Modular curve data - 272.48.0-272.p.1.22

Formats: - HTML - YAML - JSON - 2024-06-05T11:09:53.599348

• 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': '16C0', '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': [[0, 1, 235, 86], [0, 3, 101, 86], [0, 271, 3, 220], [0, 271, 241, 118], [1, 0, 16, 1], [1, 16, 0, 1], [16, 221, 187, 50], [17, 16, 256, 257], [256, 17, 255, 18], [256, 85, 51, 18]], 'cm_discriminants': [], 'coarse_class': '272.24.0.p', 'coarse_class_num': 16, 'coarse_index': 24, 'coarse_label': '272.24.0.p.1', 'coarse_level': 272, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 2]], 'cusp_widths': [[1, 4], [4, 1], [16, 1]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 22, 'generators': [[84, 159, 21, 246], [96, 13, 167, 102], [260, 131, 5, 42], [261, 124, 182, 19], [265, 16, 198, 219]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1], [17, 18, 1], [34, 18, 1], [34, 36, 1], [68, 18, 2], [68, 72, 1], [136, 18, 2], [136, 36, 1], [136, 144, 1], [272, 36, 2], [272, 72, 1], [272, 288, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [17, 144, 1], [34, 144, 1], [34, 288, 1], [68, 288, 2], [68, 1152, 1], [136, 576, 2], [136, 1152, 1], [136, 4608, 1], [272, 2304, 2], [272, 4608, 1], [272, 18432, 1]], 'label': '272.48.0-272.p.1.22', 'lattice_labels': None, 'lattice_x': None, 'level': 272, 'level_is_squarefree': False, 'level_radical': 34, 'log_conductor': None, 'models': None, 'mults': None, '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, 2, 2], [4, 8, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [16, 8, 2], [16, 16, 1], [16, 32, 1], [16, 128, 1], [17, 288, 1], [34, 288, 1], [34, 576, 1], [68, 576, 2], [68, 2304, 1], [136, 1152, 2], [136, 2304, 1], [136, 9216, 1], [272, 2304, 2], [272, 4608, 1], [272, 9216, 1], [272, 36864, 1]], 'parents': ['16.24.0-8.n.1.8', '136.24.0-8.n.1.12'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '16.24.0.b.1', 'psl2level': 16, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.8', '136.24.0-8.n.1.12'], 'scalar_label': '4.2.1', 'simple': None, 'sl2label': '16.24.0.b.1', 'sl2level': 16, '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': '16C0', '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': [[0, 1, 31, 154], [0, 1, 235, 86], [0, 1, 269, 52], [0, 3, 101, 86], [1, 0, 16, 1], [1, 16, 0, 1], [17, 16, 256, 257], [256, 17, 255, 18], [256, 51, 85, 222], [256, 85, 51, 18]], 'cm_discriminants': [], 'coarse_class': '272.24.0.p', 'coarse_class_num': 16, 'coarse_index': 24, 'coarse_label': '272.24.0.p.1', 'coarse_level': 272, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 2]], 'cusp_widths': [[1, 4], [4, 1], [16, 1]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[0, 267, 3, 200], [99, 18, 98, 251], [126, 59, 87, 218], [210, 257, 109, 238], [218, 31, 245, 212], [244, 249, 267, 18]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1], [17, 18, 1], [34, 18, 1], [34, 36, 1], [68, 18, 2], [68, 72, 1], [136, 18, 2], [136, 36, 1], [136, 144, 1], [272, 36, 2], [272, 72, 1], [272, 288, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [17, 144, 1], [34, 144, 1], [34, 288, 1], [68, 288, 2], [68, 1152, 1], [136, 576, 2], [136, 1152, 1], [136, 4608, 1], [272, 2304, 2], [272, 4608, 1], [272, 18432, 1]], 'label': '272.24.0.p.1', 'lattice_labels': None, 'lattice_x': None, 'level': 272, 'level_is_squarefree': False, 'level_radical': 34, 'log_conductor': None, 'models': None, 'mults': None, '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, 2], [8, 8, 1], [8, 32, 1], [16, 16, 2], [16, 32, 1], [16, 128, 1], [17, 288, 1], [34, 288, 1], [34, 576, 1], [68, 576, 2], [68, 2304, 1], [136, 1152, 2], [136, 2304, 1], [136, 9216, 1], [272, 4608, 2], [272, 9216, 1], [272, 36864, 1]], 'parents': ['8.12.0.n.1'], 'parents_conj': [[1, 0, 0, 1]], 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '16.24.0.b.1', 'psl2level': 16, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '4.6.0.c.1', '8.12.0.n.1', '8.12.0.n.1', '8.12.0.n.1'], 'scalar_label': '1.1.1', 'simple': None, 'sl2label': '16.24.0.b.1', 'sl2level': 16, 'squarefree': None, 'trace_hash': None, 'traces': None}
• modcurve 272.24.0.p.1 does not appear in modcurve_models
• domain_label 272.24.0.p.1 does not appear in modcurve_modelmaps
• curve_label 272.24.0.p.1 does not appear in modcurve_points