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gps_gl2zhat_fine • Show schema
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{'CPlabel': '16A1', 'Glabel': None, 'RSZBlabel': '48.48.1.252', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [1, 0, 47, 1], 'canonical_generators': [[0, 1, 29, 4], [0, 7, 25, 18], [0, 7, 29, 22], [0, 7, 29, 38], [1, 0, 16, 1], [1, 16, 0, 1], [16, 21, 3, 22], [16, 33, 15, 22], [17, 16, 32, 33], [32, 45, 27, 38]], 'cm_discriminants': [], 'coarse_class': '48.24.1.a', 'coarse_class_num': 1, 'coarse_index': 24, 'coarse_label': '48.24.1.a.1', 'coarse_level': 48, 'coarse_num': 1, 'conductor': [[2, 6], [3, 2]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4]], 'cusp_widths': [[2, 2], [4, 1], [16, 1]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 3, 'generators': [[11, 29, 4, 27], [17, 39, 40, 11], [19, 47, 24, 41], [35, 42, 20, 5], [37, 14, 32, 9]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [12, 4, 2], [12, 16, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1], [24, 4, 2], [24, 8, 1], [24, 32, 1], [48, 8, 2], [48, 16, 1], [48, 64, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [12, 8, 2], [12, 32, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [24, 16, 2], [24, 32, 1], [24, 128, 1], [48, 64, 2], [48, 128, 1], [48, 512, 1]], 'label': '48.48.1-48.a.1.3', 'lattice_labels': None, 'lattice_x': None, 'level': 48, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '6.35610766069589123929', 'prec': 74}, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 8, 'num_known_degree1_noncusp_points': 8, 'num_known_degree1_points': 9, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [12, 16, 2], [12, 64, 1], [16, 8, 2], [16, 16, 1], [16, 32, 1], [16, 128, 1], [24, 32, 2], [24, 64, 1], [24, 256, 1], [48, 64, 2], [48, 128, 1], [48, 256, 1], [48, 1024, 1]], 'parents': ['16.24.0-8.n.1.8', '24.24.0-8.n.1.2'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 24, 'psl2label': '16.24.1.a.1', 'psl2level': 16, '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', '4.6.0.c.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0-8.n.1.8', '24.24.0-8.n.1.2'], 'scalar_label': '4.2.1', 'simple': True, 'sl2label': '16.48.1-16.a.1.2', 'sl2level': 16, 'squarefree': True, 'trace_hash': 1086616701052248176, 'traces': None}
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gps_gl2zhat_fine • Show schema
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{'CPlabel': '16A1', 'Glabel': None, 'RSZBlabel': '48.24.1.1', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [1, 0, 47, 1], 'canonical_generators': [[0, 1, 29, 4], [0, 7, 25, 18], [0, 7, 29, 22], [0, 7, 29, 38], [1, 0, 16, 1], [1, 16, 0, 1], [16, 3, 21, 10], [16, 21, 3, 22], [16, 33, 15, 22], [17, 16, 32, 33]], 'cm_discriminants': [], 'coarse_class': '48.24.1.a', 'coarse_class_num': 1, 'coarse_index': 24, 'coarse_label': '48.24.1.a.1', 'coarse_level': 48, 'coarse_num': 1, 'conductor': [[2, 6], [3, 2]], 'contains_negative_one': True, 'curve_label': '576.c3', 'cusp_orbits': [[1, 4]], 'cusp_widths': [[2, 2], [4, 1], [16, 1]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[3, 22, 20, 13], [7, 40, 4, 45], [9, 29, 44, 13], [31, 7, 4, 3], [33, 35, 32, 39], [47, 15, 44, 35]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [12, 4, 2], [12, 16, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1], [24, 4, 2], [24, 8, 1], [24, 32, 1], [48, 8, 2], [48, 16, 1], [48, 64, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 2, 2], [8, 4, 1], [8, 16, 1], [12, 8, 2], [12, 32, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [24, 16, 2], [24, 32, 1], [24, 128, 1], [48, 64, 2], [48, 128, 1], [48, 512, 1]], 'label': '48.24.1.a.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '48.24.1.a.1'], 'lattice_x': [5000, 5000, 5000, 5000, 5000], 'level': 48, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '6.35610766069589123929', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['576.2.a.c'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 8, 'num_known_degree1_noncusp_points': 8, 'num_known_degree1_points': 9, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [12, 16, 2], [12, 64, 1], [16, 16, 2], [16, 32, 1], [16, 128, 1], [24, 32, 2], [24, 64, 1], [24, 256, 1], [48, 128, 2], [48, 256, 1], [48, 1024, 1]], 'parents': ['8.12.0.n.1'], 'parents_conj': [[39, 23, 14, 17]], 'pointless': False, 'power': True, 'psl2index': 24, 'psl2label': '16.24.1.a.1', 'psl2level': 16, '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', '4.6.0.c.1', '4.6.0.c.1', '8.12.0.n.1', '8.12.0.n.1', '8.12.0.n.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '16.24.1.a.1', 'sl2level': 16, 'squarefree': True, 'trace_hash': 1086616701052248176, 'traces': [0, 0, -2, 0, 0, -6, -2, 0, 0, -10, 0, 2, -10, 0, 0, 14, 0, 10, 0, 0, -6, 0, 0, -10, 18, -2, 0, 0, -6, 14, 0, 0, 22, 0, 14, 0, -22, 0, 0, -26, 0, 18, 0, -14, -2, 0, 0, 0, 0, -30, -26, 0, -30, 0, -2, 0, -26, 0, 18, -10, 0, -34, 0, 0, 26, 22, 0, 18, 0, 10, -34, 0, 0, -14, 0, 0, -34, -38, -2, -6, 0, -30, 0, 34, 0, 0, 14, 42, 38, 0, 0, 0, 0, 0, 0, 0, -10, 22, 0, 42, 0, 38, 0, -26, 0, 2, 0, 46, 0, 10, 0, 34, 38, 0, 0, -50, 0, 0, -26, 0, 50, -46, -2, 0, 0, -10, -30, 0, 0, -54, 0, 0, 0, 18, 38, 50, -34, 0, 22, -10, 0, -50, 0, 0, -54, 0, -46, -58, 0, 0, 58, -50, 0, 0, 0, 0, 0, 46, -38, -58, 0, -26, 0, 0, 62, 0, 0, -62]}
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modcurve_models • Show schema
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{'dont_display': False, 'equation': ['x^3-y^2*z-36*x*z^2'], 'modcurve': '48.24.1.a.1', 'model_type': 5, 'number_variables': 3, 'smooth': True, 'upload_id': None}
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modcurve_modelmaps • Show schema
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{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['243*x^2*y^4*z^2+36*x*y^6*z+19683*x*y^2*z^5+y^8+531441*z^8', 'z^5*y^2*x'], 'degree': 24, 'domain_label': '48.24.1.a.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^8', '3^8'], 'upload_id': None}
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modcurve_points • Show schema
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id: 693
{'Elabel': '24.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 24, 'coordinates': {'5': ['18:-72:1', '18:72:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 21.8435147413671, 'jinv': '3065617154/9', 'jorig': '3065617154/9', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 798
{'Elabel': '24.a5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 24, 'coordinates': {'5': ['-3:-9:1', '-3:9:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 7.6246189861594, 'jinv': '2048/3', 'jorig': '2048/3', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 1788712
{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['0:1:0', '0:0:1', '6:0:1', '-6:0:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, '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: 716
{'Elabel': '24.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 24, 'coordinates': {'5': ['12:-36:1', '12:36:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 17.1743649278345, 'jinv': '28756228/3', 'jorig': '28756228/3', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 824
{'Elabel': '24.a6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 24, 'coordinates': {'5': ['-2:-8:1', '-2:8:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 12.2435899856901, 'jinv': '207646/6561', 'jorig': '207646/6561', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 3878
{'Elabel': '210.e1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': {'5': ['294:-5040:1', '294:5040:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 55.0183600369297, 'jinv': '783736670177727068275201/360150', 'jorig': '783736670177727068275201/360150', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 3933
{'Elabel': '210.e3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': {'5': ['-6/49:-720/343:1', '-6/49:720/343:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 46.681793380871, 'jinv': '-187778242790732059201/4984939585440150', 'jorig': '-187778242790732059201/4984939585440150', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 4015
{'Elabel': '210.e6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': {'5': ['25/4:-35/8:1', '25/4:35/8:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 32.5399032257378, 'jinv': '135487869158881/51438240000', 'jorig': '135487869158881/51438240000', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 4072
{'Elabel': '210.e8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': {'5': ['-144/25:-504/125:1', '-144/25:504/125:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.a.1', 'curve_level': 48, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 33.2263458355123, 'jinv': '226523624554079/269165039062500', 'jorig': '226523624554079/269165039062500', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}