Modular curve data - 272.192.1-272.bf.2.1

Formats: - HTML - YAML - JSON - 2024-06-01T16:06:17.215720

• 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': '16M1', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 17], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 16, 1], [1, 0, 34, 1], [1, 16, 0, 1], [3, 8, 1, 117], [3, 16, 9, 33], [3, 16, 9, 49], [5, 8, 46, 13], [17, 16, 256, 257], [137, 0, 34, 137], [169, 0, 238, 169], [267, 256, 249, 89]], 'cm_discriminants': [], 'coarse_class': '272.96.1.bf', 'coarse_class_num': 32, 'coarse_index': 96, 'coarse_label': '272.96.1.bf.2', 'coarse_level': 272, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [4, 3]], 'cusp_widths': [[2, 8], [4, 4], [16, 4]], 'cusps': 16, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 1, 'generators': [[33, 104, 252, 93], [103, 224, 33, 217], [197, 256, 210, 161], [215, 96, 3, 17]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 192, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 4], [8, 8, 1], [16, 2, 4], [16, 16, 1], [17, 18, 1], [34, 18, 1], [34, 36, 1], [68, 18, 2], [68, 72, 1], [136, 18, 4], [136, 144, 1], [272, 36, 4], [272, 288, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 2, 4], [8, 16, 1], [16, 4, 4], [16, 8, 2], [16, 64, 1], [17, 144, 1], [34, 144, 1], [34, 288, 1], [68, 288, 2], [68, 1152, 1], [136, 576, 4], [136, 4608, 1], [272, 1152, 4], [272, 2304, 2], [272, 18432, 1]], 'label': '272.192.1-272.bf.2.1', 'lattice_labels': None, 'lattice_x': None, 'level': 272, 'level_is_squarefree': False, 'level_radical': 34, 'log_conductor': None, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, '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], [4, 1, 2], [4, 2, 1], [4, 4, 2], [8, 2, 4], [8, 4, 2], [8, 16, 2], [16, 4, 8], [16, 16, 2], [16, 64, 2], [17, 288, 1], [34, 288, 1], [34, 576, 1], [68, 288, 2], [68, 576, 1], [68, 1152, 2], [136, 576, 4], [136, 1152, 2], [136, 4608, 2], [272, 1152, 8], [272, 4608, 2], [272, 18432, 2]], 'parents': ['16.96.0-16.j.1.2', '136.96.0-136.bf.2.7', '272.96.0-16.j.1.8', '272.96.0-136.bf.2.5', '272.96.0-272.bs.1.6', '272.96.0-272.bs.1.9', '272.96.0-272.bt.1.4', '272.96.0-272.bt.1.9', '272.96.1-272.g.1.2', '272.96.1-272.g.1.14', '272.96.1-272.bq.1.6', '272.96.1-272.bq.1.9', '272.96.1-272.br.1.6', '272.96.1-272.br.1.9'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 96, 'psl2label': '16.96.1.a.1', 'psl2level': 16, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 4, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.24.0-4.d.1.1', '4.24.0-4.d.1.1', '8.48.0-8.q.1.2', '16.96.0-16.j.1.2', '136.96.0-136.bf.2.7'], 'scalar_label': '8.4.1', 'simple': True, 'sl2label': '16.96.1.a.1', 'sl2level': 16, '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': '16M1', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 17], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 16, 1], [1, 0, 34, 1], [1, 16, 0, 1], [3, 8, 1, 117], [3, 16, 9, 33], [3, 16, 9, 49], [5, 8, 46, 13], [5, 16, 23, 183], [17, 16, 256, 257], [103, 0, 34, 103], [137, 0, 34, 137]], 'cm_discriminants': [], 'coarse_class': '272.96.1.bf', 'coarse_class_num': 32, 'coarse_index': 96, 'coarse_label': '272.96.1.bf.2', 'coarse_level': 272, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [4, 3]], 'cusp_widths': [[2, 8], [4, 4], [16, 4]], 'cusps': 16, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[11, 224, 242, 119], [197, 184, 136, 213], [221, 64, 142, 193], [265, 80, 135, 135], [267, 192, 41, 65]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 4], [8, 8, 1], [16, 2, 4], [16, 16, 1], [17, 18, 1], [34, 18, 1], [34, 36, 1], [68, 18, 2], [68, 72, 1], [136, 18, 4], [136, 144, 1], [272, 36, 4], [272, 288, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 2, 4], [8, 16, 1], [16, 4, 4], [16, 8, 2], [16, 64, 1], [17, 144, 1], [34, 144, 1], [34, 288, 1], [68, 288, 2], [68, 1152, 1], [136, 576, 4], [136, 4608, 1], [272, 1152, 4], [272, 2304, 2], [272, 18432, 1]], 'label': '272.96.1.bf.2', 'lattice_labels': None, 'lattice_x': None, 'level': 272, 'level_is_squarefree': False, 'level_radical': 34, 'log_conductor': None, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, '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], [4, 2, 2], [4, 8, 1], [8, 4, 4], [8, 32, 1], [16, 8, 4], [16, 16, 2], [16, 128, 1], [17, 288, 1], [34, 288, 1], [34, 576, 1], [68, 576, 2], [68, 2304, 1], [136, 1152, 4], [136, 9216, 1], [272, 2304, 4], [272, 4608, 2], [272, 36864, 1]], 'parents': ['16.48.0.j.1', '136.48.0.bf.2', '272.48.0.bs.1', '272.48.0.bt.1', '272.48.1.g.1', '272.48.1.bq.1', '272.48.1.br.1'], 'parents_conj': [[1, 0, 0, 1], [25, 204, 0, 93], [28, 147, 255, 23], [28, 79, 255, 23], [1, 0, 0, 1], [28, 79, 85, 261], [28, 11, 85, 261]], 'pointless': False, 'power': True, 'psl2index': 96, 'psl2label': '16.96.1.a.1', 'psl2level': 16, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 4, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.12.0.d.1', '4.12.0.d.1', '8.24.0.q.1', '16.48.0.j.1', '136.48.0.bf.2'], 'scalar_label': '8.2.2', 'simple': True, 'sl2label': '16.96.1.a.1', 'sl2level': 16, 'squarefree': True, 'trace_hash': None, 'traces': None}
• modcurve 272.96.1.bf.2 does not appear in modcurve_models
• domain_label 272.96.1.bf.2 does not appear in modcurve_modelmaps
• curve_label 272.96.1.bf.2 does not appear in modcurve_points