Modular curve data - 120.96.1-60.l.1.11

Formats: - HTML - YAML - JSON - 2024-05-25T11:48:22.814689

• 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': '12P1', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 12, 1], [1, 0, 60, 1], [1, 3, 16, 5], [1, 11, 52, 9], [1, 12, 0, 1], [1, 60, 0, 1], [51, 10, 20, 31], [59, 0, 0, 119], [61, 60, 60, 61], [79, 110, 100, 99], [107, 108, 72, 71], [117, 115, 116, 67], [119, 70, 80, 99], [119, 109, 104, 105], [119, 118, 92, 75]], 'cm_discriminants': [], 'coarse_class': '60.48.1.l', 'coarse_class_num': 12, 'coarse_index': 48, 'coarse_label': '60.48.1.l.1', 'coarse_level': 60, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[2, 2], [4, 2], [6, 2], [12, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.4.0.a.1', '40.24.0-20.h.1.2'], 'fine_num': 11, 'generators': [[49, 107, 72, 107], [51, 1, 64, 27], [67, 51, 0, 13], [91, 11, 60, 89], [93, 1, 64, 9], [97, 80, 28, 111]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [5, 6, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 2, 2], [8, 8, 1], [10, 6, 1], [10, 12, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [15, 6, 1], [15, 18, 1], [20, 6, 2], [20, 24, 1], [24, 2, 2], [24, 6, 2], [24, 8, 1], [24, 24, 1], [30, 6, 1], [30, 12, 1], [30, 18, 1], [30, 36, 1], [40, 12, 2], [40, 48, 1], [60, 6, 2], [60, 18, 2], [60, 24, 1], [60, 72, 1], [120, 12, 2], [120, 36, 2], [120, 48, 1], [120, 144, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [5, 12, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 4, 2], [8, 16, 1], [10, 12, 1], [10, 24, 1], [12, 2, 2], [12, 6, 2], [12, 8, 1], [12, 24, 1], [15, 24, 1], [15, 72, 1], [20, 24, 2], [20, 96, 1], [24, 8, 2], [24, 24, 2], [24, 32, 1], [24, 96, 1], [30, 24, 1], [30, 48, 1], [30, 72, 1], [30, 144, 1], [40, 96, 2], [40, 384, 1], [60, 48, 2], [60, 144, 2], [60, 192, 1], [60, 576, 1], [120, 192, 2], [120, 576, 2], [120, 768, 1], [120, 2304, 1]], 'label': '120.96.1-60.l.1.11', 'lattice_labels': None, 'lattice_x': None, 'level': 120, 'level_is_squarefree': False, 'level_radical': 30, 'log_conductor': None, 'models': None, 'mults': [1], '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], [3, 2, 1], [3, 6, 1], [4, 2, 2], [4, 8, 1], [5, 24, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [8, 8, 2], [8, 32, 1], [10, 24, 1], [10, 48, 1], [12, 4, 2], [12, 12, 2], [12, 16, 1], [12, 48, 1], [15, 48, 1], [15, 144, 1], [20, 48, 2], [20, 192, 1], [24, 16, 2], [24, 48, 2], [24, 64, 1], [24, 192, 1], [30, 48, 1], [30, 96, 1], [30, 144, 1], [30, 288, 1], [40, 192, 2], [40, 768, 1], [60, 96, 2], [60, 288, 2], [60, 384, 1], [60, 1152, 1], [120, 384, 2], [120, 1152, 2], [120, 1536, 1], [120, 4608, 1]], 'parents': ['24.48.0-12.g.1.13', '40.24.0-20.h.1.2', '120.48.0-12.g.1.3'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '12.48.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 4, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '3.4.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '6.12.0.a.1', '8.12.0-4.c.1.4', '12.24.0.g.1', '20.12.0.h.1', '24.48.0-12.g.1.13', '40.24.0-20.h.1.2', '60.48.1.l.1'], 'scalar_label': '4.2.1', 'simple': True, 'sl2label': '12.48.1.a.1', 'sl2level': 12, 'squarefree': True, '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': '12P1', 'Glabel': None, 'RSZBlabel': '60.48.1.74', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [42, 5, 25, 37], 'canonical_generators': [[1, 0, 12, 1], [1, 2, 28, 45], [1, 3, 16, 5], [1, 11, 16, 15], [1, 11, 52, 9], [1, 12, 0, 1], [1, 50, 40, 21], [3, 5, 4, 53], [13, 12, 48, 49], [41, 10, 20, 21], [51, 10, 20, 31]], 'cm_discriminants': [], 'coarse_class': '60.48.1.l', 'coarse_class_num': 12, 'coarse_index': 48, 'coarse_label': '60.48.1.l.1', 'coarse_level': 60, 'coarse_num': 1, 'conductor': [[2, 4], [3, 1], [5, 2]], 'contains_negative_one': True, 'curve_label': '1200.d4', 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[2, 2], [4, 2], [6, 2], [12, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.4.0.a.1', '20.12.0.h.1'], 'fine_num': 0, 'generators': [[19, 4, 24, 1], [29, 40, 9, 37], [29, 52, 57, 47], [35, 44, 21, 17], [43, 48, 15, 37]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [5, 6, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [10, 6, 1], [10, 12, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [15, 6, 1], [15, 18, 1], [20, 6, 2], [20, 24, 1], [30, 6, 1], [30, 12, 1], [30, 18, 1], [30, 36, 1], [60, 6, 2], [60, 18, 2], [60, 24, 1], [60, 72, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [5, 12, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [10, 12, 1], [10, 24, 1], [12, 2, 2], [12, 6, 2], [12, 8, 1], [12, 24, 1], [15, 24, 1], [15, 72, 1], [20, 24, 2], [20, 96, 1], [30, 24, 1], [30, 48, 1], [30, 72, 1], [30, 144, 1], [60, 48, 2], [60, 144, 2], [60, 192, 1], [60, 576, 1]], 'label': '60.48.1.l.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '20.2.0.a.1', '20.6.0.a.1', '20.6.0.e.1', '20.12.0.h.1', '60.8.0.a.1', '60.24.0.o.1', '60.24.1.y.1', '60.48.1.l.1'], 'lattice_x': [2948, 5387, 940, 8869, 4778, 8945, 2948, 3990, 6785, 7827, 1728, 3659, 5769, 6455], 'level': 60, 'level_is_squarefree': False, 'level_radical': 30, 'log_conductor': {'__RealLiteral__': 0, 'data': '7.09007683577609167827', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['1200.2.a.d'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': 2, 'num_known_degree1_noncusp_points': 2, 'num_known_degree1_points': 3, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 6, 1], [4, 2, 2], [4, 8, 1], [5, 24, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [10, 24, 1], [10, 48, 1], [12, 4, 2], [12, 12, 2], [12, 16, 1], [12, 48, 1], [15, 48, 1], [15, 144, 1], [20, 48, 2], [20, 192, 1], [30, 48, 1], [30, 96, 1], [30, 144, 1], [30, 288, 1], [60, 96, 2], [60, 288, 2], [60, 384, 1], [60, 1152, 1]], 'parents': ['12.24.0.g.1', '20.12.0.h.1', '60.24.0.o.1', '60.24.1.y.1'], 'parents_conj': [[8, 25, 57, 14], [1, 0, 0, 1], [11, 41, 3, 52], [25, 11, 27, 50]], 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '12.48.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 4, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '3.4.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '6.12.0.a.1', '12.24.0.g.1', '20.12.0.h.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '12.48.1.a.1', 'sl2level': 12, 'squarefree': True, 'trace_hash': 1822500199031106786, 'traces': [0, -1, 0, 0, -4, 2, -2, 4, -8, 6, -8, -6, -6, 4, 0, 2, -4, -2, -4, -8, -10, 8, -4, -6, -2, -18, 16, -12, -2, -18, -8, 4, 6, 12, 14, 16, 2, 12, 24, -6, -12, 6, 0, -2, 18, -16, 20, -8, 12, 22, -10, 16, 18, -20, -2, -8, -10, -8, 26, 26, -28, 18, 12, 24, 6, -6, -20, -18, -12, 30, -2, 24, -8, 10, -20, 0, -2, -14, -30, -6, -12, -10, -32, 14, 0, 20, -14, 22, -26, 8, -36, 16, -32, 12, -12, 24, 6, 26, 4, -18, 44, 26, 28, 10, -36, -2, -44, 14, -24, -38, -40, -38, -42, 44, -16, -14, 12, 8, -6, -12, -10, -34, 2, 4, 4, 6, -10, 32, 48, -14, 4, -8, -24, -38, -22, 2, 18, 28, -22, 26, -4, 30, -16, -28, -50, 24, 10, -42, 12, -32, 18, 50, -4, 8, 4, -16, -16, 50, -42, 6, 12, 54, -16, -36, 30, -24, -40, 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-108*x*z^2-288*z^3'], 'modcurve': '60.48.1.l.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': ['80*x^2*y^14-4818750*x^2*y^12*z^2+88036875000*x^2*y^10*z^4-246983154296875*x^2*y^8*z^6-4441892822265625000*x^2*y^6*z^8+1094319911041259765625*x^2*y^4*z^10-89439631271362304687500*x^2*y^2*z^12+2439999420642852783203125*x^2*z^14+2980*x*y^14*z-179662500*x*y^12*z^3+3416795859375*x*y^10*z^5-17822307031250000*x*y^8*z^7-45172169531250000000*x*y^6*z^9+11736315453186035156250*x*y^4*z^11-974241467189788818359375*x*y^2*z^13+26640002317428588867187500*x*z^15+y^16-18780*y^14*z^2-1267181250*y^12*z^4+42106286171875*y^10*z^6-357415946728515625*y^8*z^8-21720038134765625000*y^6*z^10+19382122755584716796875*y^4*z^12-1957795452022552490234375*y^2*z^14+57960055618286132812500000*z^16', 'z^2*y^2*(70*x^2*y^10+1121250*x^2*y^8*z^2+4204375000*x^2*y^6*z^4+6398496093750*x^2*y^4*z^6+4319890136718750*x^2*y^2*z^8+1079995880126953125*x^2*z^10+2295*x*y^10*z+21127500*x*y^8*z^3+62850078125*x*y^6*z^5+83207578125000*x*y^4*z^7+51120494384765625*x*y^2*z^9+11880016479492187500*x*z^11+y^12+51755*y^10*z^2+268572500*y^8*z^4+521351484375*y^6*z^6+464132705078125*y^4*z^8+186490162353515625*y^2*z^10+25920395507812500000*z^12)'], 'degree': 48, 'domain_label': '60.48.1.l.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-1', '5^3'], '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: 1825578
    {'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['0:1:0', '-8:0:1', '12:0:1', '-3:0:1']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '60.48.1.l.1', 'curve_level': 60, '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: 1825579
    {'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-18,0:0,-30:1,0', '2,0:0,10:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '60.48.1.l.1', 'curve_level': 60, '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': '2.0.20.1', 'upload_id': None}
  • id: 3646
    {'Elabel': '210.b3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': {'5': ['-27/4:-75/8:1', '-27/4:75/8:1', '72:-600:1', '72:600:1']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '60.48.1.l.1', 'curve_level': 60, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 41.3764832039423, 'jinv': '-932348627918877961/358766164249920', 'jorig': '-932348627918877961/358766164249920', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 3705
    {'Elabel': '210.b8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': {'5': ['-4:-8:1', '-4:8:1', '17:-50:1', '17:50:1']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '60.48.1.l.1', 'curve_level': 60, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 34.297715626934, 'jinv': '785793873833639/637994920500', 'jorig': '785793873833639/637994920500', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}