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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [12, 0, 36, 0, 36, 0, -6, 0, -12, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 4874877920083968, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[12, 1]]], [7, [[3, 2], [2, 1], [1, 4]]], [11, [[6, 2]]], [13, [[3, 2], [2, 2], [1, 2]]], [17, [[4, 1], [2, 4]]], [19, [[6, 1], [3, 2]]], [23, [[6, 2]]], [29, [[12, 1]]], [31, [[6, 1], [3, 2]]], [37, [[6, 2]]], [41, [[12, 1]]], [43, [[6, 1], [3, 2]]], [47, [[6, 2]]], [53, [[4, 1], [2, 4]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3216, 2016], 'galois_label': '12T208', 'galt': 208, 'grd': 47.351920772780936, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 7, 'label': '12.0.4874877920083968.7', 'local_algs': ['2.12.22.67', '3.12.19.45'], 'minimal_sibling': [12, 0, -36, 0, 36, 0, 6, 0, -12, 0, 0, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [2, 3], 'rd': 20.2922550392, 'regulator': {'__RealLiteral__': 0, 'data': '4623.87292695', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '4.0.0.-2.0.0.1'], 'torsion_gen': '\\( \\frac{1}{2} a^{6} - 3 a^{2} - 1 \\)', 'torsion_order': 6, 'units': ['\\( \\frac{1}{7} a^{10} + \\frac{1}{14} a^{8} - \\frac{27}{14} a^{6} - \\frac{11}{7} a^{4} + \\frac{48}{7} a^{2} + \\frac{46}{7} \\)', '\\( \\frac{1}{14} a^{10} - \\frac{3}{14} a^{8} - \\frac{3}{14} a^{6} + \\frac{5}{7} a^{4} + \\frac{3}{7} a^{2} + \\frac{2}{7} \\)', '\\( \\frac{1}{7} a^{11} + \\frac{5}{14} a^{10} + \\frac{1}{14} a^{9} - \\frac{1}{14} a^{8} - \\frac{27}{14} a^{7} - \\frac{57}{14} a^{6} - \\frac{11}{7} a^{5} - \\frac{3}{7} a^{4} + \\frac{48}{7} a^{3} + \\frac{85}{7} a^{2} + \\frac{53}{7} a + \\frac{38}{7} \\)', '\\( \\frac{2}{7} a^{11} + \\frac{1}{7} a^{10} + \\frac{1}{7} a^{9} - \\frac{3}{7} a^{8} - \\frac{47}{14} a^{7} - \\frac{27}{14} a^{6} - \\frac{15}{7} a^{5} + \\frac{17}{7} a^{4} + \\frac{68}{7} a^{3} + \\frac{55}{7} a^{2} + \\frac{50}{7} a + \\frac{11}{7} \\)', '\\( \\frac{5}{14} a^{11} - \\frac{5}{7} a^{10} - \\frac{15}{14} a^{9} + \\frac{23}{14} a^{8} - \\frac{29}{14} a^{7} + \\frac{43}{7} a^{6} + \\frac{32}{7} a^{5} - \\frac{64}{7} a^{4} + \\frac{36}{7} a^{3} - \\frac{100}{7} a^{2} + \\frac{17}{7} a - \\frac{41}{7} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6', '1/2*a^7', '1/2*a^8', '1/2*a^9', '1/14*a^10 - 3/14*a^8 - 3/14*a^6 - 2/7*a^4 + 3/7*a^2 + 2/7', '1/14*a^11 - 3/14*a^9 - 3/14*a^7 - 2/7*a^5 + 3/7*a^3 + 2/7*a']}
Number field data - 12.0.4874877920083968.7