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gps_gl2zhat_fine • Show schema
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{'CPlabel': '36J8', 'Glabel': '1296.2567', 'RSZBlabel': '36.288.8.123', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [29, 0, 7, 1], 'canonical_generators': [[0, 1, 7, 18], [0, 11, 13, 26], [0, 19, 7, 0], [0, 23, 25, 26], [0, 25, 19, 6], [0, 35, 1, 26]], 'cm_discriminants': [], 'coarse_class': '36.144.8.f', 'coarse_class_num': 6, 'coarse_index': 144, 'coarse_label': '36.144.8.f.2', 'coarse_level': 36, 'coarse_num': 2, 'conductor': [[2, 12], [3, 24]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[3, 2], [6, 1], [9, 2], [12, 2], [18, 1], [36, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': [1, 1, 4], 'factorization': [], 'fine_num': 4, 'generators': [[5, 11, 24, 1], [19, 6, 0, 25], [29, 28, 12, 31]], 'genus': 8, 'genus_minus_rank': 8, 'has_obstruction': -1, 'index': 288, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [9, 3, 1], [9, 9, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [18, 3, 1], [18, 6, 1], [18, 9, 1], [18, 18, 1], [36, 3, 2], [36, 9, 2], [36, 12, 1], [36, 36, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [9, 9, 1], [9, 27, 1], [12, 2, 2], [12, 4, 2], [12, 6, 2], [12, 24, 1], [18, 9, 1], [18, 18, 1], [18, 27, 1], [18, 54, 1], [36, 18, 2], [36, 36, 2], [36, 54, 2], [36, 216, 1]], 'label': '36.288.8-36.f.2.4', 'lattice_labels': None, 'lattice_x': None, 'level': 36, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '34.68446109475397630649', 'prec': 77}, 'models': None, 'mults': [2, 2, 1], 'name': None, 'newforms': None, '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': None, 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 3, 2], [4, 2, 2], [4, 8, 1], [6, 2, 1], [6, 3, 2], [6, 4, 1], [6, 6, 2], [9, 18, 1], [9, 27, 2], [12, 4, 2], [12, 6, 4], [12, 8, 2], [12, 24, 2], [18, 18, 1], [18, 27, 2], [18, 36, 1], [18, 54, 2], [36, 36, 2], [36, 54, 4], [36, 72, 2], [36, 216, 2]], 'parents': ['12.96.0-12.c.3.3', '36.144.4-36.f.1.3', '36.144.4-36.f.1.8'], 'parents_conj': None, 'pointless': False, 'power': False, 'psl2index': 144, 'psl2label': '36.144.8.d.1', 'psl2level': 36, 'q_gonality': 3, 'q_gonality_bounds': [3, 3], 'qbar_gonality': 3, 'qbar_gonality_bounds': [3, 3], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '9.24.0-9.b.1.1', '12.96.0-12.c.3.3', '18.72.2-18.d.1.2'], 'scalar_label': '12.4.1', 'simple': False, 'sl2label': '36.288.8-36.d.1.2', 'sl2level': 36, 'squarefree': False, 'trace_hash': 1154402941090637402, 'traces': None}
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gps_gl2zhat_fine • Show schema
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{'CPlabel': '36J8', 'Glabel': None, 'RSZBlabel': '36.144.8.9', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [29, 0, 7, 1], 'canonical_generators': [[0, 1, 7, 18], [0, 1, 35, 10], [0, 11, 13, 26], [0, 11, 17, 30], [0, 13, 11, 10], [0, 17, 29, 0]], 'cm_discriminants': [], 'coarse_class': '36.144.8.f', 'coarse_class_num': 6, 'coarse_index': 144, 'coarse_label': '36.144.8.f.2', 'coarse_level': 36, 'coarse_num': 2, 'conductor': [[2, 12], [3, 24]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[3, 2], [6, 1], [9, 2], [12, 2], [18, 1], [36, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': [1, 1, 4], 'factorization': [], 'fine_num': 0, 'generators': [[5, 4, 24, 23], [5, 33, 0, 29], [23, 6, 0, 11], [29, 24, 0, 7]], 'genus': 8, 'genus_minus_rank': 8, 'has_obstruction': -1, 'index': 144, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [9, 3, 1], [9, 9, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [18, 3, 1], [18, 6, 1], [18, 9, 1], [18, 18, 1], [36, 3, 2], [36, 9, 2], [36, 12, 1], [36, 36, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [9, 9, 1], [9, 27, 1], [12, 2, 2], [12, 4, 2], [12, 6, 2], [12, 24, 1], [18, 9, 1], [18, 18, 1], [18, 27, 1], [18, 54, 1], [36, 18, 2], [36, 36, 2], [36, 54, 2], [36, 216, 1]], 'label': '36.144.8.f.2', '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', '9.12.0.b.1', '12.24.0.g.1', '12.48.0.c.3', '18.36.2.d.1', '36.72.4.f.1', '36.144.8.f.2'], 'lattice_x': [3602, 5166, 2085, 8246, 5166, 1280, 6825, 6825, 2701, 3412, 5118], 'level': 36, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '34.68446109475397630649', 'prec': 77}, 'models': 2, 'mults': [2, 2, 1], 'name': None, 'newforms': ['54.2.a.a', '54.2.a.b', '108.2.b.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], [3, 2, 1], [3, 6, 1], [4, 2, 2], [4, 8, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [9, 18, 1], [9, 54, 1], [12, 4, 2], [12, 8, 2], [12, 12, 2], [12, 48, 1], [18, 18, 1], [18, 36, 1], [18, 54, 1], [18, 108, 1], [36, 36, 2], [36, 72, 2], [36, 108, 2], [36, 432, 1]], 'parents': ['12.48.0.c.3', '36.72.4.f.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': False, 'psl2index': 144, 'psl2label': '36.144.8.d.1', 'psl2level': 36, 'q_gonality': 3, 'q_gonality_bounds': [3, 3], 'qbar_gonality': 3, 'qbar_gonality_bounds': [3, 3], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '9.12.0.b.1', '12.48.0.c.3', '18.36.2.d.1'], 'scalar_label': '12.2.1', 'simple': False, 'sl2label': '36.144.8.d.1', 'sl2level': 36, 'squarefree': False, 'trace_hash': 1154402941090637402, 'traces': [0, 0, 0, -4, 0, -8, 0, 8, 0, 0, 20, -8, 0, -40, 0, 0, 0, 16, 56, 0, -8, 32, 0, 0, 40, 0, -16, 0, -8, 0, -28, 0, 0, -16, 0, 68, 64, 80, 0, 0, 0, -128, 0, -80, 0, -28, -88, 32, 0, 64, 0, 0, 16, 0, 0, 0, 0, -100, 112, 0, 56, 0, -64, 0, -56, 0, -40, -128, 0, -104, 0, 0, 68, 88, 80, 0, 0, 136, 0, 64, 0, 16, 0, 64, -76, 0, 0, -128, 0, -52, 0, 0, -64, 0, 56, 0, 0, 0, -64, 64, 32, 0, 0, 0, -16, 208, 0, 0, 0, 16, 128, 16, 0, -112, -100, 0, -16, 0, 0, 0, -8, 16, 0, 0, 176, 0, 304, 0, -4, -56, -64, 0, 164, -128, 0, -80, 0, 128, 0, 0, 8, 0, -124, 0, 160, 0, -32, 0, -160, 0, -224, 0, 8, 0, 104, 0, 116, 0, -80, 0, 0, 0, 92, 0, 0, 0, 188, -56]}
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modcurve_models • Show schema
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id: 42110
{'dont_display': False, 'equation': ['y*v-z*u', 'x*v-y*v-w*u', 'x*v+y*t', 'x*u-x*r-w*t', 'z*t+z*v+w*v', 't*v-u^2+u*r+v^2', 't^2-u^2-v^2+r^2', 'x*t+y*v-w*u-w*r', 'y*u-y*r+w*v', 'y*t-y*v-z*u-z*r', 'x*z-y*z-y*w', 't*u-2*u*v-v*r', 'x*u+2*y*u+y*r', 'x*y+3*y^2+z*w', 'x^2+3*x*y+z*w+w^2', 'x^2*y+x*z^2+u*v*r+v^3', '2*x^2*z-x^2*w+t*u*v+t*v*r', 'x^2*w+z^2*w+z*w^2-t*v*r-u*v^2', 'x^2*y-y*z^2+y*w^2+t*v^2+u*v*r', 'x^3-x^2*y+x*z*w-t*u*r-u^2*v'], 'modcurve': '36.144.8.f.2', 'model_type': 0, 'number_variables': 8, 'smooth': True, 'upload_id': None}
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id: 42111
{'dont_display': False, 'equation': ['-9*x^8*y^3-18*x^6*y^3*z^2+x^7*z^4-8*x^4*y^3*z^4-x^5*z^6+2*x^2*y^3*z^6+y^3*z^8'], 'modcurve': '36.144.8.f.2', 'model_type': 2, 'number_variables': 3, 'smooth': False, 'upload_id': None}
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modcurve_modelmaps • Show schema
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id: 42132
{'codomain_label': '36.72.4.f.1', 'codomain_model_type': 0, 'coordinates': ['-x', 'y', '-t', 'v'], 'degree': 2, 'domain_label': '36.144.8.f.2', 'domain_model_type': 0, 'dont_display': False, 'factored': True, 'leading_coefficients': None, 'upload_id': None}
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id: 42133
{'codomain_label': '36.144.8.f.2', 'codomain_model_type': 2, 'coordinates': ['u', '1/4*w', 'v'], 'degree': 1, 'domain_label': '36.144.8.f.2', 'domain_model_type': 0, 'dont_display': False, 'factored': False, 'leading_coefficients': None, 'upload_id': None}
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modcurve_points • Show schema
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id: 1764563
{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0:0:0:0:0:1:0:1', '0:0:0:0:1:-1:1:1', '0:0:0:0:-1:-1:-1:1', '0:0:1:0:0:0:0:0']}, 'curve_genus': 8, 'curve_index': 144, 'curve_label': '36.144.8.f.2', 'curve_level': 36, '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: 1764564
{'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0,0:0,0:0,0:0,0:0,1:0,0:0,0:1,0']}, 'curve_genus': 8, 'curve_index': 144, 'curve_label': '36.144.8.f.2', 'curve_level': 36, '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': '2.0.4.1', 'upload_id': None}
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id: 1764565
{'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0,0:0,-1/3:-1,0:1,0:0,0:0,0:0,0:0,0']}, 'curve_genus': 8, 'curve_index': 144, 'curve_label': '36.144.8.f.2', 'curve_level': 36, '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': '2.2.12.1', 'upload_id': None}
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id: 1764566
{'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['1/2,-1:1/6,-1/3:1/2,0:1,0:0,0:0,0:0,0:0,0']}, 'curve_genus': 8, 'curve_index': 144, 'curve_label': '36.144.8.f.2', 'curve_level': 36, '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': '2.0.3.1', 'upload_id': None}