Modular curve data - 30.48.1-30.d.2.4

Formats: - HTML - YAML - JSON - 2024-05-13T22:57:35.856380

• 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': '10D1', 'Glabel': None, 'RSZBlabel': '30.48.1.8', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [1, 1, 29, 0], 'canonical_generators': [[0, 19, 1, 22], [0, 23, 1, 23], [0, 29, 11, 2], [1, 0, 10, 1], [1, 10, 0, 1], [11, 10, 20, 21], [20, 9, 21, 17]], 'cm_discriminants': [], 'coarse_class': '30.24.1.d', 'coarse_class_num': 4, 'coarse_index': 24, 'coarse_label': '30.24.1.d.2', 'coarse_level': 30, 'coarse_num': 2, 'conductor': [[2, 2], [3, 2], [5, 1]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 1]], 'cusp_widths': [[2, 2], [10, 2]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['5.24.0-5.a.2.2', '6.2.0.a.1'], 'fine_num': 4, 'generators': [[1, 20, 5, 9], [11, 10, 12, 23], [21, 25, 23, 14]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 3, 1], [3, 4, 1], [5, 1, 1], [5, 5, 1], [6, 12, 1], [10, 3, 1], [10, 15, 1], [15, 4, 1], [15, 20, 1], [30, 12, 1], [30, 60, 1]], 'kummer_orbits': [[2, 3, 1], [3, 4, 1], [5, 2, 1], [5, 5, 2], [6, 12, 1], [10, 6, 1], [10, 15, 2], [15, 16, 1], [15, 40, 2], [30, 48, 1], [30, 120, 2]], 'label': '30.48.1-30.d.2.4', 'lattice_labels': None, 'lattice_x': None, 'level': 30, 'level_is_squarefree': True, 'level_radical': 30, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.19295685089021037623', 'prec': 74}, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 2, 'obstructions': None, 'orbits': [[2, 3, 1], [3, 8, 1], [5, 4, 1], [5, 5, 4], [6, 24, 1], [10, 12, 1], [10, 15, 4], [15, 32, 1], [15, 40, 4], [30, 96, 1], [30, 120, 4]], 'parents': ['5.24.0-5.a.2.2', '30.24.0-5.a.2.1'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 24, 'psl2label': '10.24.1.a.1', 'psl2level': 10, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '5.24.0-5.a.2.2', '5.24.0-5.a.2.2', '5.24.0-5.a.2.2', '6.2.0.a.1'], 'scalar_label': '5.4.1', 'simple': True, 'sl2label': '10.48.1-10.a.1.1', 'sl2level': 10, 'squarefree': True, 'trace_hash': 54573415799175087, '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': '10D1', 'Glabel': None, 'RSZBlabel': '30.24.1.5', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [1, 1, 29, 0], 'canonical_generators': [[0, 1, 19, 28], [0, 7, 29, 7], [0, 19, 1, 22], [1, 0, 10, 1], [1, 10, 0, 1], [10, 21, 9, 13], [11, 10, 20, 21]], 'cm_discriminants': [], 'coarse_class': '30.24.1.d', 'coarse_class_num': 4, 'coarse_index': 24, 'coarse_label': '30.24.1.d.2', 'coarse_level': 30, 'coarse_num': 2, 'conductor': [[2, 2], [3, 2], [5, 1]], 'contains_negative_one': True, 'curve_label': '180.a1', 'cusp_orbits': [[1, 2], [2, 1]], 'cusp_widths': [[2, 2], [10, 2]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['5.12.0.a.2', '6.2.0.a.1'], 'fine_num': 0, 'generators': [[9, 25, 10, 3], [9, 25, 17, 4], [21, 5, 14, 11]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 24, 'isogeny_orbits': [[2, 3, 1], [3, 4, 1], [5, 1, 1], [5, 5, 1], [6, 12, 1], [10, 3, 1], [10, 15, 1], [15, 4, 1], [15, 20, 1], [30, 12, 1], [30, 60, 1]], 'kummer_orbits': [[2, 3, 1], [3, 4, 1], [5, 2, 1], [5, 5, 2], [6, 12, 1], [10, 6, 1], [10, 15, 2], [15, 16, 1], [15, 40, 2], [30, 48, 1], [30, 120, 2]], 'label': '30.24.1.d.2', 'lattice_labels': ['1.1.0.a.1', '5.6.0.a.1', '5.12.0.a.2', '6.2.0.a.1', '30.12.0.a.1', '30.12.1.d.1', '30.24.1.d.2'], 'lattice_x': [6650, 4631, 4877, 8670, 1330, 8424, 4877], 'level': 30, 'level_is_squarefree': True, 'level_radical': 30, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.19295685089021037623', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['180.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 2, 'obstructions': [], 'orbits': [[2, 3, 1], [3, 8, 1], [5, 4, 1], [5, 10, 2], [6, 24, 1], [10, 12, 1], [10, 30, 2], [15, 32, 1], [15, 80, 2], [30, 96, 1], [30, 240, 2]], 'parents': ['5.12.0.a.2', '30.12.0.a.1', '30.12.1.d.1'], 'parents_conj': [[5, 6, 7, 5], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 24, 'psl2label': '10.24.1.a.1', 'psl2level': 10, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '5.12.0.a.2', '5.12.0.a.2', '5.12.0.a.2', '6.2.0.a.1'], 'scalar_label': '5.2.1', 'simple': True, 'sl2label': '10.24.1.a.1', 'sl2level': 10, 'squarefree': True, 'trace_hash': 54573415799175087, 'traces': [0, 0, 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-y^2*z-372*x*z^2+2761*z^3'], 'modcurve': '30.24.1.d.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': ['2184*x^2*y^6-49819344840*x^2*y^4*z^2+3422526853924728*x^2*y^2*z^4-27039497222900331576*x^2*z^6-1674672*x*y^6*z+2876294021616*x*y^4*z^3-100451964128318928*x*y^2*z^5+602183388702393227664*x*z^7-y^8+510498348*y^6*z^2-106591444126974*y^4*z^4+1503562500387405180*y^2*z^6-3352238111755385915049*z^8', 'y^2*(x^2*y^4-594*x^2*y^2*z^2-729*x^2*z^4+44*x*y^4*z-6453*x*y^2*z^3-8019*x*z^5+466*y^4*z^2+150876*y^2*z^4+182979*z^6)'], 'degree': 24, 'domain_label': '30.24.1.d.2', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['1', '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: 1975
    {'Elabel': '75.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 75, 'coordinates': {'5': ['2:-45:1', '2:45:1', '12:-5:1', '12:5:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '30.24.1.d.2', 'curve_level': 30, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 4, 'j_field': '1.1.1.1', 'j_height': 11.5366419915875, 'jinv': '-102400/3', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1758783
    {'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['11:0:1', '0:1:0']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '30.24.1.d.2', 'curve_level': 30, '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: 1758784
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['2,-15:0,0:1,0']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '30.24.1.d.2', 'curve_level': 30, '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}