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nf_fields • Show schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [1, 0, 0, 0, 0, 0, 543, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 14281868906496000000000000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[6, 3]]], [11, [[2, 9]]], [13, [[3, 6]]], [17, [[2, 8], [1, 2]]], [19, [[6, 3]]], [23, [[2, 9]]], [29, [[2, 8], [1, 2]]], [31, [[6, 3]]], [37, [[3, 6]]], [41, [[2, 8], [1, 2]]], [43, [[6, 3]]], [47, [[2, 9]]], [53, [[2, 8], [1, 2]]], [59, [[2, 9]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48, 42, 24], 'galois_label': '18T12', 'galt': 12, 'grd': 26.545737424498032, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '18.0.14281868906496000000000000.2', 'local_algs': ['2.1.6.8a1.1', '2.2.6.16a1.5', '3.2.3.6a2.1', '3.2.6.14a1.3', '5.1.3.2a1.1', '5.1.3.2a1.1', '5.2.3.4a1.2', '5.2.3.4a1.2'], 'maximal_cm_subfield': [1, 0, 1], 'monogenic': 0, 'narrow_class_group': [3], 'narrow_class_number': 3, 'num_ram': 3, 'r2': 9, 'ramps': [2, 3, 5], 'rd': 24.9739971551, 'regulator': {'__RealLiteral__': 0, 'data': '314523.34710628784', 'prec': 60}, 'res': {'sib': ['-27,0,0,0,0,0,67,0,0,0,0,0,-49,0,0,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '-5.0.0.1', '-2.0.0.1', '-20.0.0.1', '-3.-3.-1.1', '2.0.0.-2.0.0.1', '25.0.0.0.0.0.1', '50.0.0.-10.0.0.1', '2.-8.16.-6.2.-2.1', '1.0.0.23.0.0.-7.0.0.1'], 'torsion_gen': '\\( \\frac{7}{162} a^{15} + \\frac{10}{81} a^{9} + \\frac{3775}{162} a^{3} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{7}{162} a^{16} + \\frac{10}{81} a^{10} + \\frac{3775}{162} a^{4} \\)', '\\( \\frac{5}{18} a^{17} - \\frac{1}{81} a^{14} + \\frac{5}{6} a^{11} - \\frac{7}{162} a^{8} + \\frac{1358}{9} a^{5} - \\frac{1049}{162} a^{2} + 1 \\)', '\\( \\frac{5}{18} a^{17} + \\frac{1}{81} a^{14} + \\frac{5}{6} a^{11} + \\frac{7}{162} a^{8} + \\frac{1358}{9} a^{5} + \\frac{1049}{162} a^{2} - 1 \\)', '\\( \\frac{29}{486} a^{16} - \\frac{4}{243} a^{14} - \\frac{1}{486} a^{12} + \\frac{44}{243} a^{10} - \\frac{14}{243} a^{8} + \\frac{5}{243} a^{6} + \\frac{15683}{486} a^{4} - \\frac{2179}{243} a^{2} - \\frac{673}{486} \\)', '\\( \\frac{187}{486} a^{17} + \\frac{26}{243} a^{16} + \\frac{23}{486} a^{15} + \\frac{4}{243} a^{14} - \\frac{1}{243} a^{13} - \\frac{1}{243} a^{12} + \\frac{280}{243} a^{11} + \\frac{155}{486} a^{10} + \\frac{67}{486} a^{9} + \\frac{14}{243} a^{8} - \\frac{7}{486} a^{7} - \\frac{7}{486} a^{6} + \\frac{101551}{486} a^{5} + \\frac{28219}{486} a^{4} + \\frac{6268}{243} a^{3} + \\frac{2179}{243} a^{2} - \\frac{1211}{486} a - \\frac{725}{486} \\)', '\\( \\frac{1}{6} a^{17} + \\frac{1}{162} a^{14} + \\frac{1}{2} a^{11} - \\frac{1}{162} a^{8} + \\frac{271}{3} a^{5} + \\frac{233}{81} a^{2} \\)', '\\( \\frac{83}{486} a^{17} - \\frac{29}{486} a^{15} - \\frac{2}{243} a^{13} + \\frac{125}{243} a^{11} - \\frac{44}{243} a^{9} - \\frac{7}{243} a^{7} + \\frac{45113}{486} a^{5} - \\frac{15683}{486} a^{3} - \\frac{1211}{243} a \\)', '\\( \\frac{1}{6} a^{17} + \\frac{1}{9} a^{16} + \\frac{7}{162} a^{15} + \\frac{1}{54} a^{14} + \\frac{1}{162} a^{13} + \\frac{1}{2} a^{11} + \\frac{1}{3} a^{10} + \\frac{10}{81} a^{9} + \\frac{5}{54} a^{8} - \\frac{5}{81} a^{7} + \\frac{1}{9} a^{6} + \\frac{271}{3} a^{5} + \\frac{545}{9} a^{4} + \\frac{3775}{162} a^{3} + \\frac{272}{27} a^{2} + \\frac{511}{162} a + \\frac{4}{9} \\)'], 'used_grh': True, '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', '1/18*a^9 - 1/18*a^6 - 5/18*a^3 + 5/18', '1/18*a^10 - 1/18*a^7 - 5/18*a^4 + 5/18*a', '1/18*a^11 - 1/18*a^8 - 5/18*a^5 + 5/18*a^2', '1/162*a^12 + 4/81*a^6 - 65/162', '1/162*a^13 + 4/81*a^7 - 65/162*a', '1/162*a^14 + 4/81*a^8 - 65/162*a^2', '1/162*a^15 - 1/162*a^9 - 1/18*a^6 - 10/81*a^3 + 5/18', '1/486*a^16 - 1/486*a^14 + 1/486*a^12 - 5/243*a^10 + 5/243*a^8 - 5/243*a^6 + 187/486*a^4 - 187/486*a^2 + 187/486', '1/486*a^17 - 1/486*a^15 + 1/486*a^13 - 5/243*a^11 + 5/243*a^9 - 5/243*a^7 + 187/486*a^5 - 187/486*a^3 + 187/486*a']}
Number field data - 18.0.14281868906496000000000000.2