-
nf_fields • Show schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [1, 1, 9, 36, 86, 166, 506, -158, -181, 299, -3, -74, 40, -4, 0, 8, -3, -1, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 18283008447003871936512, 'disc_rad': 42, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 3]]], [7, [0]], [11, [[6, 3]]], [13, [[6, 2], [3, 2]]], [17, [[2, 9]]], [19, [[6, 2], [3, 2]]], [23, [[2, 9]]], [29, [[6, 3]]], [31, [[3, 6]]], [37, [[6, 2], [3, 2]]], [41, [[2, 9]]], [43, [[6, 2], [3, 2]]], [47, [[2, 9]]], [53, [[6, 3]]], [59, [[6, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [66, 18, 24], 'galois_label': '18T11', 'galt': 11, 'grd': 22.58643281430495, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '18.0.18283008447003871936512.1', 'local_algs': ['2.6.4.1', '2.12.22.60', '3.2.1.2', '3.2.1.2', '3.2.1.2', '3.4.2.1', '3.4.2.1', '3.4.2.1', '7.9.6.1', '7.9.6.1'], 'minimal_sibling': [1, 2, -3, 0, 3, -2, 1], 'monogenic': -1, 'num_ram': 3, 'r2': 9, 'ramps': [2, 3, 7], 'rd': 17.2496554813, 'regulator': {'__RealLiteral__': 0, 'data': '19737.264553893918', 'prec': 60}, 'res': {'sib': ['1,2,-3,0,3,-2,1', '-1,-1,8,22,0,10,-6,4,-1,1', '-8,0,-32,0,80,0,428,0,-408,0,60,0,50,0,-16,0,-2,0,1', '1,2,7,-6,6,-14,15,-10,12,-6,1,-2,1', '6,12,34,-8,94,-40,55,112,-210,248,-153,-16,180,-212,175,-88,34,-8,1']}, 'subfield_mults': [1, 1, 3, 1, 1, 3], 'subfields': ['1.-1.1', '-6.-2.-1.1', '1.5.-1.1', '36.12.-2.14.3.-1.1', '27.9.-8.-3.4.-3.1', '-1.-1.8.22.0.10.-6.4.-1.1'], 'torsion_gen': '\\( -\\frac{3624966722}{26248345407} a^{17} + \\frac{699944263}{2916482823} a^{16} + \\frac{2844671768}{8749448469} a^{15} - \\frac{156287396}{109825713} a^{14} + \\frac{84953176}{109825713} a^{13} + \\frac{17157904432}{26248345407} a^{12} - \\frac{155269516996}{26248345407} a^{11} + \\frac{5409210236}{380410803} a^{10} - \\frac{19355383378}{2916482823} a^{9} - \\frac{1115445049474}{26248345407} a^{8} + \\frac{1450174831468}{26248345407} a^{7} + \\frac{192424131008}{26248345407} a^{6} - \\frac{2307495793820}{26248345407} a^{5} + \\frac{664545306056}{26248345407} a^{4} + \\frac{13389354656}{1141232409} a^{3} + \\frac{185544828760}{26248345407} a^{2} + \\frac{32238400738}{26248345407} a + \\frac{29430407450}{26248345407} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{31111425883}{297481247946} a^{17} - \\frac{371443856}{2916482823} a^{16} - \\frac{26657367895}{99160415982} a^{15} + \\frac{541867331}{622345707} a^{14} - \\frac{290409677}{1244691414} a^{13} - \\frac{31305839968}{148740623973} a^{12} + \\frac{620731584688}{148740623973} a^{11} - \\frac{18778102490}{2155661217} a^{10} + \\frac{113015924900}{49580207991} a^{9} + \\frac{4349524158085}{148740623973} a^{8} - \\frac{3689362135810}{148740623973} a^{7} - \\frac{901636168571}{148740623973} a^{6} + \\frac{14642039807275}{297481247946} a^{5} + \\frac{745828285495}{148740623973} a^{4} + \\frac{225480857939}{12933967302} a^{3} + \\frac{39190186937}{148740623973} a^{2} + \\frac{188541351343}{297481247946} a - \\frac{29712965969}{148740623973} \\)', '\\( \\frac{6918849455}{26248345407} a^{17} - \\frac{85654181659}{297481247946} a^{16} - \\frac{24447183775}{33053471994} a^{15} + \\frac{4007228482}{1867037121} a^{14} - \\frac{487295402}{1867037121} a^{13} - \\frac{369397615643}{446221871919} a^{12} + \\frac{9438017309563}{892443743838} a^{11} - \\frac{4920825637}{239517913} a^{10} + \\frac{611575354015}{297481247946} a^{9} + \\frac{68384344075057}{892443743838} a^{8} - \\frac{2851057255631}{52496690814} a^{7} - \\frac{13288074594220}{446221871919} a^{6} + \\frac{116643054046625}{892443743838} a^{5} + \\frac{13045896935069}{446221871919} a^{4} + \\frac{618897250412}{19400950953} a^{3} + \\frac{4066291942603}{446221871919} a^{2} + \\frac{2603676765017}{892443743838} a + \\frac{872354640625}{892443743838} \\)', '\\( \\frac{21305852804}{446221871919} a^{17} - \\frac{10854863323}{148740623973} a^{16} - \\frac{13769443967}{99160415982} a^{15} + \\frac{911628239}{1867037121} a^{14} - \\frac{548362517}{3734074242} a^{13} - \\frac{173724723319}{446221871919} a^{12} + \\frac{924863554846}{446221871919} a^{11} - \\frac{9566803543}{2155661217} a^{10} + \\frac{257763459401}{297481247946} a^{9} + \\frac{7250388895114}{446221871919} a^{8} - \\frac{7475837532220}{446221871919} a^{7} - \\frac{4225126692110}{446221871919} a^{6} + \\frac{30801782979607}{892443743838} a^{5} - \\frac{982210137887}{446221871919} a^{4} - \\frac{488669526487}{38801901906} a^{3} - \\frac{229608742690}{446221871919} a^{2} + \\frac{249848145770}{446221871919} a + \\frac{30761095945}{446221871919} \\)', '\\( \\frac{310675655}{892443743838} a^{17} - \\frac{2986038719}{99160415982} a^{16} + \\frac{2815742551}{297481247946} a^{15} + \\frac{13396292}{109825713} a^{14} - \\frac{702070711}{3734074242} a^{13} - \\frac{173013738955}{892443743838} a^{12} + \\frac{95128758167}{446221871919} a^{11} - \\frac{14403150989}{12933967302} a^{10} + \\frac{68238079030}{49580207991} a^{9} + \\frac{1823414597329}{892443743838} a^{8} - \\frac{4282733299715}{446221871919} a^{7} - \\frac{716236103573}{892443743838} a^{6} + \\frac{10492978501931}{892443743838} a^{5} - \\frac{5805646098415}{446221871919} a^{4} - \\frac{39267859951}{2282464818} a^{3} - \\frac{883892689177}{892443743838} a^{2} + \\frac{542183046575}{892443743838} a - \\frac{202444508242}{446221871919} \\)', '\\( \\frac{3166393589}{148740623973} a^{17} + \\frac{6137374270}{148740623973} a^{16} - \\frac{24223623128}{148740623973} a^{15} + \\frac{15583264}{622345707} a^{14} + \\frac{373621811}{622345707} a^{13} - \\frac{58627839065}{148740623973} a^{12} + \\frac{97474802914}{148740623973} a^{11} + \\frac{6875855485}{6466983651} a^{10} - \\frac{918401762578}{148740623973} a^{9} + \\frac{26491847584}{2916482823} a^{8} + \\frac{713063187223}{49580207991} a^{7} - \\frac{421135023757}{16526735997} a^{6} + \\frac{465031267349}{49580207991} a^{5} + \\frac{652751793553}{16526735997} a^{4} - \\frac{5198689774}{718553739} a^{3} + \\frac{393599590162}{148740623973} a^{2} - \\frac{72336010945}{148740623973} a - \\frac{3039031169}{8749448469} \\)', '\\( \\frac{79291655296}{446221871919} a^{17} - \\frac{12400506689}{148740623973} a^{16} - \\frac{61705862045}{99160415982} a^{15} + \\frac{2128545985}{1867037121} a^{14} + \\frac{1357897156}{1867037121} a^{13} - \\frac{608954726467}{892443743838} a^{12} + \\frac{6067482499213}{892443743838} a^{11} - \\frac{40692975995}{4311322434} a^{10} - \\frac{2181331258235}{297481247946} a^{9} + \\frac{23534178028742}{446221871919} a^{8} - \\frac{4159307448079}{892443743838} a^{7} - \\frac{38547359384219}{892443743838} a^{6} + \\frac{67810281219383}{892443743838} a^{5} + \\frac{32888220483026}{446221871919} a^{4} + \\frac{651848650817}{19400950953} a^{3} + \\frac{17428399673195}{892443743838} a^{2} + \\frac{3529885218047}{892443743838} a + \\frac{1077006016621}{892443743838} \\)', '\\( \\frac{40318581470}{446221871919} a^{17} - \\frac{24842294090}{148740623973} a^{16} - \\frac{55410508211}{297481247946} a^{15} + \\frac{1745257493}{1867037121} a^{14} - \\frac{2340045467}{3734074242} a^{13} - \\frac{117959652025}{446221871919} a^{12} + \\frac{1714718234086}{446221871919} a^{11} - \\frac{63256163383}{6466983651} a^{10} + \\frac{1716485645155}{297481247946} a^{9} + \\frac{11712176945944}{446221871919} a^{8} - \\frac{17177134602736}{446221871919} a^{7} + \\frac{953916464974}{446221871919} a^{6} + \\frac{47653074010273}{892443743838} a^{5} - \\frac{10315060065065}{446221871919} a^{4} + \\frac{33431468183}{38801901906} a^{3} - \\frac{2924653346230}{446221871919} a^{2} - \\frac{351679086397}{446221871919} a - \\frac{84856150676}{446221871919} \\)', '\\( \\frac{98238587336}{148740623973} a^{17} - \\frac{270193589071}{297481247946} a^{16} - \\frac{262495256222}{148740623973} a^{15} + \\frac{7544395829}{1244691414} a^{14} - \\frac{2335348583}{1244691414} a^{13} - \\frac{868377293725}{297481247946} a^{12} + \\frac{8148555026651}{297481247946} a^{11} - \\frac{378511081259}{6466983651} a^{10} + \\frac{2240351969948}{148740623973} a^{9} + \\frac{195003784390}{972160941} a^{8} - \\frac{6383397471967}{33053471994} a^{7} - \\frac{3475824940280}{49580207991} a^{6} + \\frac{18846057206107}{49580207991} a^{5} - \\frac{679116891655}{99160415982} a^{4} - \\frac{19323100513}{4311322434} a^{3} - \\frac{927478864645}{297481247946} a^{2} + \\frac{1045402606171}{297481247946} a - \\frac{23510763199}{17498896938} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/3*a^8 + 1/3*a^7 + 1/3*a^4 - 1/3*a + 1/3', '1/3*a^9 - 1/3*a^7 + 1/3*a^5 - 1/3*a^4 - 1/3*a^2 - 1/3*a - 1/3', '1/3*a^10 + 1/3*a^7 + 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^3 - 1/3*a^2 + 1/3*a + 1/3', '1/3*a^11 - 1/3*a^6 + 1/3*a^5 + 1/3*a^4 - 1/3*a^3 + 1/3*a^2 - 1/3*a - 1/3', '1/6*a^12 - 1/6*a^10 - 1/3*a^7 - 1/2*a^6 + 1/3*a^5 - 1/3*a^4 + 1/3*a^3 - 1/2*a^2 - 1/3*a - 1/6', '1/6*a^13 - 1/6*a^11 - 1/6*a^7 + 1/3*a^6 - 1/3*a^5 - 1/3*a^4 - 1/2*a^3 - 1/3*a^2 - 1/2*a + 1/3', '1/18*a^14 - 1/18*a^10 - 1/9*a^9 - 1/18*a^8 - 2/9*a^7 + 1/18*a^6 - 1/9*a^5 - 1/2*a^4 + 4/9*a^2 + 1/9*a + 7/18', '1/18*a^15 - 1/18*a^11 - 1/9*a^10 - 1/18*a^9 + 1/9*a^8 + 7/18*a^7 - 1/9*a^6 - 1/2*a^5 + 1/3*a^4 + 4/9*a^3 + 1/9*a^2 + 1/18*a + 1/3', '1/918*a^16 + 7/918*a^15 - 11/918*a^14 - 23/306*a^13 - 1/918*a^12 + 20/153*a^11 + 73/459*a^10 - 7/918*a^9 - 35/459*a^8 + 1/27*a^7 - 86/459*a^6 + 421/918*a^5 - 265/918*a^4 - 287/918*a^3 - 397/918*a^2 - 7/17*a + 361/918', '1/892443743838*a^17 + 116991155/297481247946*a^16 + 917158316/148740623973*a^15 + 94295551/3734074242*a^14 - 206168921/3734074242*a^13 - 37246972451/892443743838*a^12 + 34480183991/892443743838*a^11 + 764644733/6466983651*a^10 + 36867991495/297481247946*a^9 - 28510051646/446221871919*a^8 + 355141804543/892443743838*a^7 - 19754763872/446221871919*a^6 - 27112564195/446221871919*a^5 + 157817220161/892443743838*a^4 + 10089029663/38801901906*a^3 + 162334114921/892443743838*a^2 - 162094802527/446221871919*a - 25895071651/892443743838']}
Number field data - 18.0.18283008447003871936512.1