-
gps_gl2zhat_fine • Show schema
Hide schema
{'CPlabel': '20D2', 'Glabel': None, 'RSZBlabel': '40.80.2.2', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [25, 2, 16, 13], 'canonical_generators': [[0, 1, 3, 5], [0, 1, 19, 5], [0, 27, 37, 35], [0, 37, 39, 25], [1, 0, 20, 1], [1, 20, 0, 1], [3, 1, 8, 9], [4, 1, 7, 17], [8, 5, 15, 17], [19, 0, 0, 39], [21, 20, 20, 21]], 'cm_discriminants': [], 'coarse_class': '20.40.2.b', 'coarse_class_num': 2, 'coarse_index': 40, 'coarse_label': '20.40.2.b.1', 'coarse_level': 20, 'coarse_num': 1, 'conductor': [[2, 5], [5, 4]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2]], 'cusp_widths': [[20, 2]], 'cusps': 2, 'determinant_label': '1.1.1', 'dims': [1, 1], 'factorization': ['5.5.0.a.1', '8.16.0-4.b.1.1'], 'fine_num': 1, 'generators': [[2, 13, 21, 33], [22, 3, 19, 14], [39, 1, 5, 22]], 'genus': 2, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 80, 'isogeny_orbits': [[2, 3, 1], [4, 3, 2], [5, 6, 1], [8, 6, 2], [10, 18, 1], [20, 18, 2], [40, 36, 2]], 'kummer_orbits': [[2, 3, 1], [4, 3, 2], [5, 12, 1], [8, 12, 2], [10, 36, 1], [20, 72, 2], [40, 288, 2]], 'label': '40.80.2-20.b.1.1', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '9.90348755253612804549', 'prec': 74}, 'models': None, 'mults': [1, 1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 4, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 2, 'num_known_degree1_noncusp_points': 2, 'num_known_degree1_points': 3, 'obstructions': None, 'orbits': [[2, 3, 1], [4, 6, 2], [5, 24, 1], [8, 24, 2], [10, 72, 1], [20, 144, 2], [40, 576, 2]], 'parents': ['8.16.0-4.b.1.1', '40.20.0-20.a.1.1'], 'parents_conj': None, 'pointless': False, 'power': False, 'psl2index': 40, 'psl2label': '20.40.2.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': ['1.1.0.a.1', '4.8.0.b.1', '5.5.0.a.1', '5.5.0.a.1', '8.16.0-4.b.1.1', '20.40.2.b.1'], 'scalar_label': '4.2.1', 'simple': False, 'sl2label': '20.80.2-20.a.1.1', 'sl2level': 20, 'squarefree': True, 'trace_hash': 295585698756402682, 'traces': None}
-
gps_gl2zhat_fine • Show schema
Hide schema
{'CPlabel': '20D2', 'Glabel': None, 'RSZBlabel': '20.40.2.3', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [9, 17, 0, 1], 'canonical_generators': [[0, 1, 3, 5], [0, 1, 19, 5], [0, 3, 1, 15], [0, 13, 3, 5], [3, 1, 8, 9], [4, 1, 7, 17], [8, 5, 15, 17]], 'cm_discriminants': [], 'coarse_class': '20.40.2.b', 'coarse_class_num': 2, 'coarse_index': 40, 'coarse_label': '20.40.2.b.1', 'coarse_level': 20, 'coarse_num': 1, 'conductor': [[2, 5], [5, 4]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2]], 'cusp_widths': [[20, 2]], 'cusps': 2, 'determinant_label': '1.1.1', 'dims': [1, 1], 'factorization': ['4.8.0.b.1', '5.5.0.a.1'], 'fine_num': 0, 'generators': [[7, 11, 3, 2], [14, 9, 13, 6], [17, 12, 1, 3]], 'genus': 2, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 40, 'isogeny_orbits': [[2, 3, 1], [4, 3, 2], [5, 6, 1], [10, 18, 1], [20, 18, 2]], 'kummer_orbits': [[2, 3, 1], [4, 3, 2], [5, 12, 1], [10, 36, 1], [20, 72, 2]], 'label': '20.40.2.b.1', 'lattice_labels': ['1.1.0.a.1', '4.2.0.a.1', '4.4.0.a.1', '4.8.0.b.1', '5.5.0.a.1', '20.10.0.a.1', '20.20.1.c.1', '20.40.2.b.1'], 'lattice_x': [4516, 7460, 3750, 8911, 1694, 7460, 3750, 6694], 'level': 20, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '9.90348755253612804549', 'prec': 74}, 'models': 3, 'mults': [1, 1], 'name': None, 'newforms': ['50.2.a.b', '400.2.a.a'], 'nu2': 0, 'nu3': 4, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 2, 'num_known_degree1_noncusp_points': 2, 'num_known_degree1_points': 3, 'obstructions': [], 'orbits': [[2, 3, 1], [4, 6, 2], [5, 24, 1], [10, 72, 1], [20, 144, 2]], 'parents': ['4.8.0.b.1', '20.10.0.a.1', '20.20.1.c.1'], 'parents_conj': [[13, 9, 6, 19], [1, 0, 0, 1], [10, 9, 7, 7]], 'pointless': False, 'power': False, 'psl2index': 40, 'psl2label': '20.40.2.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': ['1.1.0.a.1', '4.8.0.b.1', '5.5.0.a.1', '5.5.0.a.1'], 'scalar_label': '1.1.1', 'simple': False, 'sl2label': '20.40.2.a.1', 'sl2level': 20, 'squarefree': True, 'trace_hash': 295585698756402682, 'traces': [1, -4, 0, 0, -4, 0, -2, 4, -8, -8, -8, 4, -6, 8, -8, -12, -8, 12, 12, 24, -14, -16, -4, 6, 12, -12, 8, -12, 4, 18, -8, 24, -10, -4, 8, 0, 12, -4, -24, 16, 4, 4, -8, 30, 20, 48, -12, 0, -24, 24, -12, -24, 10, 12, -12, 24, -16, 8, -40, -20, -12, -4, -4, -32, -4, -24, 44, -6, 20, -28, 4, 48, 48, -36, -20, 0, 60, 24, 18, -6, -12, -40, 16, 14, -56, -12, -54, -18, 24, -32, -40, 8, -40, -24, 24, 0, 4, -38, -76, 0, -36, 16, -8, 2, -8, 26, 36, -30, 0, 30, -32, 4, 36, -24, -8, 36, -8, 0, 28, 36, 56, -20, 80, 36, 36, -16, -8, -16, -24, -32, 8, 24, 8, -64, -6, 18, 24, -24, -84, -12, -72, 4, 32, 36, 0, 16, -4, 6, -36, 72, 24, 12, -36, 16, 40, -16, 24, 28, 18, 16, 88, 78, -32, 28, -74, 0, -96, 40]}
-
modcurve_models • Show schema
Hide schema
-
id: 5516
{'dont_display': False, 'equation': ['x^3-x^2*y-x*y^2+y^3+2*x^2*z+x*y*z-y^2*z-x*z^2-x^2*w+x*y*w', 'x^3-x^2*y-x*y^2+y^3+x*y*z+y^2*z+5*x*z^2+2*y*z^2-x^2*w+x*y*w-z*w^2', '3*x^3-5*x^2*y+x*y^2+y^3+x*y*z+y^2*z+x*z^2-x*y*w+y^2*w+x*z*w', 'x^3+x^2*y-x*y^2-y^3+2*x^2*z-5*x*y*z-3*y^2*z-x*z^2-x^2*w+x*y*w+y*w^2', '2*x^2*w-2*y^2*w-6*x*z*w-2*y*z*w+w^3', '3*x^3-x^2*y-3*x*y^2+y^3-4*x^2*z-x*y*z-y^2*z-x*z^2-x^2*w+x*y*w+x*w^2'], 'modcurve': '20.40.2.b.1', 'model_type': 8, 'number_variables': 4, 'smooth': True, 'upload_id': None}
-
id: 5517
{'dont_display': False, 'equation': ['7*x^4-2*x^3*y+2*x^2*y^2+2*x*y^3-6*x^3*z-x^2*y*z+2*x*y^2*z-4*x^2*z^2+2*x*y*z^2+2*x*z^3+y*z^3+z^4'], 'modcurve': '20.40.2.b.1', 'model_type': 2, 'number_variables': 3, 'smooth': False, 'upload_id': None}
-
id: 5518
{'dont_display': False, 'equation': ['2*x^4*z^2+x^3*y-4*x^2*z^4+x*y*z^2+y^2+2*z^6'], 'modcurve': '20.40.2.b.1', 'model_type': 5, 'number_variables': 3, 'smooth': True, 'upload_id': None}
-
modcurve_modelmaps • Show schema
Hide schema
-
id: 5764
{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['92643732*x*y*w^7+1830391792*x*z^8+704600656*x*z^7*w+765751308*x*z^6*w^2+1097628608*x*z^5*w^3+932961020*x*z^4*w^4+977869364*x*z^3*w^5+974080990*x*z^2*w^6-324610178*x*z*w^7-46291798*x*w^8-2048*y^8*w-3072*y^7*w^2-2816*y^6*w^3+4864*y^5*w^4+8832*y^4*w^5+7056*y^3*w^6+459346432*y^2*z^7+94920256*y^2*z^6*w+152880232*y^2*z^5*w^2+221339156*y^2*z^4*w^3+169133640*y^2*z^3*w^4+188878224*y^2*z^2*w^5+184921992*y^2*z*w^6-92632984*y^2*w^7+645060848*y*z^8+262237264*y*z^7*w+347178564*y*z^6*w^2+451762414*y*z^5*w^3+394746876*y*z^4*w^4+418863858*y*z^3*w^5+416515334*y*z^2*w^6-46343278*y*z*w^7+46315134*y*w^8-368*z^9+720*z^8*w-322532064*z^7*w^2-131117248*z^6*w^3-153360434*z^5*w^4-204580447*z^4*w^5-177283027*z^3*w^6-186746369*z^2*w^7-185187568*z*w^8+46325707*w^9', '13126*x*y*w^7+636*x*z^8+2464*x*z^7*w+7196*x*z^6*w^2-9812*x*z^5*w^3-55074*x*z^4*w^4-23814*x*z^3*w^5+97160*x*z^2*w^6-30392*x*z*w^7-2831*x*w^8+168*y^2*z^7+468*y^2*z^6*w+1236*y^2*z^5*w^2-1564*y^2*z^4*w^3-9124*y^2*z^3*w^4-4516*y^2*z^2*w^5+15324*y^2*z*w^6-13126*y^2*w^7+228*y*z^8+942*y*z^7*w+2548*y*z^6*w^2-4158*y*z^5*w^3-19594*y*z^4*w^4-6644*y*z^3*w^5+33752*y*z^2*w^6-13184*y*z*w^7+2831*y*w^8-114*z^7*w^2-471*z^6*w^3-1271*z^5*w^4+2107*z^4*w^5+10019*z^3*w^6+3389*z^2*w^7-18170*z*w^8+5197*w^9'], 'degree': 40, 'domain_label': '20.40.2.b.1', 'domain_model_type': 8, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-1', '1'], 'upload_id': None}
-
id: 5765
{'codomain_label': '20.40.2.b.1', 'codomain_model_type': 2, 'coordinates': ['x', '1/2*w', 'y'], 'degree': 1, 'domain_label': '20.40.2.b.1', 'domain_model_type': 8, 'dont_display': False, 'factored': False, 'leading_coefficients': None, 'upload_id': None}
-
id: 5766
{'codomain_label': '20.40.2.b.1', 'codomain_model_type': 5, 'coordinates': ['2/3*x-1/6*w', '-26/27*x^3-4/27*x^2*y+1/27*x^2*w+10/27*x*y^2+1/27*x*y*w-2/27*x*w^2+4/27*y^3+2/27*y^2*w', '-1/3*x-1/3*y-1/6*w'], 'degree': 1, 'domain_label': '20.40.2.b.1', 'domain_model_type': 8, 'dont_display': False, 'factored': False, 'leading_coefficients': None, 'upload_id': None}
-
modcurve_points • Show schema
Hide schema
-
id: 1715387
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['1:1:0:0', '0:0:1:0']}, 'curve_genus': 2, 'curve_index': 40, 'curve_label': '20.40.2.b.1', 'curve_level': 20, '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: 8162
{'Elabel': '648.b1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 648, 'coordinates': {'2': ['1:-2:1', '0:-1:1'], '5': ['1:-1:0', '1:0:0'], '8': ['-1/4:-1/4:-1/2:1', '0:-1/2:-1/2:1']}, 'curve_genus': 2, 'curve_index': 40, 'curve_label': '20.40.2.b.1', 'curve_level': 20, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 4, 'j_field': '1.1.1.1', 'j_height': 3.58351893845611, 'jinv': '-36', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
-
id: 35974
{'Elabel': '4418.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 4418, 'coordinates': {'2': ['2/3:-1/6:1', '-1/3:2/3:1'], '5': ['-1:0:1', '1:-2:1'], '8': ['-2:-3:1/2:1', '-1/4:3/4:2:1']}, 'curve_genus': 2, 'curve_index': 40, 'curve_label': '20.40.2.b.1', 'curve_level': 20, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 4, 'j_field': '1.1.1.1', 'j_height': 17.9787382056471, 'jinv': '-64278657/1024', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}