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gps_gl2zhat_fine • Show schema
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{'CPlabel': '8B3', 'Glabel': None, 'RSZBlabel': '40.96.3.5', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [1, 25, 8, 9], 'canonical_generators': [[1, 0, 8, 1], [1, 4, 12, 15], [1, 4, 12, 35], [1, 4, 32, 5], [1, 8, 0, 1], [1, 20, 20, 1], [7, 4, 4, 29], [9, 8, 32, 33], [31, 20, 20, 31]], 'cm_discriminants': [], 'coarse_class': '40.96.3.be', 'coarse_class_num': 31, 'coarse_index': 96, 'coarse_label': '40.96.3.be.1', 'coarse_level': 40, 'coarse_num': 1, 'conductor': [[2, 18], [5, 6]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 2], [4, 1]], 'cusp_widths': [[8, 12]], 'cusps': 12, 'determinant_label': '1.1.1', 'dims': [1, 2], 'factorization': [], 'fine_num': 0, 'generators': [[1, 34, 16, 23], [3, 22, 4, 29], [11, 10, 4, 13], [33, 14, 0, 27], [37, 2, 4, 23]], 'genus': 3, 'genus_minus_rank': 3, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [5, 6, 1], [8, 2, 4], [8, 4, 1], [10, 6, 3], [20, 6, 4], [20, 12, 1], [40, 12, 4], [40, 24, 1]], 'kummer_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [5, 12, 1], [8, 2, 4], [8, 4, 2], [8, 8, 1], [10, 12, 3], [20, 24, 4], [20, 48, 1], [40, 48, 4], [40, 96, 2], [40, 192, 1]], 'label': '40.96.3.be.1', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '2.3.0.a.1', '2.6.0.a.1', '4.6.0.b.1', '4.6.0.c.1', '4.6.0.d.1', '4.6.0.e.1', '4.12.0.a.1', '4.12.0.b.1', '4.12.0.f.1', '4.24.0.b.1', '8.24.0.e.1', '8.24.0.e.2', '8.48.0.c.1', '40.12.0.bq.1', '40.12.0.bv.1', '40.12.0.cb.1', '40.12.1.g.1', '40.24.0.j.1', '40.24.0.dr.1', '40.24.0.eb.1', '40.24.1.b.1', '40.24.1.dd.1', '40.24.1.dn.1', '40.48.1.n.1', '40.48.2.a.1', '40.96.3.be.1'], 'lattice_x': [3754, 4483, 3024, 4346, 3161, 1915, 669, 5699, 3511, 1748, 7097, 2811, 1505, 410, 1611, 9590, 5699, 4605, 8495, 6307, 8495, 5213, 4119, 9590, 7401, 5760, 2811, 2811], 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '22.13327672468361781711', 'prec': 77}, 'models': 3, 'mults': [1, 1], 'name': None, 'newforms': ['1600.2.a.n', '1600.2.d.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, 3], [4, 2, 4], [4, 4, 1], [5, 24, 1], [8, 4, 4], [8, 8, 2], [8, 16, 1], [10, 24, 3], [20, 48, 4], [20, 96, 1], [40, 96, 4], [40, 192, 2], [40, 384, 1]], 'parents': ['8.48.0.c.1', '40.48.1.n.1', '40.48.2.a.1'], 'parents_conj': [[7, 33, 20, 33], [1, 0, 0, 1], [24, 17, 1, 37]], 'pointless': False, 'power': False, 'psl2index': 96, 'psl2label': '8.96.3.b.1', 'psl2level': 8, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 4, 'reductions': ['1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.24.0.b.1', '4.24.0.b.1', '8.48.0.c.1'], 'scalar_label': '8.2.2', 'simple': False, 'sl2label': '8.96.3.b.1', 'sl2level': 8, 'squarefree': True, 'trace_hash': 1448749293447572588, 'traces': [0, 0, 0, 0, 0, 6, 10, 0, 0, 10, 0, -2, -2, 0, 0, 14, 0, 10, 0, 0, 2, 0, 0, 46, -38, 2, 0, 0, -6, -22, 0, 0, 34, 0, -14, 0, 22, 0, 0, -26, 0, 18, 0, 58, -2, 0, 0, 0, 0, -30, 34, 0, 22, 0, 58, 0, 26, 0, -18, 46, 0, -34, 0, 0, -46, 22, 0, 10, 0, 10, 26, 0, 0, 14, 0, 0, 34, 38, -10, -50, 0, -30, 0, 42, 0, 0, 70, -94, -38, 0, 0, 0, 0, 0, 0, 0, 10, -34, 0, 42, 0, 38, 0, 110, 0, -70, 0, 10, 0, -82, 0, -34, 98, 0, 0, 134, 0, 0, -26, 0, 50, 26, -2, 0, 0, 10, -30, 0, 0, 54, 0, 0, 0, -18, -146, 6, -34, 0, 22, -2, 0, 50, 0, 0, -54, 0, 46, 50, 0, 0, -58, 86, 0, 0, 0, 0, 0, -154, -30, 58, 0, -110, 0, 0, 74, 0, 0, 62]}
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modcurve_models • Show schema
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id: 46369
{'dont_display': False, 'equation': ['2*x*z*t-x*w*t-y*w*t-y*t^2', '2*x*z*w-x*w^2-y*w^2-y*w*t', '2*x*z^2-x*z*w-y*z*w-y*z*t', '2*x*y*z-x*y*w-y^2*w-y^2*t', '2*x^2*z-x^2*w-x*y*w-x*y*t', '2*x*z^2+x*z*w+3*y*z*w+y*w^2-y*z*t-x*w*t-y*w*t', '4*y*z^2+x*z*w+2*y*z*w-x*z*t', '2*x*z^2+x*z*w-y*z*w-x*w^2-y*w^2+3*y*z*t+x*w*t+y*w*t-x*t^2', '2*x*y*z-2*x^2*w+x*y*w+2*x^2*t-w^2*t-w*t^2', '2*x^2*z+2*x*y*z+2*x*y*w+y^2*w-x^2*t-x*y*t+y^2*t', '4*y^2*z+x*y*w+2*y^2*w-x*y*t', '2*y^2*z-2*x*y*w+y^2*w+2*x*y*t-2*z*w*t+w^2*t', '8*z^2*t-w^2*t-t^3', '8*z^2*w-w^3-w*t^2', '8*z^3-z*w^2-z*t^2', '5*x^2*y+5*x*y^2-x*w*t-2*y*w*t'], 'modcurve': '40.96.3.be.1', 'model_type': 8, 'number_variables': 5, 'smooth': True, 'upload_id': None}
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id: 46370
{'dont_display': False, 'equation': ['5*x^3*y^2-x^4*z+10*x^2*y^2*z-5*x^3*z^2-10*x*y^2*z^2-6*x^2*z^3-20*y^2*z^3-2*x*z^4'], 'modcurve': '40.96.3.be.1', 'model_type': 2, 'number_variables': 3, 'smooth': False, 'upload_id': None}
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id: 46371
{'dont_display': False, 'equation': ['5*x^7*z-35*x^5*z^3+35*x^3*z^5-5*x*z^7+y^2'], 'modcurve': '40.96.3.be.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: 46417
{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['78125*x^14+93750*x^12*t^2+68750*x^10*t^4-15000*x^8*t^6+142750*x^6*t^8-280800*x^4*t^10+624540*x^2*t^12+156250*x*y^13+718750*x*y^11*t^2+175000*x*y^9*t^4+775000*x*y^7*t^6+849250*x*y^5*t^8+2752550*x*y^3*t^10+6047680*x*y*t^12+312500*y^12*t^2-50000*y^10*t^4+555000*y^8*t^6+1048000*y^6*t^8+2574700*y^4*t^10+6906400*y^2*t^12-640*z*w^13+128*z*w^12*t-4352*z*w^11*t^2+256*z*w^10*t^3-43904*z*w^9*t^4+4480*z*w^8*t^5-232960*z*w^7*t^6+382152*z*w^6*t^7-1223424*z*w^5*t^8+2461408*z*w^4*t^9-3658176*z*w^3*t^10+5776040*z*w^2*t^11-4838272*z*w*t^12+640*z*t^13+224*w^14-64*w^13*t+1568*w^12*t^2-384*w^11*t^3+15456*w^10*t^4-4032*w^9*t^5+83104*w^8*t^6-153428*w^7*t^7+430884*w^6*t^8-1026920*w^5*t^9+1319744*w^4*t^10-2783260*w^3*t^11+1862948*w^2*t^12-1631160*w*t^13+224*t^14', 't^4*(125*x^6*t^4-250*x^4*t^6+590*x^2*t^8+250*x*y^5*t^4-50*x*y^3*t^6+2960*x*y*t^8+500*y^4*t^6+1360*y^2*t^8-40*z*w^9+8*z*w^8*t-272*z*w^7*t^2+16*z*w^6*t^3-904*z*w^5*t^4-88*z*w^4*t^5-2048*z*w^3*t^6-184*z*w^2*t^7-2368*z*w*t^8+14*w^10-4*w^9*t+98*w^8*t^2-24*w^7*t^3+322*w^6*t^4-68*w^5*t^5+686*w^4*t^6-236*w^3*t^7+732*w^2*t^8-508*w*t^9)'], 'degree': 96, 'domain_label': '40.96.3.be.1', 'domain_model_type': 8, 'dont_display': False, 'factored': True, 'leading_coefficients': None, 'upload_id': None}
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id: 46418
{'codomain_label': '40.96.3.be.1', 'codomain_model_type': 2, 'coordinates': ['x', '1/5*t', 'y'], 'degree': 1, 'domain_label': '40.96.3.be.1', 'domain_model_type': 8, 'dont_display': False, 'factored': False, 'leading_coefficients': None, 'upload_id': None}
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id: 46419
{'codomain_label': '40.96.3.be.1', 'codomain_model_type': 5, 'coordinates': ['-x-y', 'x^3*t+2*x^2*y*t-2*x*y^2*t-4*y^3*t', 'y'], 'degree': 1, 'domain_label': '40.96.3.be.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: 1769973
{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['0:0:-1/2:-1:1', '0:1:0:0:0', '1:0:0:0:0', '-1:1:0:0:0']}, 'curve_genus': 3, 'curve_index': 96, 'curve_label': '40.96.3.be.1', '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}
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id: 1769974
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['0,0:0,0:0,-1/4:1,0:0,0', '0,0:0,0:0,1/4:0,0:1,0']}, 'curve_genus': 3, 'curve_index': 96, 'curve_label': '40.96.3.be.1', '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': '2.2.8.1', 'upload_id': None}
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id: 1769975
{'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['0,1/5,0,1/25:0,0,0,-1/25:0,0,0,0:0,0,1/5,0:1,0,0,0']}, 'curve_genus': 3, 'curve_index': 96, 'curve_label': '40.96.3.be.1', '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': '4.0.6400.3', 'upload_id': None}