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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, -5, 0, 6, 0, 1, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 67371264, 'disc_rad': 114, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 2]]], [7, [[2, 4]]], [11, [[4, 2]]], [13, [[2, 4]]], [17, [[4, 2]]], [19, [0]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[2, 2], [1, 4]]], [37, [[2, 2], [1, 4]]], [41, [[4, 2]]], [43, [[2, 2], [1, 4]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48, 24, 16], 'galois_label': '8T18', 'galt': 18, 'grd': 28.103650443517264, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.67371264.1', 'local_algs': ['2.4.4.4', '2.4.4.4', '3.8.6.2', '19.2.1.1', '19.2.0.1', '19.2.0.1', '19.2.1.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 19], 'rd': 9.51829886184, 'regulator': {'__RealLiteral__': 0, 'data': '12.9192490854', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['1.-1.1', '3.0.-3.0.1', '4.2.-3.-1.1', '19.0.8.0.1'], 'torsion_gen': '\\( \\frac{3}{2} a^{6} + 2 a^{4} + 10 a^{2} - \\frac{7}{2} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{9}{2} a^{7} + 6 a^{5} + 29 a^{3} - \\frac{25}{2} a \\)', '\\( \\frac{7}{2} a^{7} + \\frac{3}{2} a^{6} + 5 a^{5} + 2 a^{4} + 23 a^{3} + 10 a^{2} - \\frac{17}{2} a - \\frac{7}{2} \\)', '\\( 5 a^{7} - \\frac{7}{2} a^{6} + 7 a^{5} - 5 a^{4} + 33 a^{3} - 23 a^{2} - 12 a + \\frac{17}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2', '1/2*a^7 - 1/2*a']}
Number field data - 8.0.67371264.1