Modular curve data - 40.72.1-10.a.1.1

Formats: - HTML - YAML - JSON - 2024-05-24T22:54:19.795368

• 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': '10G1', 'Glabel': None, 'RSZBlabel': '40.72.1.49', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [31, 23, 29, 16], 'canonical_generators': [[1, 0, 10, 1], [1, 2, 2, 1], [1, 2, 8, 7], [1, 4, 2, 9], [1, 10, 0, 1], [9, 0, 0, 39], [19, 0, 0, 39], [29, 30, 10, 9], [39, 32, 38, 35]], 'cm_discriminants': [], 'coarse_class': '10.36.1.a', 'coarse_class_num': 1, 'coarse_index': 36, 'coarse_label': '10.36.1.a.1', 'coarse_level': 10, 'coarse_num': 1, 'conductor': [[2, 2], [5, 1]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 6]], 'cusp_widths': [[2, 3], [10, 3]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 1, 'generators': [[3, 16, 34, 25], [7, 16, 16, 7], [9, 18, 18, 29], [9, 34, 0, 23], [33, 26, 0, 39], [33, 36, 10, 9]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 72, 'isogeny_orbits': [[2, 1, 3], [4, 2, 3], [5, 1, 1], [5, 5, 1], [8, 4, 3], [10, 1, 3], [10, 5, 3], [20, 2, 3], [20, 10, 3], [40, 4, 3], [40, 20, 3]], 'kummer_orbits': [[2, 1, 3], [4, 2, 3], [5, 2, 1], [5, 10, 1], [8, 8, 3], [10, 2, 3], [10, 10, 3], [20, 8, 3], [20, 40, 3], [40, 32, 3], [40, 160, 3]], 'label': '40.72.1-10.a.1.1', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '2.99573227355399099344', 'prec': 74}, 'models': None, 'mults': [1], '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': 1, 'obstructions': None, 'orbits': [[2, 1, 3], [4, 4, 3], [5, 4, 1], [5, 20, 1], [8, 16, 3], [10, 4, 3], [10, 20, 3], [20, 16, 3], [20, 80, 3], [40, 64, 3], [40, 320, 3]], 'parents': ['40.12.0-2.a.1.1'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 36, 'psl2label': '10.36.1.a.1', 'psl2level': 10, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 6, 'reductions': ['2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '5.6.0.a.1', '10.36.1.a.1', '10.36.1.a.1'], 'scalar_label': '4.2.1', 'simple': True, 'sl2label': '20.72.1-10.a.1.1', 'sl2level': 20, 'squarefree': True, 'trace_hash': 12896406231020588, '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': '10G1', 'Glabel': '80.30', 'RSZBlabel': '10.36.1.1', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [0, 1, 9, 9], 'canonical_generators': [[1, 2, 2, 1], [1, 2, 8, 7], [1, 4, 2, 9], [1, 8, 2, 5]], 'cm_discriminants': [], 'coarse_class': '10.36.1.a', 'coarse_class_num': 1, 'coarse_index': 36, 'coarse_label': '10.36.1.a.1', 'coarse_level': 10, 'coarse_num': 1, 'conductor': [[2, 2], [5, 1]], 'contains_negative_one': True, 'curve_label': '20.a4', 'cusp_orbits': [[1, 6]], 'cusp_widths': [[2, 3], [10, 3]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['2.6.0.a.1', '5.6.0.a.1'], 'fine_num': 0, 'generators': [[3, 0, 0, 7], [3, 8, 0, 9]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 36, 'isogeny_orbits': [[2, 1, 3], [5, 1, 1], [5, 5, 1], [10, 1, 3], [10, 5, 3]], 'kummer_orbits': [[2, 1, 3], [5, 2, 1], [5, 10, 1], [10, 2, 3], [10, 10, 3]], 'label': '10.36.1.a.1', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '2.3.0.a.1', '2.6.0.a.1', '5.6.0.a.1', '10.12.1.a.1', '10.18.0.a.1', '10.36.1.a.1'], 'lattice_x': [5968, 2885, 8538, 2885, 6364, 1067, 6364, 3241], 'level': 10, 'level_is_squarefree': True, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '2.99573227355399099344', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['20.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 1, 'obstructions': [], 'orbits': [[2, 1, 3], [5, 4, 1], [5, 20, 1], [10, 4, 3], [10, 20, 3]], 'parents': ['2.6.0.a.1', '10.12.1.a.1', '10.18.0.a.1'], 'parents_conj': [[1, 0, 0, 1], [2, 5, 3, 6], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 36, 'psl2label': '10.36.1.a.1', 'psl2level': 10, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 6, 'reductions': ['2.6.0.a.1', '5.6.0.a.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '10.36.1.a.1', 'sl2level': 10, 'squarefree': True, 'trace_hash': 12896406231020588, 'traces': [0, -2, -1, 2, 0, 2, -6, -4, 6, 6, -4, 2, 6, -10, -6, -6, 12, 2, 2, -12, 2, 8, 6, -6, 2, 6, 14, -6, 2, -6, 2, 0, 18, -4, -6, 20, -22, -10, 18, -6, -12, -10, -12, 26, 18, 8, -16, -10, -6, 14, -6, -24, 14, 0, -6, -18, 18, 20, 26, 6, 14, -30, 2, 12, -22, -6, 8, 2, -30, -10, 18, 24, -22, 26, -28, 6, -6, 2, -30, -34, 36, 26, 36, 2, 8, 6, 6, 26, 30, 14, -30, -24, 26, 0, -4, -18, 6, -6, 14, 14, 26, -30, -18, 30, 8, -22, -6, 18, 0, -10, -22, 2, -6, 20, -28, -18, 14, 42, 42, 36, -22, -46, 18, -42, 8, -30, -34, -24, -46, -22, 20, 6, -4, -22, 42, 2, -30, 26, 42, -6, -16, -54, 38, -30, 2, -48, 50, 18, -4, 6, 26, -18, 14, 18, -46, 12, -16, -42, -22, -18, 18, -6, -22, -24, 18, -18, -4, 26]}
• 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+x^2*z-y^2*z+4*x*z^2+4*z^3'], 'modcurve': '10.36.1.a.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': ['702*x^2*y^10+172801470*x^2*y^8*z^2-7293296040*x^2*y^6*z^4+58873460634*x^2*y^4*z^6-140838145082*x^2*y^2*z^8+63165448681*x^2*z^10+167859*x*y^10*z+671160132*x*y^8*z^3-9162527235*x*y^6*z^5-2073715896*x*y^4*z^7+238834250645*x*y^2*z^9-483993059328*x*z^11+y^12+14328537*y^10*z^2-537229632*y^8*z^4+16163936765*y^6*z^6-140965016207*y^4*z^8+465116093315*y^2*z^10-516640929884*z^12', 'x^2*y^10-6880*x^2*y^8*z^2-27648*x^2*y^6*z^4-3958272*x^2*y^4*z^6-53063680*x^2*y^2*z^8+33021952*x^2*z^10-40*x*y^10*z+32720*x*y^8*z^3+1071360*x*y^6*z^5+11865344*x*y^4*z^7-72558592*x*y^2*z^9-280088576*x*z^11+700*y^10*z^2-101968*y^8*z^4-1150976*y^6*z^6+13327104*y^4*z^8+49731584*y^2*z^10-313110528*z^12'], 'degree': 36, 'domain_label': '10.36.1.a.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': None, '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

  
  {'Elabel': None, 'ainvs': None, 'cardinality': 6, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-1:0:1', '0:-2:1', '4:-10:1', '4:10:1', '0:2:1', '0:1:0']}, 'curve_genus': 1, 'curve_index': 36, 'curve_label': '10.36.1.a.1', 'curve_level': 10, '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}