24.0-168.ba.1.12', '168.24.0-168.ba.1.25'], 'parents_conj': None, 'pointless': None, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.b.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [1, 2], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '12.12.0-4.c.1.1', '24.24.0-24.ba.1.12', '28.12.0.h.1', '56.24.0-28.h.1.5', '84.24.0-28.h.1.1'], 'scalar_label': '4.2.1', 'simple': None, 'sl2label': '8.24.0.b.1', 'sl2level': 8, 'squarefree': None, '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': '8G0', '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, 42, 1], [1, 8, 0, 1], [1, 8, 5, 63], [1, 8, 5, 147], [1, 8, 17, 75], [1, 8, 39, 161], [3, 4, 82, 103], [9, 8, 160, 161], [43, 0, 42, 43], [85, 0, 42, 85]], 'cm_discriminants': [], 'coarse_class': '168.24.0.cs', 'coarse_class_num': 71, 'coarse_index': 24, 'coarse_label': '168.24.0.cs.1', 'coarse_level': 168, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[2, 4], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[75, 20, 122, 153], [89, 140, 6, 79], [111, 116, 110, 33], [121, 156, 0, 65], [131, 64, 155, 35]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': -1, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [7, 8, 1], [8, 2, 2], [8, 8, 1], [12, 4, 2], [12, 16, 1], [14, 8, 1], [14, 16, 1], [21, 32, 1], [24, 8, 2], [24, 32, 1], [28, 8, 2], [28, 32, 1], [42, 32, 1], [42, 64, 1], [56, 16, 2], [56, 64, 1], [84, 32, 2], [84, 128, 1], [168, 64, 2], [168, 256, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [7, 24, 1], [8, 4, 2], [8, 16, 1], [12, 8, 2], [12, 32, 1], [14, 24, 1], [14, 48, 1], [21, 192, 1], [24, 32, 2], [24, 128, 1], [28, 48, 2], [28, 192, 1], [42, 192, 1], [42, 384, 1], [56, 192, 2], [56, 768, 1], [84, 384, 2], [84, 1536, 1], [168, 1536, 2], [168, 6144, 1]], 'label': '168.24.0.cs.1', 'lattice_labels': None, 'lattice_x': None, 'level': 168, 'level_is_squarefree': False, 'level_radical': 42, 'log_conductor': None, 'models': None, 'mults': None, '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': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [7, 48, 1], [8, 8, 2], [8, 32, 1], [12, 16, 2], [12, 64, 1], [14, 48, 1], [14, 96, 1], [21, 384, 1], [24, 64, 2], [24, 256, 1], [28, 96, 2], [28, 384, 1], [42, 384, 1], [42, 768, 1], [56, 384, 2], [56, 1536, 1], [84, 768, 2], [84, 3072, 1], [168, 3072, 2], [168, 12288, 1]], 'parents': ['24.12.0.ba.1', '28.12.0.h.1', '168.12.0.ba.1'], 'parents_conj': [[152, 61, 33, 79], [1, 0, 0, 1], [32, 151, 165, 115]], 'pointless': None, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.b.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [1, 2], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '4.6.0.c.1', '4.6.0.c.1', '24.12.0.ba.1', '28.12.0.h.1', '28.12.0.h.1', '28.12.0.h.1'], 'scalar_label': '1.1.1', 'simple': None, 'sl2label': '8.24.0.b.1', 'sl2level': 8, 'squarefree': None, 'trace_hash': None, 'traces': None}
• modcurve 168.24.0.cs.1 does not appear in modcurve_models
• domain_label 168.24.0.cs.1 does not appear in modcurve_modelmaps
• curve_label 168.24.0.cs.1 does not appear in modcurve_points