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nf_fields • Show schema
{'class_group': [3, 6], 'class_number': 18, 'cm': False, 'coeffs': [-8, 0, 0, -148, 0, 0, -490, 0, 0, 3983, 0, 0, 245, 0, 0, -37, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 178976732236484163896033906688, 'disc_rad': 66, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 9]]], [7, [[6, 3]]], [11, [0]], [13, [[6, 3]]], [17, [[2, 8], [1, 2]]], [19, [[6, 3]]], [23, [[2, 9]]], [29, [[2, 8], [1, 2]]], [31, [[3, 6]]], [37, [[3, 6]]], [41, [[2, 8], [1, 2]]], [43, [[2, 9]]], [47, [[2, 9]]], [53, [[2, 9]]], [59, [[2, 9]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 42, 30], 'galois_label': '18T12', 'galt': 12, 'grd': 42.18473888411525, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '18.2.178976732236484163896033906688.2', 'local_algs': ['2.1.3.2a1.1', '2.1.3.2a1.1', '2.2.3.4a1.2', '2.2.3.4a1.2', '3.1.6.7a1.1', '3.1.6.7a1.1', '3.1.6.7a1.1', '11.1.6.5a1.2', '11.2.6.10a1.2'], 'minimal_sibling': [729, 0, 0, -1512, 0, 0, 1215, 0, 0, -296, 0, 0, 47, 0, 0, -4, 0, 0, 1], 'monogenic': -1, 'narrow_class_group': [6, 6], 'narrow_class_number': 36, 'num_ram': 3, 'r2': 8, 'ramps': [2, 3, 11], 'rd': 42.1847388841, 'regulator': {'__RealLiteral__': 0, 'data': '28469096.209551767', 'prec': 60}, 'res': {'sib': ['729,0,0,-1512,0,0,1215,0,0,-296,0,0,47,0,0,-4,0,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-8.-1.1', '-11.0.0.1', '-22.0.0.1', '13.-7.-1.1', '-2.0.0.1', '-297.0.0.0.0.0.1', '-6.6.-8.3.1.-3.1', '-116.204.-30.-41.-21.-3.1', '-24.-36.-6.-9.15.-3.1', '-64.48.-60.51.27.-36.3.6.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2717}{29160} a^{17} - \\frac{100903}{29160} a^{14} + \\frac{679523}{29160} a^{11} + \\frac{10729433}{29160} a^{8} - \\frac{351923}{3645} a^{5} - \\frac{36751}{7290} a^{2} + 1 \\)', '\\( \\frac{1249}{5832} a^{17} + \\frac{91}{1215} a^{16} - \\frac{97}{4860} a^{15} - \\frac{231721}{29160} a^{14} - \\frac{1123}{405} a^{13} + \\frac{1201}{1620} a^{12} + \\frac{1554341}{29160} a^{11} + \\frac{22369}{1215} a^{10} - \\frac{24283}{4860} a^{9} + \\frac{24711479}{29160} a^{8} + \\frac{120653}{405} a^{7} - \\frac{127631}{1620} a^{6} - \\frac{2830691}{14580} a^{5} - \\frac{52502}{1215} a^{4} + \\frac{25661}{1215} a^{3} - \\frac{54098}{3645} a^{2} - \\frac{4114}{405} a + \\frac{337}{405} \\)', '\\( \\frac{9}{40} a^{17} - \\frac{9023}{1080} a^{14} + \\frac{2249}{40} a^{11} + \\frac{959881}{1080} a^{8} - \\frac{4547}{20} a^{5} - \\frac{110}{27} a^{2} \\)', '\\( \\frac{203}{2430} a^{17} - \\frac{3013}{972} a^{14} + \\frac{20213}{972} a^{11} + \\frac{1606423}{4860} a^{8} - \\frac{369329}{4860} a^{5} - \\frac{11473}{2430} a^{2} \\)', '\\( \\frac{937}{43740} a^{17} - \\frac{8}{2187} a^{16} - \\frac{25}{8748} a^{15} - \\frac{17341}{21870} a^{14} + \\frac{1469}{10935} a^{13} + \\frac{935}{8748} a^{12} + \\frac{115031}{21870} a^{11} - \\frac{9394}{10935} a^{10} - \\frac{6499}{8748} a^{9} + \\frac{1864187}{21870} a^{8} - \\frac{161956}{10935} a^{7} - \\frac{97105}{8748} a^{6} - \\frac{508577}{43740} a^{5} - \\frac{25432}{10935} a^{4} + \\frac{12935}{2187} a^{3} - \\frac{7409}{4374} a^{2} - \\frac{7084}{10935} a + \\frac{935}{2187} \\)', '\\( \\frac{7739}{17496} a^{17} - \\frac{7631}{43740} a^{16} + \\frac{1783}{21870} a^{15} - \\frac{286879}{17496} a^{14} + \\frac{282829}{43740} a^{13} - \\frac{33037}{10935} a^{12} + \\frac{1915907}{17496} a^{11} - \\frac{1887449}{43740} a^{10} + \\frac{220322}{10935} a^{9} + \\frac{30692369}{17496} a^{8} - \\frac{30275219}{43740} a^{7} + \\frac{707641}{2187} a^{6} - \\frac{2961029}{8748} a^{5} + \\frac{1412623}{10935} a^{4} - \\frac{256105}{4374} a^{3} - \\frac{100712}{2187} a^{2} + \\frac{199723}{10935} a - \\frac{94807}{10935} \\)', '\\( \\frac{3683}{17496} a^{17} - \\frac{509}{4374} a^{16} + \\frac{2213}{43740} a^{15} - \\frac{683411}{87480} a^{14} + \\frac{47218}{10935} a^{13} - \\frac{82093}{43740} a^{12} + \\frac{4587871}{87480} a^{11} - \\frac{316778}{10935} a^{10} + \\frac{550013}{43740} a^{9} + \\frac{72838789}{87480} a^{8} - \\frac{5035142}{10935} a^{7} + \\frac{8763311}{43740} a^{6} - \\frac{8593801}{43740} a^{5} + \\frac{2328047}{21870} a^{4} - \\frac{971219}{21870} a^{3} - \\frac{147508}{10935} a^{2} + \\frac{100177}{10935} a - \\frac{8270}{2187} \\)', '\\( \\frac{1831}{8748} a^{17} - \\frac{476}{10935} a^{16} + \\frac{38}{10935} a^{15} - \\frac{67925}{8748} a^{14} + \\frac{17563}{10935} a^{13} - \\frac{1441}{10935} a^{12} + \\frac{455173}{8748} a^{11} - \\frac{114818}{10935} a^{10} + \\frac{10601}{10935} a^{9} + \\frac{7249555}{8748} a^{8} - \\frac{381505}{2187} a^{7} + \\frac{143033}{10935} a^{6} - \\frac{402035}{2187} a^{5} + \\frac{7136}{2187} a^{4} - \\frac{160714}{10935} a^{3} - \\frac{53750}{2187} a^{2} + \\frac{61018}{10935} a - \\frac{18967}{10935} \\)', '\\( \\frac{1825}{17496} a^{17} - \\frac{964}{10935} a^{16} - \\frac{16}{2187} a^{15} - \\frac{338737}{87480} a^{14} + \\frac{7147}{2187} a^{13} + \\frac{2938}{10935} a^{12} + \\frac{2276717}{87480} a^{11} - \\frac{47735}{2187} a^{10} - \\frac{18788}{10935} a^{9} + \\frac{36074423}{87480} a^{8} - \\frac{3822577}{10935} a^{7} - \\frac{323912}{10935} a^{6} - \\frac{4457567}{43740} a^{5} + \\frac{734216}{10935} a^{4} - \\frac{50864}{10935} a^{3} - \\frac{127856}{10935} a^{2} + \\frac{47684}{10935} a + \\frac{7702}{10935} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/9*a^6 + 2/9', '1/9*a^7 + 2/9*a', '1/9*a^8 + 2/9*a^2', '1/9*a^9 + 2/9*a^3', '1/9*a^10 + 2/9*a^4', '1/27*a^11 + 1/27*a^10 + 1/27*a^9 + 1/27*a^8 + 1/27*a^7 + 1/27*a^6 + 2/27*a^5 + 2/27*a^4 + 2/27*a^3 + 2/27*a^2 + 2/27*a + 2/27', '1/810*a^12 + 1/90*a^9 + 31/810*a^6 - 7/90*a^3 - 133/405', '1/810*a^13 + 1/90*a^10 + 31/810*a^7 - 7/90*a^4 - 133/405*a', '1/4860*a^14 + 1/2430*a^13 - 1/2430*a^12 - 1/60*a^11 - 1/30*a^10 + 1/30*a^9 - 239/4860*a^8 + 31/2430*a^7 - 31/2430*a^6 + 9/20*a^5 - 1/10*a^4 + 1/10*a^3 + 407/2430*a^2 - 538/1215*a + 538/1215', '1/14580*a^15 - 1/2916*a^12 + 17/2916*a^9 + 223/14580*a^6 - 2347/7290*a^3 - 734/3645', '1/29160*a^16 + 13/29160*a^13 + 247/29160*a^10 + 781/29160*a^7 + 1094/3645*a^4 - 1931/7290*a', '1/87480*a^17 - 1/87480*a^16 - 1/43740*a^15 - 1/17496*a^14 - 49/87480*a^13 + 1/8748*a^12 - 307/17496*a^11 - 3811/87480*a^10 + 307/8748*a^9 - 1397/87480*a^8 + 4583/87480*a^7 + 1397/43740*a^6 - 3967/43740*a^5 - 10531/21870*a^4 + 3967/21870*a^3 - 4417/10935*a^2 - 1403/4374*a - 2101/10935']}
Number field data - 18.2.178976732236484163896033906688.2