Modular curve data - 136.96.1-136.be.2.13

Formats: - HTML - YAML - JSON - 2024-06-08T12:14:23.076841

• 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': '8G1', '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, 8, 1], [1, 8, 0, 1], [1, 34, 68, 1], [3, 2, 72, 49], [9, 8, 128, 129], [33, 102, 68, 33], [131, 134, 88, 89], [135, 134, 112, 17], [135, 134, 112, 119]], 'cm_discriminants': [], 'coarse_class': '136.48.1.be', 'coarse_class_num': 31, 'coarse_index': 48, 'coarse_label': '136.48.1.be.2', 'coarse_level': 136, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 3]], 'cusp_widths': [[4, 4], [8, 4]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 13, 'generators': [[5, 108, 72, 1], [7, 124, 36, 65], [67, 26, 0, 39], [127, 104, 44, 103]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [8, 2, 2], [8, 4, 2], [17, 18, 1], [34, 18, 3], [68, 18, 2], [68, 36, 2], [136, 36, 2], [136, 72, 2]], 'kummer_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [8, 4, 4], [8, 8, 1], [17, 144, 1], [34, 144, 3], [68, 288, 2], [68, 576, 2], [136, 1152, 4], [136, 2304, 1]], 'label': '136.96.1-136.be.2.13', 'lattice_labels': None, 'lattice_x': None, 'level': 136, '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, 3], [4, 2, 2], [4, 4, 2], [8, 8, 6], [17, 288, 1], [34, 288, 3], [68, 576, 2], [68, 1152, 2], [136, 2304, 6]], 'parents': ['8.48.0-8.e.1.15', '136.48.0-8.e.1.9', '136.48.0-136.h.1.2', '136.48.0-136.h.1.18', '136.48.1-136.c.1.6', '136.48.1-136.c.1.20'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '8.48.1.b.1', 'psl2level': 8, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.e.1.15', '68.24.0-4.b.1.3'], 'scalar_label': '8.4.1', 'simple': True, 'sl2label': '8.48.1.b.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': '8G1', '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, 8, 1], [1, 2, 24, 17], [1, 2, 24, 119], [1, 8, 0, 1], [1, 34, 68, 1], [3, 2, 72, 49], [5, 2, 48, 47], [9, 8, 128, 129], [103, 34, 68, 103]], 'cm_discriminants': [], 'coarse_class': '136.48.1.be', 'coarse_class_num': 31, 'coarse_index': 48, 'coarse_label': '136.48.1.be.2', 'coarse_level': 136, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 3]], 'cusp_widths': [[4, 4], [8, 4]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[11, 132, 60, 95], [39, 8, 36, 127], [45, 122, 68, 39], [99, 72, 24, 47], [99, 100, 12, 89]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 48, 'isogeny_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [8, 2, 2], [8, 4, 2], [17, 18, 1], [34, 18, 3], [68, 18, 2], [68, 36, 2], [136, 36, 2], [136, 72, 2]], 'kummer_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [8, 4, 4], [8, 8, 1], [17, 144, 1], [34, 144, 3], [68, 288, 2], [68, 576, 2], [136, 1152, 4], [136, 2304, 1]], 'label': '136.48.1.be.2', 'lattice_labels': None, 'lattice_x': None, 'level': 136, '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, 3], [4, 2, 2], [4, 4, 2], [8, 8, 4], [8, 16, 1], [17, 288, 1], [34, 288, 3], [68, 576, 2], [68, 1152, 2], [136, 2304, 4], [136, 4608, 1]], 'parents': ['8.24.0.e.1', '136.24.0.h.1', '136.24.1.c.1'], 'parents_conj': [[8, 69, 75, 14], [1, 0, 0, 1], [11, 11, 118, 105]], 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '8.48.1.b.1', 'psl2level': 8, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.12.0.b.1', '4.12.0.b.1', '8.24.0.e.1'], 'scalar_label': '8.2.2', 'simple': True, 'sl2label': '8.48.1.b.1', 'sl2level': 8, 'squarefree': True, 'trace_hash': None, 'traces': None}
• modcurve 136.48.1.be.2 does not appear in modcurve_models
• domain_label 136.48.1.be.2 does not appear in modcurve_modelmaps
• curve_label 136.48.1.be.2 does not appear in modcurve_points