Modular curve data - 84.96.1-84.b.1.8

Formats: - HTML - YAML - JSON - 2024-06-06T19:37:49.732077

• 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': '12P1', '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, 12, 1], [1, 8, 18, 35], [1, 8, 18, 77], [1, 12, 0, 1], [13, 12, 72, 73], [29, 70, 56, 57], [69, 14, 28, 41], [83, 70, 56, 27], [83, 76, 38, 21], [83, 76, 38, 63]], 'cm_discriminants': [], 'coarse_class': '84.48.1.b', 'coarse_class_num': 2, 'coarse_index': 48, 'coarse_label': '84.48.1.b.1', 'coarse_level': 84, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[2, 2], [4, 2], [6, 2], [12, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.8.0-3.a.1.1', '28.12.0.b.1'], 'fine_num': 8, 'generators': [[5, 36, 68, 25], [27, 74, 46, 23], [29, 82, 74, 81], [53, 12, 62, 73], [63, 82, 34, 69]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [7, 8, 1], [12, 2, 3], [12, 6, 3], [14, 8, 3], [21, 8, 1], [21, 24, 1], [28, 16, 3], [42, 8, 3], [42, 24, 3], [84, 16, 3], [84, 48, 3]], 'kummer_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [7, 24, 1], [12, 4, 3], [12, 12, 3], [14, 24, 3], [21, 48, 1], [21, 144, 1], [28, 96, 3], [42, 48, 3], [42, 144, 3], [84, 192, 3], [84, 576, 3]], 'label': '84.96.1-84.b.1.8', 'lattice_labels': None, 'lattice_x': None, 'level': 84, 'level_is_squarefree': False, 'level_radical': 42, 'log_conductor': None, 'models': None, 'mults': [1], '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, 3], [3, 2, 1], [3, 3, 2], [4, 4, 3], [6, 2, 3], [6, 3, 6], [7, 48, 1], [12, 8, 3], [12, 12, 6], [14, 48, 3], [21, 96, 1], [21, 144, 2], [28, 192, 3], [42, 96, 3], [42, 144, 6], [84, 384, 3], [84, 576, 6]], 'parents': ['6.48.0-6.a.1.2', '84.48.0-6.a.1.7', '84.48.0-84.o.1.2', '84.48.0-84.o.1.15', '84.48.1-84.o.1.1', '84.48.1-84.o.1.16'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '12.48.1.a.1', 'psl2level': 12, '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', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '3.8.0-3.a.1.1', '3.8.0-3.a.1.1', '6.48.0-6.a.1.2', '6.48.0-6.a.1.2', '6.48.0-6.a.1.2', '28.12.0.b.1'], 'scalar_label': '3.2.1', 'simple': True, 'sl2label': '12.48.1.a.1', 'sl2level': 12, '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': '12P1', '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, 12, 1], [1, 8, 18, 35], [1, 8, 18, 77], [1, 8, 46, 21], [1, 8, 46, 63], [1, 12, 0, 1], [1, 14, 28, 57], [13, 12, 72, 73], [15, 70, 56, 43], [29, 70, 56, 57]], 'cm_discriminants': [], 'coarse_class': '84.48.1.b', 'coarse_class_num': 2, 'coarse_index': 48, 'coarse_label': '84.48.1.b.1', 'coarse_level': 84, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[2, 2], [4, 2], [6, 2], [12, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.4.0.a.1', '28.12.0.b.1'], 'fine_num': 0, 'generators': [[45, 8, 82, 83], [47, 76, 74, 45], [61, 30, 28, 41], [69, 46, 46, 27], [75, 16, 22, 15], [75, 52, 70, 9]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 48, 'isogeny_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [7, 8, 1], [12, 2, 3], [12, 6, 3], [14, 8, 3], [21, 8, 1], [21, 24, 1], [28, 16, 3], [42, 8, 3], [42, 24, 3], [84, 16, 3], [84, 48, 3]], 'kummer_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [7, 24, 1], [12, 4, 3], [12, 12, 3], [14, 24, 3], [21, 48, 1], [21, 144, 1], [28, 96, 3], [42, 48, 3], [42, 144, 3], [84, 192, 3], [84, 576, 3]], 'label': '84.48.1.b.1', 'lattice_labels': None, 'lattice_x': None, 'level': 84, 'level_is_squarefree': False, 'level_radical': 42, 'log_conductor': None, 'models': None, 'mults': [1], '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, 3], [3, 2, 1], [3, 6, 1], [4, 4, 3], [6, 2, 3], [6, 6, 3], [7, 48, 1], [12, 8, 3], [12, 24, 3], [14, 48, 3], [21, 96, 1], [21, 288, 1], [28, 192, 3], [42, 96, 3], [42, 288, 3], [84, 384, 3], [84, 1152, 3]], 'parents': ['6.24.0.a.1', '28.12.0.b.1', '84.24.0.o.1', '84.24.1.o.1'], 'parents_conj': [[82, 77, 73, 51], [34, 77, 77, 83], [1, 0, 0, 1], [71, 0, 21, 71]], 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '12.48.1.a.1', 'psl2level': 12, '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', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '3.4.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '6.24.0.a.1', '6.24.0.a.1', '28.12.0.b.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '12.48.1.a.1', 'sl2level': 12, 'squarefree': True, 'trace_hash': None, 'traces': None}
• modcurve 84.48.1.b.1 does not appear in modcurve_models
• domain_label 84.48.1.b.1 does not appear in modcurve_modelmaps
• curve_label 84.48.1.b.1 does not appear in modcurve_points