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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 9, -10, -6, 11, -1, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 8719893, 'disc_rad': 273, 'disc_sign': 1, 'frobs': [[2, [[8, 1]]], [3, [0]], [5, [[8, 1]]], [7, [0]], [11, [[8, 1]]], [13, [0]], [17, [[2, 4]]], [19, [[4, 1], [1, 4]]], [23, [[4, 2]]], [29, [[2, 4]]], [31, [[4, 1], [1, 4]]], [37, [[4, 1], [2, 2]]], [41, [[8, 1]]], [43, [[2, 2], [1, 4]]], [47, [[8, 1]]], [53, [[2, 4]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '8T17', 'galt': 17, 'index': 1, 'inessentialp': [], 'is_galois': False, 'iso_number': 1, 'label': '8.0.8719893.1', 'local_algs': ['3.8.4.1', '7.2.1.2', '7.2.1.2', '7.4.0.1', '13.4.3.3', '13.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [3, 7, 13], 'rd': 7.37163620696, 'regulator': {'__RealLiteral__': 0, 'data': '3.28851213295', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '1.1.-1.-1.1'], 'torsion_gen': '\\( \\frac{1}{17} a^{7} + \\frac{2}{17} a^{6} - \\frac{8}{17} a^{5} - \\frac{12}{17} a^{4} + \\frac{36}{17} a^{3} + a^{2} - \\frac{42}{17} a + \\frac{10}{17} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{3}{17} a^{7} - \\frac{11}{17} a^{6} - \\frac{7}{17} a^{5} + \\frac{49}{17} a^{4} - \\frac{11}{17} a^{3} - 4 a^{2} + \\frac{27}{17} a + \\frac{13}{17} \\)', '\\( \\frac{4}{17} a^{7} - \\frac{9}{17} a^{6} - \\frac{15}{17} a^{5} + \\frac{54}{17} a^{4} - \\frac{9}{17} a^{3} - 4 a^{2} + \\frac{53}{17} a - \\frac{11}{17} \\)', '\\( \\frac{1}{17} a^{7} - \\frac{15}{17} a^{6} + \\frac{26}{17} a^{5} + \\frac{39}{17} a^{4} - \\frac{100}{17} a^{3} - a^{2} + \\frac{94}{17} a - \\frac{24}{17} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/17*a^7 + 2/17*a^6 - 8/17*a^5 + 5/17*a^4 + 2/17*a^3 - 8/17*a - 7/17']}
Number field data - 8.0.8719893.1