Modular curve data - 24.24.1.dk.1

Formats: - HTML - YAML - JSON - 2024-06-03T13:29:45.434550

• 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': '8C1', 'Glabel': None, 'RSZBlabel': '24.24.1.61', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [5, 0, 3, 11], 'canonical_generators': [[0, 1, 7, 16], [1, 0, 8, 1], [1, 8, 0, 1], [2, 1, 9, 14], [2, 1, 15, 2], [2, 1, 17, 6], [9, 8, 16, 17], [16, 3, 21, 4], [16, 9, 15, 4], [16, 21, 3, 4]], 'cm_discriminants': [-4, -12], 'coarse_class': '24.24.1.dk', 'coarse_class_num': 89, 'coarse_index': 24, 'coarse_label': '24.24.1.dk.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': [[2, 6], [3, 2]], 'contains_negative_one': True, 'curve_label': '576.c2', 'cusp_orbits': [[2, 2]], 'cusp_widths': [[4, 2], [8, 2]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[3, 16, 22, 13], [7, 2, 4, 19], [19, 8, 4, 19], [19, 17, 22, 9]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 4, 1], [8, 8, 1], [12, 8, 1], [12, 16, 1], [24, 16, 1], [24, 32, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 8, 1], [8, 16, 1], [12, 16, 1], [12, 32, 1], [24, 64, 1], [24, 128, 1]], 'label': '24.24.1.dk.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.e.1', '8.12.0.s.1', '24.12.0.bu.1', '24.12.1.by.1', '24.24.1.dk.1'], 'lattice_x': [5000, 5000, 5000, 1364, 5000, 8636, 5000], 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '6.35610766069589123929', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['576.2.a.c'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 2, 'num_known_degree1_noncusp_points': 2, 'num_known_degree1_points': 2, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 4, 1], [4, 8, 1], [6, 8, 1], [6, 16, 1], [8, 16, 1], [8, 32, 1], [12, 32, 1], [12, 64, 1], [24, 128, 1], [24, 256, 1]], 'parents': ['8.12.0.s.1', '24.12.0.bu.1', '24.12.1.by.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 24, 'psl2label': '8.24.1.b.1', 'psl2level': 8, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.e.1', '4.6.0.e.1', '8.12.0.s.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '8.24.1.b.1', 'sl2level': 8, 'squarefree': True, 'trace_hash': 1086616701052248176, 'traces': [0, 0, -2, 0, 0, -6, -2, 0, 0, -10, 0, 2, -10, 0, 0, 14, 0, 10, 0, 0, -6, 0, 0, -10, 18, -2, 0, 0, -6, 14, 0, 0, 22, 0, 14, 0, -22, 0, 0, -26, 0, 18, 0, -14, -2, 0, 0, 0, 0, -30, -26, 0, -30, 0, -2, 0, -26, 0, 18, -10, 0, -34, 0, 0, 26, 22, 0, 18, 0, 10, -34, 0, 0, -14, 0, 0, -34, -38, -2, -6, 0, -30, 0, 34, 0, 0, 14, 42, 38, 0, 0, 0, 0, 0, 0, 0, -10, 22, 0, 42, 0, 38, 0, -26, 0, 2, 0, 46, 0, 10, 0, 34, 38, 0, 0, -50, 0, 0, -26, 0, 50, -46, -2, 0, 0, -10, -30, 0, 0, -54, 0, 0, 0, 18, 38, 50, -34, 0, 22, -10, 0, -50, 0, 0, -54, 0, -46, -58, 0, 0, 58, -50, 0, 0, 0, 0, 0, 46, -38, -58, 0, -26, 0, 0, 62, 0, 0, -62]}
• modcurve_models •

  Column	Type
  dont_display	boolean
  equation	text[]
  modcurve	text
  model_type	smallint
  number_variables	smallint
  smooth	boolean
  upload_id	bigint

  
  {'dont_display': False, 'equation': ['x^3-y^2*z-396*x*z^2+3024*z^3'], 'modcurve': '24.24.1.dk.1', 'model_type': 5, 'number_variables': 3, 'smooth': True, 'upload_id': None}
• modcurve_modelmaps •

  Column	Type
  codomain_label	text
  codomain_model_type	smallint
  coordinates	text[]
  degree	integer
  domain_label	text
  domain_model_type	smallint
  dont_display	boolean
  factored	boolean
  leading_coefficients	text[]
  upload_id	bigint

  
  {'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['312*x^2*y^6-180556272*x^2*y^4*z^2+6653452409856*x^2*y^2*z^4-44673552633996288*x^2*z^6-42168*x*y^6*z+7912594944*x*y^4*z^3-190470929469696*x*y^2*z^5+1026176675378909184*x*z^7-y^8+3287168*y^6*z^2-228433858560*y^4*z^4+2605015062042624*y^2*z^6-5881128527428227072*z^8', '24*x^2*y^6+22032*x^2*y^4*z^2-2239488*x^2*y^2*z^4-60466176*x^2*z^6+72*x*y^6*z+248832*x*y^4*z^3-28553472*x*y^2*z^5-725594112*x*z^7-y^8-10368*y^6*z^2-5971968*y^4*z^4+524040192*y^2*z^6+15237476352*z^8'], 'degree': 24, 'domain_label': '24.24.1.dk.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^6*3^3', '1'], 'upload_id': None}
• modcurve_points •

  Column	Type
  Elabel	text
  ainvs	text
  cardinality	integer
  cm	smallint
  conductor_norm	numeric
  coordinates	jsonb
  curve_genus	integer
  curve_index	integer
  curve_label	text
  curve_level	integer
  curve_name	text
  cusp	boolean
  degree	smallint
  isolated	smallint
  j_field	text
  j_height	double precision
  jinv	text
  jorig	text
  quo_info	smallint[]
  residue_field	text
  upload_id	bigint

  
  
  • id: 1719160
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-6,12:0,0:1,0']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '24.24.1.dk.1', 'curve_level': 24, 'curve_name': None, 'cusp': True, 'degree': 2, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '2.2.8.1', 'upload_id': None}
  • id: 1719161
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['18,0:0,24:1,0']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '24.24.1.dk.1', 'curve_level': 24, 'curve_name': None, 'cusp': True, 'degree': 2, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '2.2.12.1', 'upload_id': None}
  • id: 94639
    {'Elabel': '16128.e2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 16128, 'coordinates': {'5': ['16:-28:1', '16:28:1', '21:-63:1', '21:63:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '24.24.1.dk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 27.5048027866628, 'jinv': '-881422385472/5764801', 'jorig': '-881422385472/5764801', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 152687
    {'Elabel': '30636.d1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 30636, 'coordinates': {'5': ['-134/9:-2024/27:1', '-134/9:2024/27:1', '1290/121:-4968/1331:1', '1290/121:4968/1331:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '24.24.1.dk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 54.3932417594652, 'jinv': '419454394725624777846000/146767394485224241', 'jorig': '419454394725624777846000/146767394485224241', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}