Modular curve data - 72.48.2-72.a.1.5

Formats: - HTML - YAML - JSON - 2024-06-02T15:14:33.612649

• 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': '18B2', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[0, 1, 35, 58], [0, 1, 43, 18], [0, 1, 59, 10], [0, 17, 55, 59], [0, 29, 67, 59], [0, 67, 65, 22], [0, 71, 55, 14], [1, 0, 18, 1], [1, 18, 0, 1], [19, 18, 54, 55], [69, 17, 61, 62]], 'cm_discriminants': [], 'coarse_class': '72.24.2.a', 'coarse_class_num': 1, 'coarse_index': 24, 'coarse_label': '72.24.2.a.1', 'coarse_level': 72, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2]], 'cusp_widths': [[6, 1], [18, 1]], 'cusps': 2, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 5, 'generators': [[1, 44, 64, 51], [54, 35, 19, 32], [67, 29, 33, 32]], 'genus': 2, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 48, 'isogeny_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [8, 12, 1], [9, 3, 1], [9, 9, 1], [12, 6, 1], [12, 18, 1], [18, 9, 1], [18, 27, 1], [24, 12, 1], [24, 36, 1], [36, 18, 1], [36, 54, 1], [72, 36, 1], [72, 108, 1]], 'kummer_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [8, 24, 1], [9, 9, 1], [9, 27, 1], [12, 12, 1], [12, 36, 1], [18, 27, 1], [18, 81, 1], [24, 48, 1], [24, 144, 1], [36, 108, 1], [36, 324, 1], [72, 432, 1], [72, 1296, 1]], 'label': '72.48.2-72.a.1.5', 'lattice_labels': None, 'lattice_x': None, 'level': 72, 'level_is_squarefree': False, 'level_radical': 6, '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, 3, 1], [3, 2, 1], [3, 6, 1], [4, 12, 1], [6, 6, 1], [6, 18, 1], [8, 48, 1], [9, 18, 1], [9, 54, 1], [12, 24, 1], [12, 72, 1], [18, 54, 1], [18, 162, 1], [24, 96, 1], [24, 288, 1], [36, 216, 1], [36, 648, 1], [72, 864, 1], [72, 2592, 1]], 'parents': ['24.16.0-24.a.1.2', '36.24.1-9.a.1.4', '72.24.1-9.a.1.4'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '18.24.2.a.1', 'psl2level': 18, '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', '1.1.0.a.1', '3.4.0.a.1', '3.4.0.a.1', '8.2.0.a.1', '9.12.1.a.1', '9.12.1.a.1', '12.8.0-3.a.1.3', '24.16.0-24.a.1.2', '36.24.1-9.a.1.4'], 'scalar_label': '3.2.1', 'simple': False, 'sl2label': '18.24.2.a.1', 'sl2level': 18, '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': '18B2', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[0, 1, 17, 58], [0, 1, 35, 58], [0, 1, 43, 18], [0, 1, 59, 10], [0, 5, 7, 50], [0, 43, 5, 13], [0, 55, 17, 13], [1, 0, 18, 1], [1, 18, 0, 1], [3, 55, 11, 10], [19, 18, 54, 55]], 'cm_discriminants': [], 'coarse_class': '72.24.2.a', 'coarse_class_num': 1, 'coarse_index': 24, 'coarse_label': '72.24.2.a.1', 'coarse_level': 72, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2]], 'cusp_widths': [[6, 1], [18, 1]], 'cusps': 2, 'determinant_label': '1.1.1', 'dims': None, 'factorization': ['8.2.0.a.1', '9.12.1.a.1'], 'fine_num': 0, 'generators': [[22, 51, 39, 46], [41, 3, 14, 7], [41, 36, 44, 49], [59, 10, 48, 1]], 'genus': 2, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 24, 'isogeny_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [8, 12, 1], [9, 3, 1], [9, 9, 1], [12, 6, 1], [12, 18, 1], [18, 9, 1], [18, 27, 1], [24, 12, 1], [24, 36, 1], [36, 18, 1], [36, 54, 1], [72, 36, 1], [72, 108, 1]], 'kummer_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [8, 24, 1], [9, 9, 1], [9, 27, 1], [12, 12, 1], [12, 36, 1], [18, 27, 1], [18, 81, 1], [24, 48, 1], [24, 144, 1], [36, 108, 1], [36, 324, 1], [72, 432, 1], [72, 1296, 1]], 'label': '72.24.2.a.1', 'lattice_labels': None, 'lattice_x': None, 'level': 72, 'level_is_squarefree': False, 'level_radical': 6, '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, 3, 1], [3, 2, 1], [3, 6, 1], [4, 12, 1], [6, 6, 1], [6, 18, 1], [8, 48, 1], [9, 18, 1], [9, 54, 1], [12, 24, 1], [12, 72, 1], [18, 54, 1], [18, 162, 1], [24, 96, 1], [24, 288, 1], [36, 216, 1], [36, 648, 1], [72, 864, 1], [72, 2592, 1]], 'parents': ['9.12.1.a.1', '24.8.0.a.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '18.24.2.a.1', 'psl2level': 18, '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', '1.1.0.a.1', '3.4.0.a.1', '3.4.0.a.1', '3.4.0.a.1', '8.2.0.a.1', '9.12.1.a.1', '9.12.1.a.1', '9.12.1.a.1', '24.8.0.a.1'], 'scalar_label': '1.1.1', 'simple': False, 'sl2label': '18.24.2.a.1', 'sl2level': 18, 'squarefree': None, 'trace_hash': None, 'traces': None}
• modcurve 72.24.2.a.1 does not appear in modcurve_models
• domain_label 72.24.2.a.1 does not appear in modcurve_modelmaps
• curve_label 72.24.2.a.1 does not appear in modcurve_points