Modular curve data - 40.96.0-40.s.1.15

Formats: - HTML - YAML - JSON - 2024-06-01T15:30:51.902987

• 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': '8O0', 'Glabel': None, 'RSZBlabel': '40.96.0.701', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [31, 6, 21, 7], 'canonical_generators': [[1, 0, 8, 1], [1, 4, 12, 35], [1, 8, 0, 1], [1, 8, 6, 15], [9, 8, 32, 33], [31, 0, 10, 31], [39, 0, 30, 39], [39, 32, 34, 35], [39, 36, 38, 5]], 'cm_discriminants': [], 'coarse_class': '40.48.0.s', 'coarse_class_num': 19, 'coarse_index': 48, 'coarse_label': '40.48.0.s.1', 'coarse_level': 40, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 5]], 'cusp_widths': [[2, 4], [4, 2], [8, 4]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 15, 'generators': [[1, 24, 34, 19], [11, 32, 34, 19], [19, 16, 28, 13], [35, 12, 2, 1]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': 0, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [5, 6, 1], [8, 2, 2], [8, 4, 2], [10, 6, 3], [20, 6, 2], [20, 12, 2], [40, 12, 2], [40, 24, 2]], 'kummer_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [5, 12, 1], [8, 4, 4], [8, 8, 1], [10, 12, 3], [20, 24, 2], [20, 48, 2], [40, 96, 4], [40, 192, 1]], 'label': '40.96.0-40.s.1.15', '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': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 0, 'obstructions': None, 'orbits': [[2, 1, 3], [4, 2, 2], [4, 4, 2], [5, 24, 1], [8, 8, 6], [10, 24, 3], [20, 48, 2], [20, 96, 2], [40, 192, 6]], 'parents': ['8.48.0-8.e.1.15', '40.48.0-8.e.1.14', '40.48.0-40.h.2.21', '40.48.0-40.h.2.26', '40.48.0-40.l.1.18', '40.48.0-40.l.1.20'], 'parents_conj': None, 'pointless': None, 'power': None, 'psl2index': 48, 'psl2label': '8.48.0.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', '2.6.0.a.1', '2.6.0.a.1', '4.12.0.b.1', '4.12.0.b.1', '8.48.0-8.e.1.15'], 'scalar_label': '8.4.1', 'simple': None, 'sl2label': '8.96.0-8.b.1.2', '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': '8O0', 'Glabel': None, 'RSZBlabel': '40.48.0.306', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [19, 30, 39, 33], 'canonical_generators': [[1, 0, 8, 1], [1, 0, 10, 1], [1, 4, 2, 35], [1, 4, 12, 35], [1, 8, 0, 1], [1, 8, 6, 5], [1, 8, 6, 15], [9, 8, 32, 33], [31, 0, 10, 31]], 'cm_discriminants': [], 'coarse_class': '40.48.0.s', 'coarse_class_num': 19, 'coarse_index': 48, 'coarse_label': '40.48.0.s.1', 'coarse_level': 40, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 5]], 'cusp_widths': [[2, 4], [4, 2], [8, 4]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[9, 32, 16, 21], [15, 16, 4, 15], [29, 8, 24, 27], [31, 20, 8, 21], [39, 4, 26, 35]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': 0, 'index': 48, 'isogeny_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [5, 6, 1], [8, 2, 2], [8, 4, 2], [10, 6, 3], [20, 6, 2], [20, 12, 2], [40, 12, 2], [40, 24, 2]], 'kummer_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [5, 12, 1], [8, 4, 4], [8, 8, 1], [10, 12, 3], [20, 24, 2], [20, 48, 2], [40, 96, 4], [40, 192, 1]], 'label': '40.48.0.s.1', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '2.3.0.a.1', '2.6.0.a.1', '4.6.0.c.1', '4.6.0.d.1', '4.12.0.b.1', '8.24.0.e.1', '40.12.0.y.1', '40.12.0.bb.1', '40.24.0.h.2', '40.24.0.l.1', '40.48.0.s.1'], 'lattice_x': [2880, 1327, 4434, 1618, 6796, 4142, 3560, 4466, 9126, 6796, 2136, 6796, 4466], 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 0, 'obstructions': [], 'orbits': [[2, 1, 3], [4, 2, 2], [4, 4, 2], [5, 24, 1], [8, 8, 4], [8, 16, 1], [10, 24, 3], [20, 48, 2], [20, 96, 2], [40, 192, 4], [40, 384, 1]], 'parents': ['8.24.0.e.1', '40.24.0.h.2', '40.24.0.l.1'], 'parents_conj': [[2, 29, 7, 11], [33, 34, 31, 1], [1, 0, 0, 1]], 'pointless': None, 'power': None, 'psl2index': 48, 'psl2label': '8.48.0.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', '2.6.0.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': None, 'sl2label': '8.48.0.b.1', 'sl2level': 8, 'squarefree': None, 'trace_hash': 0, 'traces': []}
• 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': ['2*x^2-5*y^2+40*z^2'], 'modcurve': '40.48.0.s.1', 'model_type': 2, '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': ['(x^8+40*x^6*z^2+2000*x^4*z^4+32000*x^2*z^6+160000*z^8)^3', 'z^4*x^8*(x^2+10*z^2)^2*(x^2+20*z^2)^4'], 'degree': 48, 'domain_label': '40.48.0.s.1', 'domain_model_type': 2, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^2', '5^2'], '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: 1767033
    {'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['0,1/2:1,0:0,0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.s.1', 'curve_level': 40, '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': '2.2.40.1', 'upload_id': None}
  • id: 1767034
    {'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['0,2:0,0:1,0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.s.1', 'curve_level': 40, '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': '2.0.20.1', 'upload_id': None}
  • id: 1767035
    {'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['0,0:0,2:1,0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.s.1', 'curve_level': 40, '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: 1767036
    {'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['0,1:-2,0:1,0', '0,-1:-2,0:1,0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.s.1', 'curve_level': 40, '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': '2.0.40.1', 'upload_id': None}