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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [4, 0, 4, 0, 12, 0, 0, 0, 6, 0, -4, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 197324726861824, 'disc_rad': 38, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 2], [2, 2]]], [5, [[6, 2]]], [7, [[6, 2]]], [11, [[3, 4]]], [13, [[2, 6]]], [17, [[3, 4]]], [19, [0]], [23, [[2, 2], [1, 8]]], [29, [[4, 2], [2, 2]]], [31, [[4, 2], [2, 2]]], [37, [[4, 2], [2, 2]]], [41, [[4, 2], [2, 2]]], [43, [[3, 4]]], [47, [[6, 2]]], [53, [[4, 2], [2, 2]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [124, 24], 'galois_label': '12T21', 'galt': 21, 'grd': 26.123876537989126, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 12, 'label': '12.0.197324726861824.12', 'local_algs': ['2.12.22.61', '19.2.1.2', '19.2.1.2', '19.2.1.2', '19.2.1.2', '19.2.1.2', '19.2.1.2'], 'minimal_sibling': [2, 0, -2, 0, 0, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [2, 19], 'rd': 15.5333499252, 'regulator': {'__RealLiteral__': 0, 'data': '193.252360338', 'prec': 44}, 'res': {'sib': ['2,0,-2,0,0,0,1', '-38,0,-18,0,-2,0,1', '-2,32,-52,-24,52,-20,4,-4,1', '2,0,4,0,4,-4,4,0,1']}, 'subfield_mults': [1, 3, 1, 1, 1], 'subfields': ['5.-1.1', '-2.-2.0.1', '-38.0.-18.0.-2.0.1', '2.0.-2.0.0.0.1', '1.-3.4.-3.4.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{10} - \\frac{5}{6} a^{8} + \\frac{2}{3} a^{6} + \\frac{3}{2} a^{4} + \\frac{8}{3} a^{2} + \\frac{7}{3} \\)', '\\( \\frac{1}{12} a^{10} - \\frac{1}{3} a^{8} + \\frac{1}{3} a^{6} + \\frac{5}{6} a^{4} - \\frac{1}{3} \\)', '\\( \\frac{1}{4} a^{11} + \\frac{1}{12} a^{10} - \\frac{5}{6} a^{9} - \\frac{1}{3} a^{8} + \\frac{2}{3} a^{7} + \\frac{1}{3} a^{6} + \\frac{3}{2} a^{5} + \\frac{5}{6} a^{4} + \\frac{8}{3} a^{3} + \\frac{4}{3} a - \\frac{1}{3} \\)', '\\( \\frac{1}{12} a^{11} + \\frac{1}{12} a^{10} - \\frac{5}{6} a^{9} + \\frac{17}{6} a^{7} - \\frac{5}{6} a^{6} - \\frac{25}{6} a^{5} + \\frac{11}{6} a^{4} + 2 a^{3} + \\frac{4}{3} a^{2} - \\frac{10}{3} a + \\frac{10}{3} \\)', '\\( \\frac{1}{12} a^{11} - \\frac{1}{12} a^{10} - \\frac{2}{3} a^{9} + 2 a^{7} + \\frac{4}{3} a^{6} - \\frac{13}{6} a^{5} - \\frac{23}{6} a^{4} - \\frac{1}{3} a^{3} + \\frac{2}{3} a^{2} - \\frac{4}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6', '1/2*a^7', '1/6*a^8 + 1/6*a^6 - 1/3*a^2 + 1/3', '1/6*a^9 + 1/6*a^7 - 1/3*a^3 + 1/3*a', '1/12*a^10 + 1/6*a^6 - 1/6*a^4 + 1/3*a^2 + 1/3', '1/12*a^11 + 1/6*a^7 - 1/6*a^5 + 1/3*a^3 + 1/3*a']}
Number field data - 12.0.197324726861824.12