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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-19, 0, 38, 0, -19, 0, 1], 'conductor': 76, 'degree': 6, 'dirichlet_group': [1, 27, 49, 75, 45, 31], 'disc_abs': 158470336, 'disc_rad': 38, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 2]]], [5, [[3, 2]]], [7, [[2, 3]]], [11, [[2, 3]]], [13, [[6, 1]]], [17, [[3, 2]]], [19, [0]], [23, [[6, 1]]], [29, [[6, 1]]], [31, [[1, 6]]], [37, [[2, 3]]], [41, [[6, 1]]], [43, [[6, 1]]], [47, [[6, 1]]], [53, [[6, 1]]], [59, [[3, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_label': '6T1', 'galt': 1, 'index': 1, 'inessentialp': [], 'is_galois': True, 'iso_number': 1, 'label': '6.6.158470336.1', 'local_algs': ['2.6.6.5', '19.6.5.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 0, 'ramps': [2, 19], 'rd': 23.2625862551, 'regulator': {'__RealLiteral__': 0, 'data': '91.4119887805', 'prec': 44}, 'res': {'sex': ['7,-6,-1,1', '-19,0,1', '0,1']}, 'subfield_mults': [1, 1], 'subfields': ['-19.0.1', '7.-6.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{7} a^{4} - \\frac{16}{7} a^{2} + \\frac{11}{7} \\)', '\\( \\frac{3}{7} a^{4} - \\frac{55}{7} a^{2} + \\frac{68}{7} \\)', '\\( \\frac{3}{7} a^{5} - \\frac{3}{7} a^{4} - \\frac{55}{7} a^{3} + \\frac{55}{7} a^{2} + \\frac{75}{7} a - \\frac{68}{7} \\)', '\\( \\frac{1}{7} a^{4} - \\frac{16}{7} a^{2} - a + \\frac{11}{7} \\)', '\\( \\frac{5}{7} a^{5} + \\frac{9}{7} a^{4} - \\frac{87}{7} a^{3} - \\frac{158}{7} a^{2} + \\frac{55}{7} a + \\frac{134}{7} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/7*a^4 - 2/7*a^2 - 3/7', '1/7*a^5 - 2/7*a^3 - 3/7*a']}
Number field data - 6.6.158470336.1