Modular curve data - 24.144.4-24.ch.1.38

Formats: - HTML - YAML - JSON - 2024-06-11T03:17:49.990346

• 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': '24D4', 'Glabel': None, 'RSZBlabel': '24.144.4.35', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [17, 0, 20, 5], 'canonical_generators': [[1, 2, 8, 9], [1, 2, 8, 17], [1, 10, 16, 17], [5, 2, 8, 13], [7, 2, 8, 21], [9, 2, 16, 9], [21, 22, 8, 21], [23, 22, 16, 9], [23, 22, 16, 21]], 'cm_discriminants': [], 'coarse_class': '24.72.4.ch', 'coarse_class_num': 60, 'coarse_index': 72, 'coarse_label': '24.72.4.ch.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': [[2, 10], [3, 8]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 1]], 'cusp_widths': [[6, 4], [24, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1, 1], 'factorization': ['3.3.0.a.1', '8.48.0-8.i.1.2'], 'fine_num': 38, 'generators': [[7, 0, 0, 13], [7, 6, 0, 13], [7, 18, 0, 5], [11, 20, 16, 17], [17, 22, 16, 13], [21, 10, 16, 21]], 'genus': 4, 'genus_minus_rank': 4, 'has_obstruction': -1, 'index': 144, 'isogeny_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [8, 1, 2], [8, 2, 1], [8, 4, 2], [12, 4, 2], [12, 8, 2], [24, 4, 2], [24, 8, 1], [24, 16, 2]], 'kummer_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [8, 2, 2], [8, 4, 1], [8, 8, 2], [12, 8, 2], [12, 16, 2], [24, 16, 2], [24, 32, 1], [24, 64, 2]], 'label': '24.144.4-24.ch.1.38', 'lattice_labels': None, 'lattice_x': None, 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '15.72037011494433062533', 'prec': 77}, 'models': None, 'mults': [3, 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], [3, 8, 1], [4, 2, 6], [6, 8, 3], [8, 4, 4], [8, 8, 4], [12, 16, 6], [24, 32, 4], [24, 64, 4]], 'parents': ['8.48.0-8.i.1.2', '12.72.2-12.b.1.9', '24.72.2-12.b.1.30', '24.72.2-24.cj.1.5', '24.72.2-24.cj.1.44', '24.72.2-24.cw.1.5', '24.72.2-24.cw.1.28'], 'parents_conj': None, 'pointless': False, 'power': False, 'psl2index': 72, 'psl2label': '24.72.4.d.1', 'psl2level': 24, 'q_gonality': 3, 'q_gonality_bounds': [3, 3], 'qbar_gonality': 3, 'qbar_gonality_bounds': [3, 3], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.6.0.a.1', '3.3.0.a.1', '4.24.0-4.b.1.1', '6.18.1.a.1', '8.48.0-8.i.1.2', '12.72.2-12.b.1.9'], 'scalar_label': '4.2.1', 'simple': False, 'sl2label': '24.144.4-24.d.1.3', 'sl2level': 24, 'squarefree': False, 'trace_hash': 1621278907382659762, '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': '24D4', 'Glabel': None, 'RSZBlabel': '24.72.4.6', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [17, 0, 20, 5], 'canonical_generators': [[1, 2, 8, 3], [1, 2, 8, 9], [1, 2, 8, 15], [1, 2, 8, 17], [1, 10, 16, 17], [3, 2, 16, 3], [5, 2, 8, 13], [7, 2, 8, 21], [9, 2, 16, 9]], 'cm_discriminants': [], 'coarse_class': '24.72.4.ch', 'coarse_class_num': 60, 'coarse_index': 72, 'coarse_label': '24.72.4.ch.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': [[2, 10], [3, 8]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 1]], 'cusp_widths': [[6, 4], [24, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1, 1], 'factorization': ['3.3.0.a.1', '8.24.0.i.1'], 'fine_num': 0, 'generators': [[1, 6, 0, 23], [5, 0, 0, 1], [15, 2, 16, 3], [17, 22, 8, 5], [23, 16, 8, 17], [23, 20, 8, 7], [23, 22, 16, 19]], 'genus': 4, 'genus_minus_rank': 4, 'has_obstruction': -1, 'index': 72, 'isogeny_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [8, 1, 2], [8, 2, 1], [8, 4, 2], [12, 4, 2], [12, 8, 2], [24, 4, 2], [24, 8, 1], [24, 16, 2]], 'kummer_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [8, 2, 2], [8, 4, 1], [8, 8, 2], [12, 8, 2], [12, 16, 2], [24, 16, 2], [24, 32, 1], [24, 64, 2]], 'label': '24.72.4.ch.1', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '2.3.0.a.1', '2.6.0.a.1', '3.3.0.a.1', '4.6.0.c.1', '4.6.0.d.1', '4.12.0.b.1', '6.6.1.a.1', '6.9.0.a.1', '6.18.1.a.1', '8.12.0.n.1', '8.12.0.o.1', '8.24.0.i.1', '12.18.0.k.1', '12.18.1.c.1', '12.36.2.b.1', '24.36.2.cj.1', '24.36.2.cw.1', '24.72.4.ch.1'], 'lattice_x': [3078, 3078, 5010, 3702, 946, 6922, 5272, 5594, 684, 2133, 684, 7807, 9457, 7807, 2133, 3581, 3461, 4909, 6358, 5634], 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '15.72037011494433062533', 'prec': 77}, 'models': 2, 'mults': [3, 1], 'name': None, 'newforms': ['36.2.a.a', '144.2.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], [3, 8, 1], [4, 2, 2], [4, 4, 2], [6, 8, 3], [8, 4, 2], [8, 8, 1], [8, 16, 2], [12, 16, 2], [12, 32, 2], [24, 32, 2], [24, 64, 1], [24, 128, 2]], 'parents': ['8.24.0.i.1', '12.36.2.b.1', '24.36.2.cj.1', '24.36.2.cw.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': False, 'psl2index': 72, 'psl2label': '24.72.4.d.1', 'psl2level': 24, 'q_gonality': 3, 'q_gonality_bounds': [3, 3], 'qbar_gonality': 3, 'qbar_gonality_bounds': [3, 3], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.6.0.a.1', '3.3.0.a.1', '4.12.0.b.1', '6.18.1.a.1', '8.24.0.i.1', '12.36.2.b.1'], 'scalar_label': '1.1.1', 'simple': False, 'sl2label': '24.72.4.d.1', 'sl2level': 24, 'squarefree': False, 'trace_hash': 1621278907382659762, 'traces': [0, 0, 0, -8, 0, 8, 0, 16, 0, 0, -8, -40, 0, 16, 0, 0, 0, 56, -32, 0, -40, -8, 0, 0, 56, 0, 40, 0, 8, 0, 40, 0, 0, -32, 0, -8, 56, 16, 0, 0, 0, 104, 0, 8, 0, -56, -32, -56, 0, -88, 0, 0, 56, 0, 0, 0, 0, -56, 104, 0, 64, 0, -32, 0, -88, 0, 64, -136, 0, 56, 0, 0, -8, 152, 16, 0, 0, -136, 0, 152, 0, -88, 0, 8, -56, 0, 0, -40, 0, 40, 0, 0, 88, 0, 64, 0, 0, 0, 16, -184, -80, 0, 0, 0, -32, -184, 0, 0, 0, 104, 40, -40, 0, 64, 88, 0, -80, 0, 0, 0, 152, 200, 0, 0, 16, 0, -88, 0, 88, 200, -32, 0, -104, 104, 0, 8, 0, 112, 0, 0, 112, 0, -104, 0, -184, 0, -232, 0, 112, 0, -136, 0, 16, 0, -80, 0, -104, 0, 104, 0, 0, 0, 40, 0, 0, 0, 88, -40]}
• modcurve_models •

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

  
  
  • id: 13496
    {'dont_display': False, 'equation': ['4*y^2+z*w', 'x^3+y*z^2-y*w^2'], 'modcurve': '24.72.4.ch.1', 'model_type': 0, 'number_variables': 4, 'smooth': True, 'upload_id': None}
  • id: 13497
    {'dont_display': False, 'equation': ['x^5+2*y^3*z^2-x*z^4'], 'modcurve': '24.72.4.ch.1', 'model_type': 2, 'number_variables': 3, 'smooth': False, '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

  
  
  • id: 13598
    {'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['(z^4-z^2*w^2+w^4)^3', 'w^4*z^4*(z-w)^2*(z+w)^2'], 'degree': 72, 'domain_label': '24.72.4.ch.1', 'domain_model_type': 0, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^8', '1'], 'upload_id': None}
  • id: 13599
    {'codomain_label': '24.72.4.ch.1', 'codomain_model_type': 2, 'coordinates': ['y', '1/2*x', '1/2*w'], 'degree': 1, 'domain_label': '24.72.4.ch.1', 'domain_model_type': 0, 'dont_display': False, 'factored': False, '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

  
  
  • id: 1723627
    {'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0:0:1:0', '0:1/2:-1:1', '0:0:0:1', '0:-1/2:-1:1']}, 'curve_genus': 4, 'curve_index': 72, 'curve_label': '24.72.4.ch.1', 'curve_level': 24, '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: 1723628
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0,0:0,1/2:1,0:1,0']}, 'curve_genus': 4, 'curve_index': 72, 'curve_label': '24.72.4.ch.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': '2.0.4.1', 'upload_id': None}