-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-3, 0, 81, 0, -540, 0, 1386, 0, -1782, 0, 1287, 0, -546, 0, 135, 0, -18, 0, 1], 'conductor': 108, 'degree': 18, 'dirichlet_group': [1, 71, 73, 11, 13, 83, 85, 23, 25, 95, 97, 35, 37, 107, 47, 49, 59, 61], 'disc_abs': 774455350146061749097070592, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[18, 1]]], [7, [[18, 1]]], [11, [[9, 2]]], [13, [[9, 2]]], [17, [[6, 3]]], [19, [[6, 3]]], [23, [[9, 2]]], [29, [[18, 1]]], [31, [[18, 1]]], [37, [[3, 6]]], [41, [[18, 1]]], [43, [[18, 1]]], [47, [[9, 2]]], [53, [[2, 9]]], [59, [[9, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [18, 45], 'galois_label': '18T1', 'galt': 1, 'grd': 31.176914536239792, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '18.18.774455350146061749097070592.1', 'local_algs': ['2.18.18.118', 'm3.18.1.45'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [2, 3], 'rd': 31.1769145362, 'regulator': {'__RealLiteral__': 0, 'data': '43670324.6529', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-3.0.1', '-1.-3.0.1', '-3.0.9.0.-6.0.1', '-1.9.0.-30.0.27.0.-9.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{6} - 6 a^{4} + 9 a^{2} - 1 \\)', '\\( a^{6} - 6 a^{4} + 9 a^{2} - 2 \\)', '\\( a^{8} - 7 a^{6} + 15 a^{4} - 10 a^{2} + 1 \\)', '\\( a^{8} - 8 a^{6} + 20 a^{4} - 16 a^{2} + 2 \\)', '\\( a^{16} - 15 a^{14} + 91 a^{12} - 286 a^{10} + 494 a^{8} - 455 a^{6} + 194 a^{4} - 23 a^{2} - 1 \\)', '\\( a^{14} - 15 a^{12} + 90 a^{10} - 275 a^{8} + 449 a^{6} - 371 a^{4} + 125 a^{2} - 5 \\)', '\\( a^{12} - 13 a^{10} + 65 a^{8} - 156 a^{6} + 182 a^{4} - 91 a^{2} + 13 \\)', '\\( a^{4} - 4 a^{2} + 2 \\)', '\\( a^{15} - 15 a^{13} + 90 a^{11} - 275 a^{9} + 450 a^{7} - 378 a^{5} + 139 a^{3} - 12 a - 1 \\)', '\\( a^{12} - 12 a^{10} + 54 a^{8} - 112 a^{6} + 105 a^{4} + a^{3} - 36 a^{2} - 3 a + 2 \\)', '\\( a^{5} - 5 a^{3} + 5 a - 1 \\)', '\\( a^{13} - 13 a^{11} + 65 a^{9} - 156 a^{7} + 182 a^{5} - 91 a^{3} + 13 a - 1 \\)', '\\( a^{13} - 13 a^{11} + 65 a^{9} - 156 a^{7} + 181 a^{5} - 86 a^{3} + 8 a - 1 \\)', '\\( a^{11} - 11 a^{9} + 43 a^{7} - 70 a^{5} + 41 a^{3} - 4 a + 1 \\)', '\\( a + 1 \\)', '\\( a^{17} - 17 a^{15} + a^{14} + 119 a^{13} - 14 a^{12} - 441 a^{11} + 77 a^{10} + 924 a^{9} - 209 a^{8} - 1078 a^{7} + 286 a^{6} + 638 a^{5} - 176 a^{4} - 154 a^{3} + 34 a^{2} + 11 a - 2 \\)', '\\( a^{7} - 7 a^{5} + 14 a^{3} - 7 a + 1 \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', 'a^15', 'a^16', 'a^17']}