Modular curve data - 280.24.0-28.e.1.3

Formats: - HTML - YAML - JSON - 2024-06-04T20:09:39.361936

• 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': '4E0', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5, 7], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 28, 1], [1, 0, 60, 1], [1, 0, 70, 1], [1, 170, 20, 231], [1, 170, 65, 21], [141, 0, 0, 1], [209, 0, 210, 209], [219, 220, 200, 199], [223, 0, 0, 279], [251, 252, 28, 27], [279, 220, 0, 279], [279, 220, 55, 259], [279, 252, 0, 279]], 'cm_discriminants': [], 'coarse_class': '28.12.0.e', 'coarse_class_num': 5, 'coarse_index': 12, 'coarse_label': '28.12.0.e.1', 'coarse_level': 28, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 2]], 'cusp_widths': [[2, 2], [4, 2]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 3, 'generators': [[25, 276, 43, 121], [27, 28, 117, 15], [35, 194, 184, 169], [67, 66, 120, 253]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': 1, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 6, 1], [7, 8, 1], [8, 4, 1], [8, 8, 1], [10, 6, 1], [10, 12, 1], [14, 8, 1], [14, 16, 1], [20, 12, 1], [20, 24, 1], [28, 16, 1], [28, 32, 1], [35, 48, 1], [40, 24, 1], [40, 48, 1], [56, 32, 1], [56, 64, 1], [70, 48, 1], [70, 96, 1], [140, 96, 1], [140, 192, 1], [280, 192, 1], [280, 384, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 12, 1], [7, 24, 1], [8, 8, 1], [8, 16, 1], [10, 12, 1], [10, 24, 1], [14, 24, 1], [14, 48, 1], [20, 48, 1], [20, 96, 1], [28, 96, 1], [28, 192, 1], [35, 576, 1], [40, 192, 1], [40, 384, 1], [56, 384, 1], [56, 768, 1], [70, 576, 1], [70, 1152, 1], [140, 2304, 1], [140, 4608, 1], [280, 9216, 1], [280, 18432, 1]], 'label': '280.24.0-28.e.1.3', 'lattice_labels': None, 'lattice_x': None, 'level': 280, 'level_is_squarefree': False, 'level_radical': 70, 'log_conductor': None, 'models': None, 'mults': None, '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, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [5, 24, 1], [7, 48, 1], [8, 16, 1], [8, 32, 1], [10, 24, 1], [10, 48, 1], [14, 48, 1], [14, 96, 1], [20, 96, 1], [20, 192, 1], [28, 192, 1], [28, 384, 1], [35, 1152, 1], [40, 384, 1], [40, 768, 1], [56, 768, 1], [56, 1536, 1], [70, 1152, 1], [70, 2304, 1], [140, 4608, 1], [140, 9216, 1], [280, 18432, 1], [280, 36864, 1]], 'parents': ['40.12.0-4.b.1.3', '280.12.0-4.b.1.3'], 'parents_conj': None, 'pointless': True, 'power': None, 'psl2index': 12, 'psl2label': '4.12.0.a.1', 'psl2level': 4, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.b.1', '4.6.0.b.1', '4.6.0.b.1', '14.6.0.b.1', '14.6.0.b.1', '28.12.0.e.1', '28.12.0.e.1', '28.12.0.e.1', '40.12.0-4.b.1.3'], 'scalar_label': '4.2.1', 'simple': None, 'sl2label': '4.12.0.a.1', 'sl2level': 8, 'squarefree': None, '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': '4E0', 'Glabel': None, 'RSZBlabel': '28.12.0.13', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 7], 'canonical_conjugator': [5, 5, 22, 23], 'canonical_generators': [[1, 0, 4, 1], [1, 0, 14, 1], [1, 2, 9, 21], [1, 2, 20, 7], [1, 4, 0, 1], [1, 4, 1, 21], [5, 4, 24, 25], [15, 0, 14, 15]], 'cm_discriminants': [], 'coarse_class': '28.12.0.e', 'coarse_class_num': 5, 'coarse_index': 12, 'coarse_label': '28.12.0.e.1', 'coarse_level': 28, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 2]], 'cusp_widths': [[2, 2], [4, 2]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[4, 23, 23, 6], [15, 26, 2, 5]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': 1, 'index': 12, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [7, 8, 1], [14, 8, 1], [14, 16, 1], [28, 16, 1], [28, 32, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [7, 24, 1], [14, 24, 1], [14, 48, 1], [28, 96, 1], [28, 192, 1]], 'label': '28.12.0.e.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.b.1', '14.2.0.a.1', '14.6.0.b.1', '28.6.0.e.1', '28.12.0.e.1'], 'lattice_x': [3350, 5370, 5123, 1330, 1576, 8670, 5123], 'level': 28, 'level_is_squarefree': False, 'level_radical': 14, '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': [0], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [7, 48, 1], [14, 48, 1], [14, 96, 1], [28, 192, 1], [28, 384, 1]], 'parents': ['4.6.0.b.1', '14.6.0.b.1', '28.6.0.e.1'], 'parents_conj': [[9, 8, 5, 3], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': True, 'power': None, 'psl2index': 12, 'psl2label': '4.12.0.a.1', 'psl2level': 4, 'q_gonality': 2, 'q_gonality_bounds': [2, 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', '4.6.0.b.1', '14.6.0.b.1'], 'scalar_label': '1.1.1', 'simple': None, 'sl2label': '4.12.0.a.1', 'sl2level': 4, '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': ['9*x^2+3*x*y+2*y^2+112*z^2'], 'modcurve': '28.12.0.e.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': ['6561*x^8+6561*x^7*y+34992*x^6*z^2+54432*x^5*y*z^2+352512*x^4*z^4+131328*x^3*y*z^4+1363968*x^2*z^6-98304*x*y*z^6-131072*z^8', 'z^4*(9*x^2+16*z^2)^2'], 'degree': 12, 'domain_label': '28.12.0.e.1', 'domain_model_type': 2, 'dont_display': False, 'factored': True, 'leading_coefficients': ['1', '2^3'], '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: 1757785
    {'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['-1/3,1/3:1,0:0,0']}, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '28.12.0.e.1', 'curve_level': 28, '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': '2.0.7.1', 'upload_id': None}
  • id: 1757786
    {'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['0,4/3:0,6:1,0']}, 'curve_genus': 0, 'curve_index': 12, 'curve_label': '28.12.0.e.1', 'curve_level': 28, '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': '2.0.4.1', 'upload_id': None}