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gps_gl2zhat_fine • Show schema
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{'CPlabel': '8G1', 'Glabel': None, 'RSZBlabel': '56.48.1.204', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 7], 'canonical_conjugator': [43, 0, 21, 43], 'canonical_generators': [[1, 0, 8, 1], [1, 1, 38, 33], [1, 1, 54, 35], [1, 1, 54, 49], [1, 3, 34, 7], [1, 8, 0, 1], [1, 42, 28, 1], [9, 8, 48, 49], [15, 42, 28, 15]], 'cm_discriminants': [], 'coarse_class': '56.48.1.it', 'coarse_class_num': 228, 'coarse_index': 48, 'coarse_label': '56.48.1.it.2', 'coarse_level': 56, 'coarse_num': 2, 'conductor': [[2, 6], [7, 2]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 2], [4, 1]], 'cusp_widths': [[4, 4], [8, 4]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[2, 5, 37, 4], [12, 9, 13, 34], [30, 35, 9, 10]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': 1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [7, 8, 1], [8, 4, 1], [8, 8, 1], [14, 8, 1], [14, 16, 1], [28, 16, 1], [28, 32, 1], [56, 32, 1], [56, 64, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [7, 24, 1], [8, 8, 3], [14, 24, 1], [14, 48, 1], [28, 96, 1], [28, 192, 1], [56, 384, 3]], 'label': '56.48.1.it.2', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.d.1', '8.12.0.w.1', '8.24.0.bl.2', '56.2.0.b.1', '56.6.0.b.1', '56.6.0.c.1', '56.12.0.bh.1', '56.12.1.a.1', '56.24.0.ef.1', '56.24.1.dh.1', '56.48.1.it.2'], 'lattice_x': [1960, 3141, 5072, 7147, 7147, 778, 922, 2997, 2997, 5072, 9222, 5072, 7147], 'level': 56, 'level_is_squarefree': False, 'level_radical': 14, 'log_conductor': {'__RealLiteral__': 0, 'data': '8.05070338147029846671', 'prec': 74}, 'models': 2, 'mults': [1], 'name': None, 'newforms': ['3136.2.a.m'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 0, 'obstructions': [0], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 1], [4, 8, 1], [7, 48, 1], [8, 16, 3], [14, 48, 1], [14, 96, 1], [28, 192, 1], [28, 384, 1], [56, 768, 3]], 'parents': ['8.24.0.bl.2', '56.24.0.ef.1', '56.24.1.dh.1'], 'parents_conj': [[7, 48, 9, 51], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': True, 'power': True, 'psl2index': 48, 'psl2label': '8.48.1.b.1', 'psl2level': 8, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.d.1', '4.6.0.d.1', '8.24.0.bl.2'], 'scalar_label': '8.2.2', 'simple': True, 'sl2label': '8.48.1.b.1', 'sl2level': 8, 'squarefree': True, 'trace_hash': 2150367284721650669, '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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id: 87494
{'dont_display': False, 'equation': ['2*x^2-x*y+y^2+x*z-2*y*z+2*z^2', 'x^2-4*x*y+4*y^2-4*x*z+8*y*z+8*z^2-2*w^2'], 'modcurve': '56.48.1.it.2', 'model_type': 8, 'number_variables': 4, 'smooth': True, 'upload_id': None}
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id: 87495
{'dont_display': False, 'equation': ['680*x^4+1232*x^3*y+896*x^2*y^2+392*x*y^3+98*y^4-65*x^2*z^2-70*x*y*z^2-21*y^2*z^2+2*z^4'], 'modcurve': '56.48.1.it.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: 86906
{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['1728*x*z^9*w^2-2304*x*z^7*w^4+224*x*z^5*w^6+320*x*z^3*w^8+12*x*z*w^10-3456*y*z^9*w^2+4608*y*z^7*w^4-448*y*z^5*w^6-640*y*z^3*w^8-24*y*z*w^10-1728*z^12+5040*z^8*w^4-3200*z^6*w^6+92*z^4*w^8+96*z^2*w^10+w^12', 'z^8*(4*x*z*w^2-8*y*z*w^2-16*z^4+w^4)'], 'degree': 48, 'domain_label': '56.48.1.it.2', 'domain_model_type': 8, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^4', '1'], 'upload_id': None}
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id: 86907
{'codomain_label': '56.48.1.it.2', 'codomain_model_type': 2, 'coordinates': ['z', 'y', '2*w'], 'degree': 1, 'domain_label': '56.48.1.it.2', '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: 1820940
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['0,-1/7:0,-1/14:1/2,0:1,0', '0,-1/7:0,-1/14:-1/2,0:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '56.48.1.it.2', 'curve_level': 56, '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': '2.0.56.1', 'upload_id': None}
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id: 1820941
{'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['0,-5/14,0,-1/28:0,1/14,0,3/28:0,0,0,0:1,0,0,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '56.48.1.it.2', 'curve_level': 56, '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': '4.0.3136.3', 'upload_id': None}