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gps_gl2zhat_fine • Show schema
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{'CPlabel': '16G0', 'Glabel': '256.14694', 'RSZBlabel': '16.96.0.192', 'RZBlabel': 'X207i', 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2], 'canonical_conjugator': [13, 3, 3, 14], 'canonical_generators': [[1, 0, 1, 3], [1, 0, 2, 1], [3, 8, 1, 9], [3, 8, 2, 11], [11, 8, 14, 3], [15, 0, 14, 11]], 'cm_discriminants': [], 'coarse_class': '16.48.0.j', 'coarse_class_num': 10, 'coarse_index': 48, 'coarse_label': '16.48.0.j.1', 'coarse_level': 16, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[2, 8], [16, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 3, 'generators': [[1, 12, 0, 13], [3, 0, 8, 3], [3, 11, 8, 1], [13, 15, 8, 7]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 4], [8, 8, 1], [16, 2, 4], [16, 16, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 2, 4], [8, 16, 1], [16, 4, 4], [16, 8, 2], [16, 64, 1]], 'label': '16.96.0-16.j.1.3', 'lattice_labels': None, 'lattice_x': None, 'level': 16, 'level_is_squarefree': False, 'level_radical': 2, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 1, 'num_known_degree1_noncm_points': 6, 'num_known_degree1_noncusp_points': 6, 'num_known_degree1_points': 7, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 2], [4, 8, 1], [8, 2, 2], [8, 4, 3], [8, 32, 1], [16, 8, 6], [16, 16, 1], [16, 128, 1]], 'parents': ['8.48.0-8.q.1.4', '16.48.0-8.q.1.3', '16.48.0-16.e.2.2', '16.48.0-16.e.2.4', '16.48.0-16.e.2.13', '16.48.0-16.e.2.15'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '16.48.0.a.1', 'psl2level': 16, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0-8.q.1.4'], 'scalar_label': '8.4.1', 'simple': None, 'sl2label': '16.96.0-16.a.1.1', 'sl2level': 16, 'squarefree': None, 'trace_hash': 0, 'traces': None}
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gps_gl2zhat_fine • Show schema
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{'CPlabel': '16G0', 'Glabel': None, 'RSZBlabel': '16.48.0.60', 'RZBlabel': 'X207', 'SZlabel': '16G0-16g', 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2], 'canonical_conjugator': [13, 3, 3, 14], 'canonical_generators': [[1, 0, 1, 3], [1, 0, 2, 1], [1, 0, 2, 5], [3, 8, 1, 9], [3, 8, 2, 11], [5, 8, 2, 13]], 'cm_discriminants': [], 'coarse_class': '16.48.0.j', 'coarse_class_num': 10, 'coarse_index': 48, 'coarse_label': '16.48.0.j.1', 'coarse_level': 16, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[2, 8], [16, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[1, 8, 0, 13], [1, 10, 0, 9], [13, 0, 8, 13], [13, 5, 8, 11], [15, 3, 0, 1]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 4], [8, 8, 1], [16, 2, 4], [16, 16, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 2, 4], [8, 16, 1], [16, 4, 4], [16, 8, 2], [16, 64, 1]], 'label': '16.48.0.j.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.2.0.a.1', '4.6.0.a.1', '4.6.0.c.1', '4.6.0.e.1', '4.12.0.d.1', '8.12.0.n.1', '8.12.0.r.1', '8.24.0.q.1', '16.24.0.e.1', '16.24.0.e.2', '16.48.0.j.1'], 'lattice_x': [4445, 5963, 2926, 2926, 5963, 9000, 6333, 3296, 9000, 6333, 3667, 1000, 3667], 'level': 16, 'level_is_squarefree': False, 'level_radical': 2, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 1, 'num_known_degree1_noncm_points': 6, 'num_known_degree1_noncusp_points': 6, 'num_known_degree1_points': 7, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 2], [4, 8, 1], [8, 4, 4], [8, 32, 1], [16, 8, 4], [16, 16, 2], [16, 128, 1]], 'parents': ['8.24.0.q.1', '16.24.0.e.1', '16.24.0.e.2'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [9, 4, 6, 11]], 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '16.48.0.a.1', 'psl2level': 16, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0.q.1'], 'scalar_label': '8.2.2', 'simple': None, 'sl2label': '16.48.0.a.1', 'sl2level': 16, 'squarefree': None, 'trace_hash': 0, 'traces': []}
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modcurve 16.48.0.j.1 does not appear in modcurve_models
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modcurve_modelmaps • Show schema
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{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['(x-y)^48*(x^8-24*x^7*y+144*x^6*y^2-304*x^5*y^3+136*x^4*y^4+288*x^3*y^5-320*x^2*y^6+64*x*y^7+16*y^8)^3*(x^8+8*x^7*y-80*x^6*y^2+144*x^5*y^3+136*x^4*y^4-608*x^3*y^5+576*x^2*y^6-192*x*y^7+16*y^8)^3', 'y^2*x^2*(x-2*y)^2*(x-y)^50*(x^2-2*y^2)^2*(x^2-4*x*y+2*y^2)^2*(x^2-2*x*y+2*y^2)^16'], 'degree': 48, 'domain_label': '16.48.0.j.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-1', '1'], 'upload_id': None}
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modcurve_points • Show schema
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id: 1848179
{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['0:1', '1:1', '2:1', '1:0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.j.1', 'curve_level': 16, '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: 4071
{'Elabel': '210.e8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.j.1', 'curve_level': 16, '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}
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id: 208879
{'Elabel': '46410.ck8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 46410, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.j.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 64.8543413346709, 'jinv': '14651516183052242700771495839/8480668142378708755560900', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 320260
{'Elabel': '82110.bs8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 82110, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.j.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 70.6540515956318, 'jinv': '4837987390362436347081585367679/4540848316592979232425603600', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 401630
{'Elabel': '110670.cm8', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 110670, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.j.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 79.7357352563433, 'jinv': '42539250356844378683161410804461759/45626792684197425842285156250000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 743033
{'Elabel': '249690.cj5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 249690, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.j.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 80.6990740845392, 'jinv': '-111471172596350616707438857829030881/18551296611518877695051385524100', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 782353
{'Elabel': '266910.ck7', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 266910, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.j.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 90.128256113009, 'jinv': '1387408316478144028202421750997946744639/4766529283100579070606788945040992400', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}