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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [2, -10, 21, -24, 36, -60, 38, 8, -6, -2, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 5435817984000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[8, 1], [2, 1]]], [11, [[8, 1], [2, 1]]], [13, [[4, 2], [1, 2]]], [17, [[5, 1], [4, 1], [1, 1]]], [19, [[8, 1], [2, 1]]], [23, [[8, 1], [2, 1]]], [29, [[4, 1], [2, 2], [1, 2]]], [31, [[4, 2], [2, 1]]], [37, [[5, 1], [2, 2], [1, 1]]], [41, [[4, 2], [1, 2]]], [43, [[4, 2], [2, 1]]], [47, [[8, 1], [2, 1]]], [53, [[4, 2], [1, 2]]], [59, [[8, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3150, 400, 600], 'galois_label': '10T33', 'galt': 33, 'grd': 88.73475173116533, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.5435817984000.1', 'local_algs': ['2.2.2.1', '2.8.27.63', '3.2.0.1', '3.4.2.1', '3.4.2.1', '5.1.0.1', '5.4.3.3', '5.5.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [2, 3, 5], 'rd': 18.7726892246, 'regulator': {'__RealLiteral__': 0, 'data': '1606.39678312', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.0.1'], 'torsion_gen': '\\( -\\frac{1}{6} a^{9} + \\frac{7}{12} a^{8} + \\frac{5}{6} a^{7} - \\frac{13}{4} a^{6} - \\frac{20}{3} a^{5} + \\frac{245}{12} a^{4} - \\frac{15}{2} a^{3} + \\frac{37}{12} a^{2} - \\frac{11}{2} a + \\frac{13}{6} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{43}{12} a^{9} - \\frac{17}{3} a^{8} - \\frac{145}{6} a^{7} + \\frac{227}{12} a^{6} + \\frac{585}{4} a^{5} - \\frac{464}{3} a^{4} + \\frac{155}{3} a^{3} - \\frac{667}{12} a^{2} + \\frac{105}{2} a - \\frac{73}{6} \\)', '\\( \\frac{101}{24} a^{9} - \\frac{45}{8} a^{8} - \\frac{233}{8} a^{7} + \\frac{347}{24} a^{6} + \\frac{4093}{24} a^{5} - \\frac{3341}{24} a^{4} + \\frac{1285}{24} a^{3} - \\frac{1549}{24} a^{2} + \\frac{85}{2} a - \\frac{137}{12} \\)', '\\( \\frac{1}{6} a^{9} - \\frac{7}{12} a^{8} - \\frac{5}{6} a^{7} + \\frac{13}{4} a^{6} + \\frac{20}{3} a^{5} - \\frac{245}{12} a^{4} + \\frac{15}{2} a^{3} - \\frac{49}{12} a^{2} + \\frac{13}{2} a - \\frac{13}{6} \\)', '\\( \\frac{17}{3} a^{9} - \\frac{16}{3} a^{8} - \\frac{165}{4} a^{7} + \\frac{19}{6} a^{6} + \\frac{691}{3} a^{5} - 97 a^{4} + \\frac{145}{4} a^{3} - \\frac{421}{6} a^{2} + \\frac{203}{6} a - \\frac{1}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/12*a^6 - 1/6*a^5 + 1/3*a^4 + 1/3*a^3 - 1/12*a^2 - 1/2*a - 1/6', '1/12*a^7 - 5/12*a^3 + 1/3*a^2 - 1/6*a - 1/3', '1/12*a^8 - 5/12*a^4 + 1/3*a^3 - 1/6*a^2 - 1/3*a', '1/24*a^9 - 1/24*a^8 - 1/24*a^7 - 1/24*a^6 + 3/8*a^5 + 5/24*a^4 - 5/24*a^3 - 5/24*a^2 + 1/4']}
Number field data - 10.0.5435817984000.1