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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -1, 1, 3, 1, -1, 0, 0, -1, -1, 0, 1], 'conductor': 0, 'degree': 11, 'dirichlet_group': [], 'disc_abs': 6660072199, 'disc_rad': 605461109, 'disc_sign': -1, 'frobs': [[2, [[11, 1]]], [3, [[7, 1], [4, 1]]], [5, [[11, 1]]], [7, [[9, 1], [2, 1]]], [11, [0]], [13, [[5, 1], [3, 2]]], [17, [[11, 1]]], [19, [[6, 1], [4, 1], [1, 1]]], [23, [[11, 1]]], [29, [[7, 1], [3, 1], [1, 1]]], [31, [[11, 1]]], [37, [[6, 1], [4, 1], [1, 1]]], [41, [[4, 1], [3, 1], [1, 4]]], [43, [[4, 1], [3, 1], [2, 1], [1, 2]]], [47, [[8, 1], [2, 1], [1, 1]]], [53, [[4, 2], [2, 1], [1, 1]]], [59, [[11, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [19958400, 19958400, 19958400], 'galois_label': '11T8', 'galt': 8, 'grd': 24606.119340521782, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '11.1.6660072199.1', 'local_algs': ['11.4.2.2', '11.7.0.1', '181.2.1.1', '181.2.0.1', '181.7.0.1', 'm304099.1.1.0', 'm304099.2.1.1', 'm304099.1.3.0', 'm304099.1.5.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [11, 181, 304099], 'rd': 7.81706169806, 'regulator': {'__RealLiteral__': 0, 'data': '1.5178724806066581', 'prec': 60}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{10} - a^{8} - a^{7} - a^{4} + a^{3} + 3 a^{2} + a - 1 \\)', '\\( \\frac{2}{3} a^{10} - \\frac{1}{3} a^{9} + \\frac{1}{3} a^{8} - \\frac{2}{3} a^{7} - \\frac{1}{3} a^{6} - \\frac{1}{3} a^{5} - \\frac{2}{3} a^{4} + \\frac{2}{3} a^{3} + a^{2} + \\frac{1}{3} a + \\frac{1}{3} \\)', '\\( a^{10} - \\frac{1}{3} a^{9} - \\frac{2}{3} a^{8} - \\frac{1}{3} a^{7} - \\frac{1}{3} a^{5} - \\frac{2}{3} a^{4} + \\frac{2}{3} a^{3} + \\frac{7}{3} a^{2} + \\frac{1}{3} a - \\frac{1}{3} \\)', '\\( \\frac{2}{3} a^{10} + \\frac{2}{3} a^{9} - \\frac{2}{3} a^{8} - \\frac{2}{3} a^{7} - \\frac{1}{3} a^{6} - \\frac{1}{3} a^{5} - \\frac{2}{3} a^{4} - \\frac{1}{3} a^{3} + 2 a^{2} + \\frac{4}{3} a + \\frac{1}{3} \\)', '\\( \\frac{1}{3} a^{10} - a^{9} + \\frac{1}{3} a^{7} + \\frac{1}{3} a^{6} + 2 a^{3} + \\frac{1}{3} a^{2} - 2 a - \\frac{2}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/3*a^9 - 1/3*a^8 + 1/3*a^7 + 1/3*a^5 - 1/3*a^4 + 1/3*a^3 - 1/3*a^2 - 1/3*a + 1/3', '1/3*a^10 + 1/3*a^7 + 1/3*a^6 + 1/3*a^2 + 1/3']}
Number field data - 11.1.6660072199.1