Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
18.2.169...264.1 |
$x^{18} - x^{14} - 3 x^{12} - 9 x^{10} + 2 x^{8} - 24 x^{6} + 9 x^{4} - x^{2} - 1$ |
$18$ |
[2,8] |
$2^{24}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$13.2987995223$ |
$20.122224041627174$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$9$ |
$522.985932438$ |
18.2.303...344.1 |
$x^{18} + 3 x^{16} + 6 x^{14} + 4 x^{12} - 3 x^{10} - 9 x^{8} - 15 x^{6} + 3 x^{4} + 3 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{30}\cdot 3^{24}$ |
$2$ |
$13.7365709106$ |
$20.58160140743025$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$9$ |
$753.250131692$ |
18.6.804...776.1 |
$x^{18} + 3 x^{16} - 35 x^{14} - 95 x^{12} + 212 x^{10} + 555 x^{8} + 380 x^{6} + 90 x^{4} + 2 x^{2} - 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
$75.34971632639669$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
$[2]$ |
$2$ |
$11$ |
$409048.073804$ |
18.6.198...224.1 |
$x^{18} + x^{16} + 8 x^{14} - 25 x^{12} - 178 x^{10} + 136 x^{8} + 680 x^{6} - 768 x^{4} + 256 x^{2} - 64$ |
$18$ |
[6,6] |
$2^{18}\cdot 31^{14}$ |
$2$ |
$28.9053331854$ |
$49.470511984396374$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$11$ |
$1874917.54273$ |
18.6.406...416.1 |
$x^{18} - 51 x^{14} - 111 x^{12} + 171 x^{10} + 498 x^{8} + 234 x^{6} - 27 x^{4} - 15 x^{2} - 1$ |
$18$ |
[6,6] |
$2^{24}\cdot 3^{30}\cdot 7^{6}$ |
$3$ |
$30.0797876098$ |
$55.715304322429894$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$11$ |
$4301651.23478$ |
18.6.188...001.1 |
$x^{18} + 7 x^{16} - 4 x^{15} - 37 x^{14} - 160 x^{13} - 248 x^{12} - 499 x^{11} - 715 x^{10} - 375 x^{9} - 1136 x^{8} - 25 x^{7} + 1614 x^{6} - 1182 x^{5} - 982 x^{4} + 973 x^{3} - 76 x^{2} - 276 x + 88$ |
$18$ |
[6,6] |
$19^{12}\cdot 31^{8}$ |
$2$ |
$32.7589384552$ |
$39.64452763115264$ |
|
|
|
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$11$ |
$9826413.58709$ |
18.18.158...569.1 |
$x^{18} - 5 x^{17} - 43 x^{16} + 310 x^{15} + 23 x^{14} - 4187 x^{13} + 8010 x^{12} + 13898 x^{11} - 59680 x^{10} + 35569 x^{9} + 95171 x^{8} - 148735 x^{7} + 24283 x^{6} + 70453 x^{5} - 28177 x^{4} - 11891 x^{3} + 3454 x^{2} + 1452 x + 121$ |
$18$ |
[18,0] |
$11^{8}\cdot 43^{14}$ |
$2$ |
$54.1148749063$ |
$76.19387402923972$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$17$ |
$9042270276.65$ |
18.18.653...784.1 |
$x^{18} - x^{17} - 36 x^{16} + 46 x^{15} + 499 x^{14} - 737 x^{13} - 3454 x^{12} + 5671 x^{11} + 12782 x^{10} - 23129 x^{9} - 24800 x^{8} + 50687 x^{7} + 22166 x^{6} - 56919 x^{5} - 4663 x^{4} + 28402 x^{3} - 2838 x^{2} - 4491 x + 783$ |
$18$ |
[18,0] |
$2^{12}\cdot 11^{6}\cdot 37^{14}$ |
$3$ |
$58.5504194789$ |
$106.71310986078944$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$17$ |
$17401289397.1$ |