Modular curve data - 40.48.0-40.t.1.2

Formats: - HTML - YAML - JSON - 2024-05-24T03:13:52.713124

• 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': '8G0', 'Glabel': None, 'RSZBlabel': '40.48.0.923', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 8, 1], [1, 2, 19, 25], [1, 2, 24, 25], [1, 8, 0, 1], [9, 8, 32, 33], [11, 0, 10, 11], [19, 0, 30, 19], [39, 0, 30, 39], [39, 34, 27, 39], [39, 34, 37, 15]], 'cm_discriminants': [], 'coarse_class': '40.24.0.t', 'coarse_class_num': 20, 'coarse_index': 24, 'coarse_label': '40.24.0.t.1', 'coarse_level': 40, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 1], [4, 1]], 'cusp_widths': [[2, 4], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 2, 'generators': [[1, 30, 38, 17], [19, 38, 11, 15], [27, 20, 12, 23]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': 0, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 6, 1], [8, 4, 1], [8, 8, 1], [10, 6, 1], [10, 12, 1], [20, 12, 1], [20, 24, 1], [40, 24, 1], [40, 48, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 12, 1], [8, 8, 1], [8, 16, 1], [10, 12, 1], [10, 24, 1], [20, 48, 1], [20, 96, 1], [40, 192, 1], [40, 384, 1]], 'label': '40.48.0-40.t.1.2', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 6, 'num_known_degree1_noncusp_points': 6, 'num_known_degree1_points': 7, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [5, 24, 1], [8, 16, 1], [8, 32, 1], [10, 24, 1], [10, 48, 1], [20, 96, 1], [20, 192, 1], [40, 384, 1], [40, 768, 1]], 'parents': ['40.24.0-20.d.1.5', '40.24.0-20.d.1.6'], 'parents_conj': None, 'pointless': None, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.b.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [1, 2], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.a.1', '8.12.0-4.a.1.1', '20.12.0.d.1'], 'scalar_label': '20.4.2', 'simple': None, 'sl2label': '8.48.0-8.b.1.3', 'sl2level': 8, 'squarefree': None, 'trace_hash': 0, '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': '8G0', 'Glabel': None, 'RSZBlabel': '40.24.0.394', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 8, 1], [1, 0, 10, 1], [1, 2, 19, 25], [1, 2, 24, 25], [1, 6, 3, 25], [1, 6, 13, 1], [1, 8, 0, 1], [9, 8, 32, 33], [11, 0, 10, 11], [21, 0, 10, 21]], 'cm_discriminants': [], 'coarse_class': '40.24.0.t', 'coarse_class_num': 20, 'coarse_index': 24, 'coarse_label': '40.24.0.t.1', 'coarse_level': 40, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 1], [4, 1]], 'cusp_widths': [[2, 4], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[21, 20, 21, 31], [21, 22, 1, 5], [31, 2, 32, 11], [31, 4, 7, 17]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': 0, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 6, 1], [8, 4, 1], [8, 8, 1], [10, 6, 1], [10, 12, 1], [20, 12, 1], [20, 24, 1], [40, 24, 1], [40, 48, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 12, 1], [8, 8, 1], [8, 16, 1], [10, 12, 1], [10, 24, 1], [20, 48, 1], [20, 96, 1], [40, 192, 1], [40, 384, 1]], 'label': '40.24.0.t.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.2.0.a.1', '4.6.0.a.1', '20.6.0.c.1', '20.6.0.e.1', '20.12.0.d.1', '40.24.0.t.1'], 'lattice_x': [3350, 5370, 1330, 1576, 5123, 8670, 5123, 5123], 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 6, 'num_known_degree1_noncusp_points': 6, 'num_known_degree1_points': 7, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [5, 24, 1], [8, 16, 1], [8, 32, 1], [10, 24, 1], [10, 48, 1], [20, 96, 1], [20, 192, 1], [40, 384, 1], [40, 768, 1]], 'parents': ['20.12.0.d.1'], 'parents_conj': [[1, 0, 0, 1]], 'pointless': None, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.b.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [1, 2], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.a.1', '4.6.0.a.1', '20.12.0.d.1'], 'scalar_label': '5.2.1', 'simple': None, 'sl2label': '8.24.0.b.1', 'sl2level': 8, 'squarefree': None, 'trace_hash': 0, 'traces': []}
• modcurve 40.24.0.t.1 does not appear in modcurve_models
• 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': ['(5*x+y)^24*(15625*x^8+625000*x^7*y-200000*x^6*y^2-2270000*x^5*y^3-1187000*x^4*y^4+436000*x^3*y^5+236800*x^2*y^6-6080*x*y^7-5744*y^8)^3', '(5*x+y)^24*(5*x^2+2*x*y+2*y^2)^8*(125*x^4-500*x^3*y-600*x^2*y^2+40*x*y^3+44*y^4)^2'], 'degree': 24, 'domain_label': '40.24.0.t.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-2^6', '5^6'], '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: 3024
    {'Elabel': '160.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 160, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '40.24.0.t.1', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 4.15888308335967, 'jinv': '-64/25', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1848440
    {'Elabel': None, 'ainvs': None, 'cardinality': 0, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-1/5:1']}, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '40.24.0.t.1', 'curve_level': 40, 'curve_name': None, 'cusp': True, 'degree': 1, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 17851
    {'Elabel': '1760.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1760, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '40.24.0.t.1', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 21.8088502488245, 'jinv': '2961169856/1890625', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 37220
    {'Elabel': '4640.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 4640, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '40.24.0.t.1', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 37.8250379962107, 'jinv': '-26742701668677184/5133056640625', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 49156
    {'Elabel': '6560.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 6560, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '40.24.0.t.1', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 28.7241170075968, 'jinv': '2983496371136/16416015625', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 122362
    {'Elabel': '22880.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 22880, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '40.24.0.t.1', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 38.1831941361075, 'jinv': '-38260488858209344/298577837154025', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 608550
    {'Elabel': '191840.b2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 191840, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '40.24.0.t.1', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 49.6082690300904, 'jinv': '3504269482473059112896/5484012603759765625', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}