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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 14, -37, 85, -174, 321, -532, 787, -1020, 1139, -1082, 865, -574, 310, -132, 42, -9, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 6646436567333419399, 'disc_rad': 123935123783, 'disc_sign': -1, 'frobs': [[2, [[9, 2]]], [3, [[8, 1], [5, 2]]], [5, [[6, 2], [3, 2]]], [7, [[12, 1], [4, 1], [2, 1]]], [11, [[5, 2], [4, 1], [2, 2]]], [13, [[6, 1], [4, 3]]], [17, [0]], [19, [[4, 2], [3, 2], [2, 2]]], [23, [[8, 1], [4, 2], [2, 1]]], [29, [[10, 1], [6, 1], [1, 2]]], [31, [[5, 2], [4, 1], [2, 1], [1, 2]]], [37, [[14, 1], [2, 2]]], [41, [[8, 1], [4, 2], [1, 2]]], [43, [0]], [47, [[8, 1], [4, 2], [1, 2]]], [53, [[4, 4], [2, 1]]], [59, [[8, 2], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [92897280, 92897280, 92897280, 92897280], 'galois_label': '18T968', 'galt': 968, 'grd': 352044.20714308025, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '18.0.6646436567333419399.1', 'local_algs': ['17.2.1.1', '17.2.1.1', '17.7.0.1', '17.7.0.1', '43.2.0.1', '43.2.0.1', '43.4.0.1', '43.4.2.1', '43.6.0.1', 'm2311.1.1.0', 'm2311.1.1.0', 'm2311.2.1.1', 'm2311.1.3.0', 'm2311.1.3.0', 'm2311.1.8.0', 'm73363.1.2.0', 'm73363.1.2.0', 'm73363.2.1.1', 'm73363.2.1.1', 'm73363.1.3.0', 'm73363.1.3.0', 'm73363.1.4.0'], 'monogenic': 0, 'num_ram': 4, 'r2': 9, 'ramps': [17, 43, 2311, 73363], 'rd': 11.1096245283, 'regulator': {'__RealLiteral__': 0, 'data': '61.0464139366', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.-3.4.-1.-2.3.-3.4.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - a + 1 \\)', '\\( 2 a^{16} - 16 a^{15} + 66 a^{14} - 182 a^{13} + 371 a^{12} - 588 a^{11} + 745 a^{10} - 766 a^{9} + 647 a^{8} - 456 a^{7} + 279 a^{6} - 158 a^{5} + 83 a^{4} - 36 a^{3} + 13 a^{2} - 4 a \\)', '\\( a^{14} - 7 a^{13} + 26 a^{12} - 65 a^{11} + 121 a^{10} - 176 a^{9} + 206 a^{8} - 197 a^{7} + 157 a^{6} - 106 a^{5} + 64 a^{4} - 35 a^{3} + 17 a^{2} - 6 a + 3 \\)', '\\( a \\)', '\\( a - 1 \\)', '\\( \\frac{2}{7} a^{17} - \\frac{24}{7} a^{16} + \\frac{128}{7} a^{15} - \\frac{431}{7} a^{14} + \\frac{1038}{7} a^{13} - \\frac{1903}{7} a^{12} + \\frac{2742}{7} a^{11} - \\frac{3152}{7} a^{10} + \\frac{2893}{7} a^{9} - \\frac{2102}{7} a^{8} + \\frac{1188}{7} a^{7} - \\frac{526}{7} a^{6} + \\frac{204}{7} a^{5} - \\frac{85}{7} a^{4} + \\frac{33}{7} a^{3} - \\frac{19}{7} a^{2} + \\frac{1}{7} a + \\frac{3}{7} \\)', '\\( \\frac{19}{7} a^{17} - \\frac{165}{7} a^{16} + \\frac{740}{7} a^{15} - \\frac{2229}{7} a^{14} + \\frac{4996}{7} a^{13} - \\frac{8779}{7} a^{12} + \\frac{12462}{7} a^{11} - \\frac{14544}{7} a^{10} + \\frac{14124}{7} a^{9} - \\frac{11527}{7} a^{8} + \\frac{8031}{7} a^{7} - \\frac{4906}{7} a^{6} + \\frac{2701}{7} a^{5} - \\frac{1336}{7} a^{4} + \\frac{583}{7} a^{3} - \\frac{212}{7} a^{2} + \\frac{62}{7} a - \\frac{10}{7} \\)', '\\( \\frac{20}{7} a^{17} - \\frac{163}{7} a^{16} + \\frac{692}{7} a^{15} - \\frac{1986}{7} a^{14} + \\frac{4269}{7} a^{13} - \\frac{7249}{7} a^{12} + \\frac{10032}{7} a^{11} - \\frac{11535}{7} a^{10} + \\frac{11178}{7} a^{9} - \\frac{9232}{7} a^{8} + \\frac{6595}{7} a^{7} - \\frac{4147}{7} a^{6} + \\frac{2313}{7} a^{5} - \\frac{1144}{7} a^{4} + \\frac{526}{7} a^{3} - \\frac{218}{7} a^{2} + \\frac{66}{7} a - \\frac{19}{7} \\)'], 'used_grh': False, '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', '1/7*a^17 + 2/7*a^16 + 1/7*a^15 - 2/7*a^14 + 1/7*a^13 - 3/7*a^12 - 1/7*a^11 - 1/7*a^10 + 1/7*a^9 - 1/7*a^8 - 1/7*a^7 + 3/7*a^6 - 3/7*a^5 + 3/7*a^4 - 1/7*a^3 + 1/7*a^2 - 3/7*a - 2/7']}
Number field data - 18.0.6646436567333419399.1