| 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 |
| 18.0.123...264.1 |
$x^{18} - 3 x^{17} + 21 x^{14} - 6 x^{13} - 23 x^{12} - 18 x^{11} + 31 x^{10} - 18 x^{9} - 22 x^{8} - 13 x^{7} + 61 x^{6} + 24 x^{5} + 28 x^{4} + 18 x^{3} + 40 x^{2} + 16 x + 32$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 59^{11}$ |
$2$ |
$19.1811218491$ |
$33.792916289896$ |
|
|
? |
$C_2^2:D_9$ (as 18T39) |
trivial |
$2$ |
$8$ |
$35431.6571722$ |
| 18.0.145...824.1 |
$x^{18} + 2 x^{16} - 4 x^{14} + x^{12} + 24 x^{10} + 100 x^{8} - 13 x^{6} + 50 x^{4} + 76 x^{2} + 59$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 59^{9}$ |
$2$ |
$19.3552744301$ |
$24.38611768097538$ |
|
|
? |
$C_2^2:D_9$ (as 18T39) |
$[2]$ |
$2$ |
$8$ |
$16588.4596368$ |
| 18.6.298...769.1 |
$x^{18} - 17 x^{16} - 28 x^{15} + 34 x^{14} + 112 x^{13} + 123 x^{12} + 168 x^{11} + 201 x^{10} + 173 x^{9} + 118 x^{8} - 92 x^{7} - 229 x^{6} - 158 x^{5} - 137 x^{4} - 75 x^{3} - 25 x^{2} - 3 x + 1$ |
$18$ |
[6,6] |
$1129^{9}$ |
$1$ |
$33.6005952328$ |
$33.60059523282288$ |
|
|
? |
$C_2^2:D_9$ (as 18T39) |
$[2]$ |
$2$ |
$11$ |
$4048618.08655$ |
| 18.6.217...601.1 |
$x^{18} - 6 x^{17} + 5 x^{16} + 68 x^{15} - 308 x^{14} + 426 x^{13} + 318 x^{12} - 1905 x^{11} + 2547 x^{10} - 5955 x^{9} + 25356 x^{8} - 55783 x^{7} + 46314 x^{6} + 41206 x^{5} - 117880 x^{4} + 80053 x^{3} + 5918 x^{2} - 26871 x + 7883$ |
$18$ |
[6,6] |
$3^{6}\cdot 1129^{9}$ |
$2$ |
$48.4604440366$ |
$58.19793810780585$ |
|
|
? |
$C_2^2:D_9$ (as 18T39) |
$[4]$ |
$2$ |
$11$ |
$42390273.4365$ |
| 18.18.781...736.1 |
$x^{18} - 46 x^{16} + 773 x^{14} - 6351 x^{12} + 28570 x^{10} - 72713 x^{8} + 101489 x^{6} - 68726 x^{4} + 16121 x^{2} - 1129$ |
$18$ |
[18,0] |
$2^{18}\cdot 1129^{9}$ |
$2$ |
$67.2011904656$ |
$95.03683496413377$ |
|
|
? |
$C_2^2:D_9$ (as 18T39) |
$[2]$ |
$2$ |
$17$ |
$26325707223.7$ |
| 18.18.140...489.1 |
$x^{18} - x^{17} - 89 x^{16} + 151 x^{15} + 2903 x^{14} - 6917 x^{13} - 41170 x^{12} + 128965 x^{11} + 226382 x^{10} - 1014925 x^{9} - 226188 x^{8} + 3486165 x^{7} - 1433009 x^{6} - 5139518 x^{5} + 3540642 x^{4} + 2797609 x^{3} - 2029989 x^{2} - 568486 x + 269671$ |
$18$ |
[18,0] |
$19^{6}\cdot 1129^{9}$ |
$2$ |
$89.6598837173$ |
$146.46159906268946$ |
|
|
? |
$C_2^2:D_9$ (as 18T39) |
$[2]$ |
$2$ |
$17$ |
$367625216248$ |
