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gps_gl2zhat_fine • Show schema
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{'CPlabel': '40F3', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[0, 1, 29, 12], [0, 3, 37, 6], [0, 9, 7, 2], [0, 11, 29, 22], [0, 13, 3, 10], [0, 21, 19, 2], [0, 67, 53, 54], [0, 69, 71, 78], [0, 71, 49, 62], [0, 79, 41, 78], [39, 0, 0, 79], [41, 40, 40, 41], [79, 0, 40, 79], [79, 40, 0, 79]], 'cm_discriminants': [], 'coarse_class': '40.72.3.bx', 'coarse_class_num': 50, 'coarse_index': 72, 'coarse_label': '40.72.3.bx.1', 'coarse_level': 40, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 8]], 'cusp_widths': [[1, 2], [2, 1], [5, 2], [8, 1], [10, 1], [40, 1]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': None, 'factorization': ['5.6.0.a.1', '16.24.0-8.n.1.8'], 'fine_num': 18, 'generators': [[2, 77, 15, 24], [11, 8, 10, 9], [12, 31, 1, 2], [26, 51, 77, 0], [49, 44, 36, 57], [51, 26, 30, 47], [65, 26, 34, 17]], 'genus': 3, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 144, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [5, 1, 1], [5, 5, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1], [20, 1, 2], [20, 4, 1], [20, 5, 2], [20, 20, 1], [40, 1, 2], [40, 2, 1], [40, 5, 2], [40, 8, 1], [40, 10, 1], [40, 40, 1], [80, 2, 2], [80, 4, 1], [80, 10, 2], [80, 16, 1], [80, 20, 1], [80, 80, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [5, 2, 1], [5, 10, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [10, 2, 1], [10, 4, 1], [10, 10, 1], [10, 20, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [20, 4, 2], [20, 16, 1], [20, 20, 2], [20, 80, 1], [40, 8, 2], [40, 16, 1], [40, 40, 2], [40, 64, 1], [40, 80, 1], [40, 320, 1], [80, 32, 2], [80, 64, 1], [80, 160, 2], [80, 256, 1], [80, 320, 1], [80, 1280, 1]], 'label': '80.144.3-40.bx.1.18', 'lattice_labels': None, 'lattice_x': None, 'level': 80, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, '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], [4, 2, 2], [4, 8, 1], [5, 4, 1], [5, 20, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [10, 4, 1], [10, 8, 1], [10, 20, 1], [10, 40, 1], [16, 8, 2], [16, 16, 1], [16, 32, 1], [16, 128, 1], [20, 8, 2], [20, 32, 1], [20, 40, 2], [20, 160, 1], [40, 16, 2], [40, 32, 1], [40, 80, 2], [40, 128, 1], [40, 160, 1], [40, 640, 1], [80, 32, 2], [80, 64, 1], [80, 128, 1], [80, 160, 2], [80, 320, 1], [80, 512, 1], [80, 640, 1], [80, 2560, 1]], 'parents': ['16.24.0-8.n.1.8'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 72, 'psl2label': '40.72.3.b.1', 'psl2level': 40, 'q_gonality': None, 'q_gonality_bounds': [2, 3], 'qbar_gonality': None, 'qbar_gonality_bounds': [2, 3], 'rank': None, 'rational_cusps': 8, 'reductions': ['2.3.0.a.1', '4.6.0.c.1', '5.6.0.a.1', '8.12.0.n.1', '10.18.0.a.1', '16.24.0-8.n.1.8', '20.36.1.c.1', '40.72.3.bx.1'], 'scalar_label': '4.2.1', 'simple': False, 'sl2label': '40.72.3.b.1', 'sl2level': 80, 'squarefree': None, 'trace_hash': None, 'traces': None}
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gps_gl2zhat_fine • Show schema
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{'CPlabel': '40F3', 'Glabel': None, 'RSZBlabel': '40.72.3.3', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [0, 9, 39, 1], 'canonical_generators': [[0, 1, 29, 12], [0, 1, 39, 2], [0, 3, 37, 6], [0, 9, 7, 2], [0, 9, 31, 18], [0, 11, 9, 2], [0, 11, 29, 22], [0, 13, 3, 10], [0, 13, 27, 26], [0, 21, 19, 2]], 'cm_discriminants': [], 'coarse_class': '40.72.3.bx', 'coarse_class_num': 50, 'coarse_index': 72, 'coarse_label': '40.72.3.bx.1', 'coarse_level': 40, 'coarse_num': 1, 'conductor': [[2, 7], [5, 3]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 8]], 'cusp_widths': [[1, 2], [2, 1], [5, 2], [8, 1], [10, 1], [40, 1]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1, 1], 'factorization': ['5.6.0.a.1', '8.12.0.n.1'], 'fine_num': 0, 'generators': [[3, 34, 0, 13], [7, 10, 0, 7], [11, 23, 0, 37], [11, 33, 0, 11], [17, 1, 0, 39], [33, 4, 0, 31], [37, 32, 0, 9]], 'genus': 3, 'genus_minus_rank': 3, 'has_obstruction': -1, 'index': 72, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [5, 1, 1], [5, 5, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [20, 1, 2], [20, 4, 1], [20, 5, 2], [20, 20, 1], [40, 1, 2], [40, 2, 1], [40, 5, 2], [40, 8, 1], [40, 10, 1], [40, 40, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [5, 2, 1], [5, 10, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [10, 2, 1], [10, 4, 1], [10, 10, 1], [10, 20, 1], [20, 4, 2], [20, 16, 1], [20, 20, 2], [20, 80, 1], [40, 8, 2], [40, 16, 1], [40, 40, 2], [40, 64, 1], [40, 80, 1], [40, 320, 1]], 'label': '40.72.3.bx.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '5.6.0.a.1', '8.12.0.n.1', '10.18.0.a.1', '20.36.1.c.1', '40.72.3.bx.1'], 'lattice_x': [2887, 4268, 6987, 1548, 8452, 2803, 5523, 6987], 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '9.68034400122191828972', 'prec': 74}, 'models': 3, 'mults': [2, 1], 'name': 'X0(40)', 'newforms': ['20.2.a.a', '40.2.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, 1], [2, 2, 1], [4, 2, 2], [4, 8, 1], [5, 4, 1], [5, 20, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [10, 4, 1], [10, 8, 1], [10, 20, 1], [10, 40, 1], [20, 8, 2], [20, 32, 1], [20, 40, 2], [20, 160, 1], [40, 16, 2], [40, 32, 1], [40, 80, 2], [40, 128, 1], [40, 160, 1], [40, 640, 1]], 'parents': ['8.12.0.n.1', '20.36.1.c.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': False, 'psl2index': 72, 'psl2label': '40.72.3.b.1', 'psl2level': 40, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 8, 'reductions': ['2.3.0.a.1', '4.6.0.c.1', '5.6.0.a.1', '8.12.0.n.1', '10.18.0.a.1', '20.36.1.c.1'], 'scalar_label': '1.1.1', 'simple': False, 'sl2label': '40.72.3.b.1', 'sl2level': 40, 'squarefree': False, 'trace_hash': 742675991071674418, 'traces': [0, -4, -1, 0, 4, 2, -10, -4, 16, 10, -16, 10, 6, -28, -8, -6, 20, 2, 12, -24, -2, 16, -4, -18, -10, 18, 32, -12, 18, 6, -8, 12, 46, 4, -22, 24, -46, -4, 48, 2, -4, -30, -16, 38, 58, 24, -36, -24, -36, 2, -18, -48, 30, -12, -42, -48, 50, 64, 42, 22, 36, -86, -4, 56, -18, -30, 4, -10, -76, 10, 38, 24, -24, 74, -76, -24, -6, 2, -42, -58, 108, 58, 32, 6, 8, 36, 30, 62, 42, 40, -52, -32, 32, 36, -36, -48, 10, -2, 20, 26, 60, -46, -20, 38, 20, -42, -60, 54, -24, -10, -56, -38, -18, 36, -40, -18, -20, 96, 50, 60, -86, -74, 58, -60, 60, -94, -30, -80, -48, -14, 76, 48, -32, -54, 78, 38, -102, 60, 66, 30, -60, -86, 80, -12, 2, -136, 138, 30, -12, 24, 98, -66, 12, 16, -44, 64, -24, -98, -82, 10, 28, -18, -80, -28, 38, 0, -48, 10]}
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modcurve_models • Show schema
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id: 45468
{'dont_display': False, 'equation': ['y^2*t-x*t^2', 'y*w^2+y*w*t+z*w*t', 'y*w*t+y*t^2+z*t^2', 'y*z*t+x*w*t+x*t^2', 'y^2*w-x*w*t', 'y*z*w+x*w^2+x*w*t', 'y*z*w+y*z*t+z^2*t', 'y^3-x*y*t', 'y^2*z+x*y*w+x*y*t', 'y^2*z-x*z*t', 'y^2*z+y*z^2+x*z*w', 'x*y^2-x^2*t', 'x*y*z+x^2*w+x^2*t', 'x*y^2+x*y*z-x*z^2-2*x^2*w-2*y*z*w+z^2*w+x*w^2-w^3+x^2*t+z^2*t-w^2*t-x*t^2', '2*x*y^2-x*y*z+x*w^2+2*x^2*t-y^2*t+y*z*t-2*z^2*t-x*w*t+w^2*t-x*t^2+w*t^2', '4*x^2*y-x^2*z+y^2*z-y*z^2-x*y*w-x*y*t+2*x*z*t-z*w*t'], 'modcurve': '40.72.3.bx.1', 'model_type': 8, 'number_variables': 5, 'smooth': True, 'upload_id': None}
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id: 45469
{'dont_display': False, 'equation': ['x^4*y+5*x^4*z-x^2*y^2*z-6*x^2*y*z^2-5*x^2*z^3+y^2*z^3+y*z^4'], 'modcurve': '40.72.3.bx.1', 'model_type': 2, 'number_variables': 3, 'smooth': False, 'upload_id': None}
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id: 45470
{'dont_display': False, 'equation': ['-2*x^6*z^2+x^4*y+x^4*z^4-2*x^2*z^6+y^2+y*z^4'], 'modcurve': '40.72.3.bx.1', 'model_type': 5, 'number_variables': 3, 'smooth': True, 'upload_id': None}
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modcurve_modelmaps • Show schema
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id: 45567
{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['x^11-705*x^10*t+170015*x^9*t^2-15035355*x^8*t^3+254385970*x^7*t^4-2560733026*x^6*t^5-4296636730*x^5*t^6-85385769230*x^4*t^7-196268373347*x^3*t^8-271804879117*x^2*t^9+320871972160*x*w*t^9+320871972235*x*t^10+25600*z^10*t-51200*z^8*w^2*t-307200*z^8*t^3+1408024*z^6*w^2*t^3-5093914*z^6*w*t^4+34899252*z^6*t^5-181832860*z^4*w^2*t^5+374770690*z^4*w*t^6-751038298*z^4*t^7+11644965696*z^2*w^2*t^7+73670355200*z^2*w*t^8+239921319936*z^2*t^9-25*w^11+25675*w^10*t-154475*w^9*t^2-199499*w^8*t^3+6543608*w^7*t^4+99804538*w^6*t^5-556106258*w^5*t^6-8994220992*w^4*t^7-60160972083*w^3*t^8-163974757569*w^2*t^9-112158658639*w*t^10', 't*(x^10+37*x^9*t+590*x^8*t^2+5410*x^7*t^3+32513*x^6*t^4+140649*x^5*t^5+474800*x^4*t^6+1439696*x^3*t^7+7013040*x^2*t^8-7372964*x*w*t^8-7372964*x*t^9-z^6*w*t^3-31*z^6*t^4-417*z^4*w^2*t^4-4034*z^4*w*t^5-24435*z^4*t^6-93104*z^2*w^2*t^6-566430*z^2*w*t^7-1709306*z^2*t^8+w^7*t^3+467*w^6*t^4+1894*w^5*t^5+114800*w^4*t^6+288975*w^3*t^7+1992057*w^2*t^8+1816454*w*t^9)'], 'degree': 72, 'domain_label': '40.72.3.bx.1', 'domain_model_type': 8, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-1', '1'], 'upload_id': None}
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id: 45568
{'codomain_label': '40.72.3.bx.1', 'codomain_model_type': 2, 'coordinates': ['y', 'w', 't'], 'degree': 1, 'domain_label': '40.72.3.bx.1', 'domain_model_type': 8, 'dont_display': False, 'factored': False, 'leading_coefficients': None, 'upload_id': None}
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id: 45569
{'codomain_label': '40.72.3.bx.1', 'codomain_model_type': 5, 'coordinates': ['-y', '-y^2*w*t-3*y^2*t^2+w*t^3', 't'], 'degree': 1, 'domain_label': '40.72.3.bx.1', 'domain_model_type': 8, 'dont_display': False, 'factored': False, 'leading_coefficients': None, 'upload_id': None}
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modcurve_points • Show schema
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id: 1708372
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['-4,0,-1:-5,0,-1:1,0,0', '4,0,1:-5,0,-1:1,0,0'], '5': ['4,0,1:28,2,7:1,0,0', '-4,0,-1:28,2,7:1,0,0'], '8': ['16,1,4:-4,0,-1:-16,-1,-4:-5,0,-1:1,0,0', '16,1,4:4,0,1:16,1,4:-5,0,-1:1,0,0']}, 'curve_genus': 3, 'curve_index': 72, 'curve_label': '40.72.3.bx.1', 'curve_level': 40, 'curve_name': 'X0(40)', 'cusp': False, 'degree': 3, 'isolated': 4, 'j_field': '3.1.283.1', 'j_height': 6.45990445437753, 'jinv': '9307/6,115/6,2381/6', 'jorig': None, 'quo_info': None, 'residue_field': '3.1.283.1', 'upload_id': None}
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id: 1708379
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['-3/2,-1/2,-1/2:-25/4,-5/4,-5/4:1,0,0', '3/2,1/2,1/2:-25/4,-5/4,-5/4:1,0,0'], '5': ['3/2,1/2,1/2:53/16,-3/16,9/16:1,0,0', '-3/2,-1/2,-1/2:53/16,-3/16,9/16:1,0,0'], '8': ['11/4,-1/4,3/4:-3/2,-1/2,-1/2:-73/8,-1/8,-21/8:-25/4,-5/4,-5/4:1,0,0', '11/4,-1/4,3/4:3/2,1/2,1/2:73/8,1/8,21/8:-25/4,-5/4,-5/4:1,0,0']}, 'curve_genus': 3, 'curve_index': 72, 'curve_label': '40.72.3.bx.1', 'curve_level': 40, 'curve_name': 'X0(40)', 'cusp': False, 'degree': 3, 'isolated': 4, 'j_field': '3.1.283.1', 'j_height': 23.6135703170795, 'jinv': '-446580445042565640341/64925062108545024,311476202902418906707/64925062108545024,5236502997779760254279/64925062108545024', 'jorig': None, 'quo_info': None, 'residue_field': '3.1.283.1', 'upload_id': None}
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id: 1708386
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['0,1/2,-1/2:-3,1/2,1/2:1,0,0', '0,-1/2,1/2:-3,1/2,1/2:1,0,0'], '5': ['0,-1/2,1/2:-9,3,1:1,0,0', '0,1/2,-1/2:-9,3,1:1,0,0'], '8': ['-3,2,0:0,1/2,-1/2:0,5/2,-3/2:-3,1/2,1/2:1,0,0', '-3,2,0:0,-1/2,1/2:0,-5/2,3/2:-3,1/2,1/2:1,0,0']}, 'curve_genus': 3, 'curve_index': 72, 'curve_label': '40.72.3.bx.1', 'curve_level': 40, 'curve_name': 'X0(40)', 'cusp': False, 'degree': 3, 'isolated': 4, 'j_field': '3.1.244.1', 'j_height': 17.0010696532185, 'jinv': '16332054839/13122,-13934498401/2187,45029180699/13122', 'jorig': None, 'quo_info': None, 'residue_field': '3.1.244.1', 'upload_id': None}
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id: 1708394
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['-1,-1/2,-1/2:10/3,5/2,5/6:1,0,0', '1,1/2,1/2:10/3,5/2,5/6:1,0,0'], '5': ['1,1/2,1/2:-47,-21,-13:1,0,0', '-1,-1/2,-1/2:-47,-21,-13:1,0,0'], '8': ['4,2,1:-1,-1/2,-1/2:43/3,11/2,23/6:10/3,5/2,5/6:1,0,0', '4,2,1:1,1/2,1/2:-43/3,-11/2,-23/6:10/3,5/2,5/6:1,0,0']}, 'curve_genus': 3, 'curve_index': 72, 'curve_label': '40.72.3.bx.1', 'curve_level': 40, 'curve_name': 'X0(40)', 'cusp': False, 'degree': 3, 'isolated': 4, 'j_field': '3.1.244.1', 'j_height': 20.4656232724335, 'jinv': '188032467820778000698737637/248832,13951747491276218965479469/41472,51218956560994249012422049/248832', 'jorig': None, 'quo_info': None, 'residue_field': '3.1.244.1', 'upload_id': None}
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id: 1708401
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['-1,-1/2,-1/2:-3,-1/2,-1/2:1,0,0', '1,1/2,1/2:-3,-1/2,-1/2:1,0,0'], '5': ['1,1/2,1/2:6,3,2:1,0,0', '-1,-1/2,-1/2:6,3,2:1,0,0'], '8': ['4,2,1:-1,-1/2,-1/2:-5,-5/2,-3/2:-3,-1/2,-1/2:1,0,0', '4,2,1:1,1/2,1/2:5,5/2,3/2:-3,-1/2,-1/2:1,0,0']}, 'curve_genus': 3, 'curve_index': 72, 'curve_label': '40.72.3.bx.1', 'curve_level': 40, 'curve_name': 'X0(40)', 'cusp': False, 'degree': 3, 'isolated': 4, 'j_field': '3.1.244.1', 'j_height': 7.84619881549743, 'jinv': '216971/768,8387/128,79631/768', 'jorig': None, 'quo_info': None, 'residue_field': '3.1.244.1', 'upload_id': None}
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id: 1708408
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'2': ['-2/3,-1/2,-1/6:-55/18,-5/6,-5/9:1,0,0', '2/3,1/2,1/6:-55/18,-5/6,-5/9:1,0,0'], '5': ['2/3,1/2,1/6:119/81,31/27,47/81:1,0,0', '-2/3,-1/2,-1/6:119/81,31/27,47/81:1,0,0'], '8': ['13/9,2/3,4/9:-2/3,-1/2,-1/6:-209/54,-31/18,-28/27:-55/18,-5/6,-5/9:1,0,0', '13/9,2/3,4/9:2/3,1/2,1/6:209/54,31/18,28/27:-55/18,-5/6,-5/9:1,0,0']}, 'curve_genus': 3, 'curve_index': 72, 'curve_label': '40.72.3.bx.1', 'curve_level': 40, 'curve_name': 'X0(40)', 'cusp': False, 'degree': 3, 'isolated': 4, 'j_field': '3.1.244.1', 'j_height': 22.6770266436446, 'jinv': '569109387339813739054103/389045294689821721632,26883008139964636326959/64840882448303620272,-318866334048273606357205/389045294689821721632', 'jorig': None, 'quo_info': None, 'residue_field': '3.1.244.1', 'upload_id': None}
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id: 1708415
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