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lf_fields • Show schema
{'associated_inertia': [1, 1, 1], 'aut': 2, 'c': 56, 'canonical_filtration': None, 'coeffs': [39, 160, 492, 1200, 2422, 4032, 5628, 6608, 6543, 5456, 3804, 2192, 1018, 368, 96, 16, 1], 'ctr': 269, 'ctr_family': 1, 'ctr_subfamily': 5, 'distinguished_residual_polynomials': ['z^4 + 1', 'z^2 + t', 't*z + t + 1'], 'e': 8, 'eisen': 'x^8 + 8*t*x^7 + 4*t*x^6 + (8*t + 8)*x^5 + 16*t*x^3 + (8*t + 8)*x^2 + (8*t + 2)', 'f': 2, 'family': '2.2.8.56a', 'gal': 1713, 'galT': 1713, 'galois_degree': 8192, 'galois_label': '16T1713', 'gms': '4.1142578125', 'gsm': [-729, 0, 12636, 0, -48438, 0, 63828, 0, -21825, 0, 972, 0, 222, 0, 24, 0, 1], 'hidden': '[2,2,3,3,7/2,7/2,15/4,31/8]^{2}', 'hw': '$i$', 'ind_of_insep': [21, 14, 8, 0], 'ind_of_insep_tmp': ['21A', '14A', '8A', '0A'], 'inertia': ['i', [-1, -1]], 'inertia_gap': None, 'is_completion': False, 'jump_set': [1, 3, 7, 15], 'label': '2.16.56.27401', 'n': 16, 'new_label': '2.2.8.56a5.269', 'num': 27401, 'old_label': '2.16.56.27401', 'p': 2, 'packet': None, 'packet_size': None, 'ppow_roots_of_unity': 1, 'ram_poly_vert': [[1, 21], [2, 14], [4, 8], [8, 0]], 'residual_polynomials': ['z^4 + 1', 'z^2 + t', 't*z + (t + 1)'], 'rf': [-1, 0], 'slopes': '[2, 2, 3, 3, 3, 7/2, 7/2, 7/2, 15/4, 31/8, 9/2]', 'slopes_tmp': ['2A', '2B', '3A', '3B', '3C', '7/2A', '7/2B', '7/2C', '15/4A', '31/8A', '9/2A'], 'subfamily': '2.2.8.56a5', 'subfield': ['2.2.0.1', '2.4.6.6', '2.8.20.47'], 'subfield_mult': [1, 1, 1], 't': 1, 'top_slope': '04.5000000009/2', 'u': 4, 'unram': 't^2 + t + 1', 'visible': '[3, 7/2, 9/2]', 'visible_tmp': ['3A', '7/2A', '9/2A'], 'wild_gap': None}
Local field data - 2.2.8.56a5.269