Modular curve data - 40.144.1-40.t.2.2

Formats: - HTML - YAML - JSON - 2024-05-17T05:31:40.486193

• 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': '20H1', 'Glabel': None, 'RSZBlabel': '40.144.1.15', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [21, 0, 5, 21], 'canonical_generators': [[0, 1, 9, 2], [0, 1, 29, 32], [0, 9, 7, 2], [0, 11, 29, 22], [0, 21, 19, 2], [0, 31, 9, 2], [0, 31, 39, 22], [1, 0, 20, 1], [1, 20, 0, 1], [21, 20, 20, 21]], 'cm_discriminants': [], 'coarse_class': '40.72.1.t', 'coarse_class_num': 20, 'coarse_index': 72, 'coarse_label': '40.72.1.t.2', 'coarse_level': 40, 'coarse_num': 2, 'conductor': [[2, 6], [5, 1]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 3], [4, 1]], 'cusp_widths': [[1, 4], [4, 2], [5, 4], [20, 2]], 'cusps': 12, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['5.24.0-5.a.1.1', '8.6.0.d.1'], 'fine_num': 2, 'generators': [[5, 11, 6, 5], [7, 32, 34, 25], [9, 17, 18, 23], [37, 4, 6, 25]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 144, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 1, 1], [5, 5, 1], [8, 4, 1], [8, 8, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [20, 2, 1], [20, 4, 1], [20, 10, 1], [20, 20, 1], [40, 4, 1], [40, 8, 1], [40, 20, 1], [40, 40, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 1, 2], [5, 10, 1], [8, 8, 1], [8, 16, 1], [10, 1, 2], [10, 2, 2], [10, 10, 1], [10, 20, 1], [20, 4, 2], [20, 8, 2], [20, 40, 1], [20, 80, 1], [40, 16, 2], [40, 32, 2], [40, 160, 1], [40, 320, 1]], 'label': '40.144.1-40.t.2.2', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.76832099579377223110', 'prec': 74}, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 2, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [5, 2, 2], [5, 20, 1], [8, 16, 1], [8, 32, 1], [10, 2, 2], [10, 4, 2], [10, 20, 1], [10, 40, 1], [20, 8, 2], [20, 16, 2], [20, 80, 1], [20, 160, 1], [40, 32, 2], [40, 64, 2], [40, 320, 1], [40, 640, 1]], 'parents': ['10.72.0-10.a.2.3', '40.72.0-10.a.2.2'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 72, 'psl2label': '20.72.1.a.1', 'psl2level': 20, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '2.3.0.a.1', '5.24.0-5.a.1.1', '8.6.0.d.1', '10.72.0-10.a.2.3', '10.72.0-10.a.2.3'], 'scalar_label': '5.4.1', 'simple': True, 'sl2label': '20.144.1-20.a.1.2', 'sl2level': 20, 'squarefree': True, 'trace_hash': 702150552534926687, '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': '20H1', 'Glabel': None, 'RSZBlabel': '40.72.1.22', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [13, 0, 25, 23], 'canonical_generators': [[0, 1, 9, 2], [0, 1, 29, 32], [0, 9, 1, 18], [0, 9, 7, 2], [0, 21, 19, 2], [0, 29, 11, 18], [0, 31, 9, 2], [1, 0, 20, 1], [1, 20, 0, 1], [21, 20, 20, 21]], 'cm_discriminants': [], 'coarse_class': '40.72.1.t', 'coarse_class_num': 20, 'coarse_index': 72, 'coarse_label': '40.72.1.t.2', 'coarse_level': 40, 'coarse_num': 2, 'conductor': [[2, 6], [5, 1]], 'contains_negative_one': True, 'curve_label': '320.a3', 'cusp_orbits': [[1, 2], [2, 3], [4, 1]], 'cusp_widths': [[1, 4], [4, 2], [5, 4], [20, 2]], 'cusps': 12, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['5.12.0.a.1', '8.6.0.d.1'], 'fine_num': 0, 'generators': [[9, 12, 36, 25], [21, 5, 38, 23], [27, 7, 24, 35], [29, 35, 12, 27], [33, 31, 26, 3]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 72, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 1, 1], [5, 5, 1], [8, 4, 1], [8, 8, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [20, 2, 1], [20, 4, 1], [20, 10, 1], [20, 20, 1], [40, 4, 1], [40, 8, 1], [40, 20, 1], [40, 40, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 1, 2], [5, 10, 1], [8, 8, 1], [8, 16, 1], [10, 1, 2], [10, 2, 2], [10, 10, 1], [10, 20, 1], [20, 4, 2], [20, 8, 2], [20, 40, 1], [20, 80, 1], [40, 16, 2], [40, 32, 2], [40, 160, 1], [40, 320, 1]], 'label': '40.72.1.t.2', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '5.6.0.a.1', '5.12.0.a.1', '8.6.0.d.1', '10.18.0.a.1', '10.36.0.a.2', '40.36.0.c.2', '40.36.1.d.1', '40.72.1.t.2'], 'lattice_x': [5030, 6332, 3767, 1913, 8777, 6174, 2229, 6095, 8935, 6095], 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.76832099579377223110', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['320.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 2, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [5, 2, 2], [5, 20, 1], [8, 16, 1], [8, 32, 1], [10, 2, 2], [10, 4, 2], [10, 20, 1], [10, 40, 1], [20, 8, 2], [20, 16, 2], [20, 80, 1], [20, 160, 1], [40, 32, 2], [40, 64, 2], [40, 320, 1], [40, 640, 1]], 'parents': ['10.36.0.a.2', '40.36.0.c.2', '40.36.1.d.1'], 'parents_conj': [[9, 28, 4, 35], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 72, 'psl2label': '20.72.1.a.1', 'psl2level': 20, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '2.3.0.a.1', '5.12.0.a.1', '8.6.0.d.1', '10.36.0.a.2', '10.36.0.a.2'], 'scalar_label': '5.2.1', 'simple': True, 'sl2label': '20.72.1.a.1', 'sl2level': 20, 'squarefree': True, 'trace_hash': 702150552534926687, '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-5*x*z^2-5*z^3'], 'modcurve': '40.72.1.t.2', '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': ['48*x^2*y^22+113536*x^2*y^20*z^2+18764800*x^2*y^18*z^4+951164928*x^2*y^16*z^6+23479582720*x^2*y^14*z^8+358406422528*x^2*y^12*z^10+3850345906176*x^2*y^10*z^12+30161743380480*x^2*y^8*z^14+174225079926784*x^2*y^6*z^16+733311978700800*x^2*y^4*z^18+2048132464508928*x^2*y^2*z^20+3429514205986816*x^2*z^22+1056*x*y^22*z+850688*x*y^20*z^3+97290240*x*y^18*z^5+4167745536*x*y^16*z^7+94294507520*x*y^14*z^9+1370033750016*x*y^12*z^11+14199916855296*x*y^10*z^13+108074127851520*x*y^8*z^15+609857975615488*x*y^6*z^17+2505920143687680*x*y^4*z^19+6864972646711296*x*y^2*z^21+11098195492864000*x*z^23+y^24+13264*y^22*z^2+4152320*y^20*z^4+290933760*y^18*z^6+9013301248*y^16*z^8+164075012096*y^14*z^10+2052266655744*y^12*z^12+18749168025600*y^10*z^14+127597354680320*y^8*z^16+650056453586944*y^6*z^18+2382959524970496*y^4*z^20+5876735031640064*y^2*z^22+7668750006353920*z^24', 'z^6*y^4*(y^2+8*z^2)^2*(x^2*y^8+1184*x^2*y^6*z^2+69248*x^2*y^4*z^4+1067008*x^2*y^2*z^6+4771840*x^2*z^8+22*x*y^8*z+6688*x*y^6*z^3+285696*x*y^4*z^5+3782656*x*y^2*z^7+15441920*x*z^9+201*y^8*z^2+21696*y^6*z^4+514688*y^4*z^6+4190208*y^2*z^8+10670080*z^10)'], 'degree': 72, 'domain_label': '40.72.1.t.2', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['1', '2^10'], '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: 1768268
    {'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-1:0:1', '0:1:0']}, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '40.72.1.t.2', '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: 1768269
    {'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-3,0:0,-2:1,0', '1,0:0,-2:1,0']}, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '40.72.1.t.2', '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': '2.0.8.1', 'upload_id': None}
  • id: 1768270
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['1,-2:0,0:1,0']}, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '40.72.1.t.2', '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': '2.2.5.1', 'upload_id': None}
  • id: 1768271
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['1,0,2,0:0,-4,0,-3:1,0,0,0']}, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '40.72.1.t.2', 'curve_level': 40, 'curve_name': None, 'cusp': True, 'degree': 4, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '4.0.1600.1', 'upload_id': None}
  • id: 1899
    {'Elabel': '66.c3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 66, 'coordinates': {'5': ['-2:-1:1', '-2:1:1', '3:-4:1', '3:4:1']}, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '40.72.1.t.2', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 23.0349790695207, 'jinv': '10091699281/2737152', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}