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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': True, 'coeffs': [49, 0, -16, 0, 20, 0, -8, 0, 1], 'conductor': 80, 'degree': 8, 'dirichlet_group': [1, 69, 39, 41, 11, 79, 51, 29], 'disc_abs': 10485760000, 'disc_rad': 10, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 2]]], [5, [0]], [7, [[1, 8]]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[2, 4]]], [19, [[4, 2]]], [23, [[1, 8]]], [29, [[4, 2]]], [31, [[2, 4]]], [37, [[4, 2]]], [41, [[2, 4]]], [43, [[4, 2]]], [47, [[2, 4]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 4], 'galois_label': '8T2', 'galt': 2, 'grd': 17.88854381999832, 'inessentialp': [7], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.10485760000.1', 'local_algs': ['2.1.8.24c1.61', '5.4.2.4a1.2'], 'maximal_cm_subfield': [49, 0, -16, 0, 20, 0, -8, 0, 1], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 4, 'ramps': [2, 5], 'rd': 17.88854382, 'regulator': {'__RealLiteral__': 0, 'data': '78.6242549932', 'prec': 44}, 'relative_class_number': 1, 'res': {}, 'subfield_mults': [1, 1, 1, 1, 1, 1], 'subfields': ['5.0.1', '-2.0.1', '10.0.1', '9.0.4.0.1', '50.0.-20.0.1', '2.0.4.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{21} a^{6} - \\frac{2}{7} a^{4} + \\frac{1}{21} a^{2} - \\frac{1}{3} \\)', '\\( \\frac{2}{21} a^{6} + \\frac{4}{21} a^{5} - \\frac{4}{7} a^{4} - \\frac{31}{21} a^{3} + \\frac{2}{21} a^{2} + \\frac{53}{21} a + \\frac{7}{3} \\)', '\\( \\frac{1}{21} a^{7} + \\frac{2}{21} a^{6} - \\frac{1}{3} a^{5} - \\frac{4}{7} a^{4} + \\frac{2}{3} a^{3} + \\frac{2}{21} a^{2} - \\frac{12}{7} a + \\frac{1}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 - 1/3*a^2 - 1/3', '1/21*a^5 + 8/21*a^3 + 8/21*a', '1/21*a^6 + 1/21*a^4 - 2/7*a^2 + 1/3', '1/21*a^7 + 1/3*a^3 - 1/21*a']}
Number field data - 8.0.10485760000.1