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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-9, 0, -54, 0, -27, 0, 12, 0, 15, 0, 6, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 328683126924509184, 'disc_rad': 6, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1], [4, 1]]], [7, [[4, 2], [2, 1], [1, 2]]], [11, [[4, 3]]], [13, [[8, 1], [4, 1]]], [17, [[2, 4], [1, 4]]], [19, [[4, 3]]], [23, [[6, 1], [1, 6]]], [29, [[8, 1], [4, 1]]], [31, [[6, 1], [3, 2]]], [37, [[4, 2], [2, 2]]], [41, [[6, 2]]], [43, [[8, 1], [2, 2]]], [47, [[4, 1], [2, 4]]], [53, [[8, 1], [4, 1]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9864, 3200], 'galois_label': '12T241', 'galt': 241, 'grd': 89.42379121066101, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 18, 'label': '12.2.328683126924509184.18', 'local_algs': ['2.2.2.6a1.5', '2.1.8.30a1.72', '3.2.6.14a1.2'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 5, 'ramps': [2, 3], 'rd': 28.8224869242, 'regulator': {'__RealLiteral__': 0, 'data': '27291.4899343', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '-4.12.-9.-4.6.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{12} a^{10} + \\frac{5}{12} a^{8} + \\frac{5}{6} a^{6} + \\frac{1}{2} a^{4} - \\frac{7}{4} a^{2} - \\frac{3}{4} \\)', '\\( \\frac{1}{12} a^{11} + \\frac{1}{24} a^{10} + \\frac{1}{3} a^{9} + \\frac{7}{24} a^{8} + \\frac{1}{2} a^{7} + \\frac{3}{4} a^{6} + \\frac{1}{4} a^{4} - \\frac{3}{4} a^{3} - \\frac{7}{8} a^{2} - \\frac{1}{8} \\)', '\\( \\frac{5}{8} a^{11} + \\frac{13}{24} a^{10} + \\frac{29}{8} a^{9} + \\frac{19}{8} a^{8} + \\frac{107}{12} a^{7} + \\frac{19}{4} a^{6} + \\frac{25}{4} a^{5} + \\frac{3}{4} a^{4} - \\frac{137}{8} a^{3} - \\frac{99}{8} a^{2} - \\frac{257}{8} a - \\frac{71}{8} \\)', '\\( \\frac{1}{12} a^{11} - \\frac{1}{24} a^{10} + \\frac{1}{3} a^{9} - \\frac{7}{24} a^{8} + \\frac{1}{2} a^{7} - \\frac{3}{4} a^{6} - \\frac{1}{4} a^{4} - \\frac{3}{4} a^{3} + \\frac{7}{8} a^{2} + \\frac{1}{8} \\)', '\\( \\frac{1}{8} a^{11} - \\frac{1}{4} a^{10} + \\frac{13}{24} a^{9} - \\frac{5}{6} a^{8} + \\frac{11}{12} a^{7} - \\frac{7}{6} a^{6} - \\frac{1}{4} a^{5} + a^{4} - \\frac{21}{8} a^{3} + \\frac{17}{4} a^{2} - \\frac{11}{8} a + \\frac{1}{2} \\)', '\\( \\frac{1}{8} a^{11} + \\frac{1}{4} a^{10} + \\frac{13}{24} a^{9} + \\frac{5}{6} a^{8} + \\frac{11}{12} a^{7} + \\frac{7}{6} a^{6} - \\frac{1}{4} a^{5} - a^{4} - \\frac{21}{8} a^{3} - \\frac{17}{4} a^{2} - \\frac{11}{8} a - \\frac{1}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6', '1/3*a^7', '1/6*a^8 - 1/2', '1/6*a^9 - 1/2*a', '1/24*a^10 - 1/12*a^9 - 1/24*a^8 + 1/12*a^6 - 1/2*a^5 + 1/4*a^4 + 1/8*a^2 - 1/4*a - 1/8', '1/24*a^11 - 1/24*a^9 - 1/12*a^8 + 1/12*a^7 + 1/4*a^5 - 1/2*a^4 + 1/8*a^3 - 1/8*a - 1/4']}
Number field data - 12.2.328683126924509184.18