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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 164341563462254592, 'disc_rad': 6, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 5], [1, 2]]], [7, [[12, 1]]], [11, [[2, 6]]], [13, [[12, 1]]], [17, [[2, 6]]], [19, [[3, 4]]], [23, [[2, 5], [1, 2]]], [29, [[2, 5], [1, 2]]], [31, [[4, 3]]], [37, [[12, 1]]], [41, [[2, 6]]], [43, [[1, 12]]], [47, [[2, 5], [1, 2]]], [53, [[2, 5], [1, 2]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [70, 28], 'galois_label': '12T12', 'galt': 12, 'grd': 27.20480503537909, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 71, 'label': '12.2.164341563462254592.71', 'local_algs': ['2.1.12.35a1.81', '3.2.6.14a1.3'], 'minimal_sibling': [54, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 5, 'ramps': [2, 3], 'rd': 27.2048050354, 'regulator': {'__RealLiteral__': 0, 'data': '17436.4884271', 'prec': 44}, 'res': {'gal': ['36,0,144,0,216,0,624,0,1644,0,1560,0,1108,0,2256,0,2040,0,512,0,90,0,12,0,1'], 'sib': ['54,0,0,0,0,0,4,0,0,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-6.0.1', '-2.0.0.1', '-2.0.-4.0.1', '-6.0.12.0.-6.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{5}{27} a^{10} + \\frac{1}{27} a^{8} - \\frac{1}{27} a^{6} + \\frac{218}{27} a^{4} + \\frac{49}{27} a^{2} + \\frac{5}{27} \\)', '\\( \\frac{2}{9} a^{10} + \\frac{89}{9} a^{4} - 1 \\)', '\\( \\frac{11}{27} a^{11} + \\frac{11}{27} a^{10} + \\frac{1}{27} a^{9} - \\frac{5}{27} a^{8} - \\frac{4}{27} a^{7} - \\frac{1}{27} a^{6} + \\frac{485}{27} a^{5} + \\frac{485}{27} a^{4} + \\frac{49}{27} a^{3} - \\frac{218}{27} a^{2} - \\frac{169}{27} a - \\frac{49}{27} \\)', '\\( \\frac{1}{9} a^{9} + \\frac{40}{9} a^{3} - 1 \\)', '\\( \\frac{1}{9} a^{9} + \\frac{40}{9} a^{3} + 1 \\)', '\\( \\frac{2}{9} a^{11} + \\frac{1}{27} a^{10} - \\frac{1}{27} a^{8} + \\frac{1}{9} a^{7} - \\frac{5}{27} a^{6} + \\frac{89}{9} a^{5} + \\frac{49}{27} a^{4} - a^{3} + \\frac{32}{27} a^{2} - \\frac{5}{9} a - \\frac{29}{27} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/9*a^6 + 4/9', '1/9*a^7 + 4/9*a', '1/9*a^8 + 4/9*a^2', '1/9*a^9 + 4/9*a^3', '1/27*a^10 - 1/27*a^8 + 1/27*a^6 - 5/27*a^4 + 5/27*a^2 - 5/27', '1/27*a^11 - 1/27*a^9 + 1/27*a^7 - 5/27*a^5 + 5/27*a^3 - 5/27*a']}
Number field data - 12.2.164341563462254592.71