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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 2518170116818978404827136, 'disc_rad': 6, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 8], [1, 2]]], [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, 74], 'galois_label': '18T12', 'galt': 12, 'grd': 24.105856857882777, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '18.0.2518170116818978404827136.2', 'local_algs': ['2.1.6.8a1.1', '2.2.6.16a1.5', '3.2.9.36b6.16'], 'maximal_cm_subfield': [1, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 9, 'ramps': [2, 3], 'rd': 22.6785788981, 'regulator': {'__RealLiteral__': 0, 'data': '428253.6181907014', 'prec': 57}, 'res': {'sib': ['1,0,0,-42,0,0,51,0,0,-70,0,0,21,0,0,-12,0,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '-12.0.0.1', '-2.0.0.1', '-6.0.0.1', '-3.0.0.1', '18.0.0.-6.0.0.1', '36.0.0.0.0.0.1', '2.0.0.-2.0.0.1', '9.0.0.0.0.0.1', '1.0.0.3.0.0.-3.0.0.1'], 'torsion_gen': '\\( \\frac{3}{10} a^{15} + \\frac{4}{5} a^{9} + \\frac{39}{10} a^{3} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{3}{10} a^{16} + \\frac{4}{5} a^{10} + \\frac{39}{10} a^{4} \\)', '\\( \\frac{1}{5} a^{16} + \\frac{1}{10} a^{13} + \\frac{7}{10} a^{10} + \\frac{1}{10} a^{7} + \\frac{31}{10} a^{4} + \\frac{9}{5} a \\)', '\\( \\frac{1}{5} a^{17} - \\frac{3}{10} a^{16} + \\frac{1}{5} a^{14} - \\frac{1}{10} a^{12} + \\frac{7}{10} a^{11} - \\frac{4}{5} a^{10} + \\frac{7}{10} a^{8} - \\frac{3}{5} a^{6} + \\frac{31}{10} a^{5} - \\frac{39}{10} a^{4} + \\frac{31}{10} a^{2} + a - \\frac{13}{10} \\)', '\\( \\frac{3}{10} a^{17} + \\frac{1}{5} a^{16} - \\frac{1}{5} a^{15} - \\frac{1}{10} a^{12} + \\frac{4}{5} a^{11} + \\frac{7}{10} a^{10} - \\frac{7}{10} a^{9} + \\frac{1}{2} a^{7} - \\frac{1}{10} a^{6} + \\frac{39}{10} a^{5} + \\frac{31}{10} a^{4} - \\frac{31}{10} a^{3} - a^{2} + \\frac{1}{2} a + \\frac{1}{5} \\)', '\\( \\frac{4}{5} a^{17} - \\frac{3}{10} a^{16} - \\frac{1}{10} a^{15} + \\frac{1}{10} a^{14} - \\frac{1}{10} a^{12} + \\frac{23}{10} a^{11} - \\frac{4}{5} a^{10} - \\frac{1}{10} a^{9} + \\frac{1}{10} a^{8} - \\frac{1}{10} a^{6} + \\frac{119}{10} a^{5} - \\frac{39}{10} a^{4} - \\frac{9}{5} a^{3} + \\frac{4}{5} a^{2} + a - \\frac{4}{5} \\)', '\\( \\frac{3}{10} a^{17} + \\frac{3}{10} a^{16} - \\frac{1}{10} a^{15} + \\frac{1}{10} a^{12} + \\frac{4}{5} a^{11} + \\frac{4}{5} a^{10} - \\frac{1}{10} a^{9} + \\frac{1}{10} a^{6} + \\frac{39}{10} a^{5} + \\frac{49}{10} a^{4} - \\frac{4}{5} a^{3} - a^{2} + \\frac{4}{5} \\)', '\\( \\frac{1}{5} a^{17} + \\frac{3}{5} a^{16} + \\frac{7}{10} a^{15} + \\frac{1}{2} a^{14} + \\frac{3}{10} a^{13} + \\frac{7}{10} a^{11} + \\frac{8}{5} a^{10} + \\frac{11}{5} a^{9} + \\frac{3}{2} a^{8} + \\frac{4}{5} a^{7} + \\frac{31}{10} a^{5} + \\frac{44}{5} a^{4} + \\frac{101}{10} a^{3} + 8 a^{2} + \\frac{39}{10} a + 1 \\)', '\\( \\frac{13}{10} a^{17} + \\frac{3}{5} a^{15} + \\frac{19}{5} a^{11} + \\frac{8}{5} a^{9} + \\frac{199}{10} a^{5} + \\frac{39}{5} a^{3} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^6 - 1/2*a^3 - 1/2', '1/2*a^10 - 1/2*a^7 - 1/2*a^4 - 1/2*a', '1/2*a^11 - 1/2*a^8 - 1/2*a^5 - 1/2*a^2', '1/10*a^12 - 2/5*a^6 + 3/10', '1/10*a^13 - 2/5*a^7 + 3/10*a', '1/10*a^14 - 2/5*a^8 + 3/10*a^2', '1/10*a^15 + 1/10*a^9 - 1/2*a^6 - 1/5*a^3 - 1/2', '1/10*a^16 + 1/10*a^10 - 1/2*a^7 - 1/5*a^4 - 1/2*a', '1/10*a^17 + 1/10*a^11 - 1/2*a^8 - 1/5*a^5 - 1/2*a^2']}
Number field data - 18.0.2518170116818978404827136.2