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nf_fields • Show schema
{'class_group': [4], 'class_number': 4, 'cm': False, 'coeffs': [16, 0, 36, 0, 24, 0, 9, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 6179217664, 'disc_rad': 34, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 2]]], [5, [[4, 2]]], [7, [[4, 2]]], [11, [[4, 2]]], [13, [[2, 4]]], [17, [0]], [19, [[2, 2], [1, 4]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[2, 2], [1, 4]]], [47, [[2, 4]]], [53, [[2, 4]]], [59, [[2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 12], 'galois_label': '8T10', 'galt': 10, 'grd': 16.74428805718538, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '8.0.6179217664.2', 'local_algs': ['2.2.2.2', '2.2.2.2', '2.4.4.1', '17.4.3.1', '17.4.3.1'], 'minimal_sibling': [1, 0, -4, 0, -11, 0, -4, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [2, 17], 'rd': 16.7442880572, 'regulator': {'__RealLiteral__': 0, 'data': '29.9811052816', 'prec': 44}, 'res': {'gal': ['16,16,-8,-56,264,-644,758,-358,-19,10,108,-138,114,-70,30,-8,1'], 'sib': ['1,0,-4,0,-11,0,-4,0,1', '16,16,-8,-56,264,-644,758,-358,-19,10,108,-138,114,-70,30,-8,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-4.-1.1', '68.0.17.0.1', '1.-1.-2.-1.1', '-17.0.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{16} a^{7} - \\frac{1}{8} a^{6} + \\frac{7}{16} a^{5} - \\frac{9}{8} a^{4} + \\frac{5}{8} a^{3} - \\frac{5}{2} a^{2} + a - 2 \\)', '\\( \\frac{1}{4} a^{7} + 2 a^{5} + \\frac{17}{4} a^{3} + \\frac{11}{2} a \\)', '\\( \\frac{1}{4} a^{5} + \\frac{3}{4} a^{3} + \\frac{1}{2} a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^2', '1/4*a^5 - 1/4*a^3 - 1/2*a', '1/8*a^6 - 1/8*a^4 - 1/2*a^3 + 1/4*a^2 - 1/2*a', '1/16*a^7 - 1/16*a^5 - 1/4*a^4 - 3/8*a^3 - 1/4*a^2 - 1/2*a']}
Number field data - 8.0.6179217664.2