-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 7, -9, 15, -24, 28, -30, 36, -39, 36, -30, 28, -24, 15, -9, 7, -4, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 11436479389438477403, 'disc_rad': 343183, 'disc_sign': -1, 'frobs': [[2, [[18, 1]]], [3, [[6, 2], [3, 2]]], [5, [[12, 1], [3, 2]]], [7, [[6, 3]]], [11, [[4, 2], [2, 4], [1, 2]]], [13, [[3, 6]]], [17, [[12, 1], [2, 2], [1, 2]]], [19, [[4, 3], [3, 2]]], [23, [0]], [29, [[6, 2], [3, 2]]], [31, [[3, 6]]], [37, [[4, 3], [2, 2], [1, 2]]], [41, [[6, 3]]], [43, [0]], [47, [[6, 3]]], [53, [[12, 1], [6, 1]]], [59, [[2, 8], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [5184, 5184, 5184], 'galois_label': '18T556', 'galt': 556, 'grd': 585.8182311946258, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '18.0.11436479389438477403.1', 'local_algs': ['23.2.0.1', '23.2.0.1', '23.2.0.1', '23.6.3.2', '23.6.3.2', '43.2.0.1', '43.4.2.1', '43.4.0.1', '43.4.0.1', '43.4.0.1', 'm347.1.1.0', 'm347.1.1.0', 'm347.1.2.0', 'm347.1.2.0', 'm347.2.1.1', 'm347.2.1.1', 'm347.2.1.1', 'm347.1.3.0', 'm347.1.3.0'], 'minimal_sibling': [1, -5, 13, -23, 30, -32, 31, -32, 36, -38, 36, -29, 21, -15, 12, -9, 6, -3, 1], 'monogenic': 1, 'num_ram': 3, 'r2': 9, 'ramps': [23, 43, 347], 'rd': 11.4496976774, 'regulator': {'__RealLiteral__': 0, 'data': '88.267766218', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['1.0.-1.1', '5.8.1.-2.-1.-1.1', '1.0.-4.2.4.-7.2.3.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{17} - 2 a^{16} + 2 a^{14} + a^{13} - 7 a^{11} + 8 a^{10} - 5 a^{9} + 7 a^{8} - 8 a^{7} + 9 a^{6} + 2 a^{4} - 3 a^{3} - a^{2} + 2 a - 1 \\)', '\\( a \\)', '\\( a^{15} - 2 a^{14} + 2 a^{12} + a^{11} - 7 a^{9} + 8 a^{8} - 6 a^{7} + 10 a^{6} - 12 a^{5} + 13 a^{4} - 5 a^{3} + 7 a^{2} - 7 a + 3 \\)', '\\( a^{17} - 2 a^{16} + 3 a^{14} - 3 a^{13} + 7 a^{12} - 15 a^{11} + 19 a^{10} - 22 a^{9} + 27 a^{8} - 27 a^{7} + 29 a^{6} - 21 a^{5} + 20 a^{4} - 14 a^{3} + 9 a^{2} - 5 a + 2 \\)', '\\( 2 a^{17} - 9 a^{16} + 18 a^{15} - 24 a^{14} + 33 a^{13} - 48 a^{12} + 57 a^{11} - 57 a^{10} + 57 a^{9} - 56 a^{8} + 49 a^{7} - 33 a^{6} + 23 a^{5} - 19 a^{4} + 9 a^{3} - 2 a^{2} - a \\)', '\\( 2 a^{17} - 9 a^{16} + 18 a^{15} - 23 a^{14} + 29 a^{13} - 41 a^{12} + 49 a^{11} - 46 a^{10} + 40 a^{9} - 36 a^{8} + 30 a^{7} - 14 a^{6} + 4 a^{5} - 2 a^{4} - 2 a^{3} + 6 a^{2} - 7 a + 3 \\)', '\\( a^{17} - 2 a^{16} + 3 a^{14} - 3 a^{13} + 7 a^{12} - 15 a^{11} + 19 a^{10} - 22 a^{9} + 27 a^{8} - 27 a^{7} + 29 a^{6} - 21 a^{5} + 20 a^{4} - 14 a^{3} + 9 a^{2} - 5 a + 3 \\)', '\\( 3 a^{17} - 11 a^{16} + 15 a^{15} - 12 a^{14} + 21 a^{13} - 37 a^{12} + 32 a^{11} - 24 a^{10} + 35 a^{9} - 37 a^{8} + 25 a^{7} - 14 a^{6} + 20 a^{5} - 22 a^{4} + 4 a^{3} - 2 a^{2} + 7 a - 4 \\)'], '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', 'a^17']}
Number field data - 18.0.11436479389438477403.1