| 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 |
| 18.2.238...125.1 |
$x^{18} - 4 x^{17} + 5 x^{16} - x^{15} - 4 x^{13} + 6 x^{12} + 15 x^{11} - x^{10} + 60 x^{7} + 25 x^{6} + 64 x^{3} + 64 x^{2} + 20 x + 1$ |
$18$ |
[2,8] |
$5^{15}\cdot 23^{8}$ |
$2$ |
$15.4059106653$ |
$18.337449110889978$ |
|
|
? |
$D_{18}$ (as 18T13) |
trivial |
$2$ |
$9$ |
$2645.14483524$ |
| 18.0.246...336.1 |
$x^{18} + x^{16} - 2 x^{14} - 7 x^{12} + 10 x^{10} + 33 x^{8} + 13 x^{6} + 20 x^{4} + 16 x^{2} + 4$ |
$18$ |
[0,9] |
$-\,2^{24}\cdot 59^{8}$ |
$2$ |
$15.4318739072$ |
$19.355274430100316$ |
|
|
? |
$D_{18}$ (as 18T13) |
trivial |
$4$ |
$8$ |
$6192.4028326$ |
| 18.0.523...083.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} + 36 x^{14} - 69 x^{13} + 124 x^{12} - 87 x^{11} + 237 x^{10} - 80 x^{9} + 306 x^{8} - 24 x^{7} + 173 x^{6} + 75 x^{5} + 51 x^{4} + 33 x^{3} + 27 x^{2} + 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 29^{8}$ |
$2$ |
$16.091485179$ |
$19.401730279803232$ |
|
|
? |
$D_{18}$ (as 18T13) |
trivial |
$6$ |
$8$ |
$10792.8653088$ |
| 18.2.505...469.1 |
$x^{18} - x^{15} + 4 x^{12} + 4 x^{9} + 11 x^{6} - 13 x^{3} - 1$ |
$18$ |
[2,8] |
$3^{20}\cdot 29^{9}$ |
$2$ |
$18.2529778346$ |
$19.401730279803232$ |
|
|
? |
$D_{18}$ (as 18T13) |
trivial |
$2$ |
$9$ |
$17778.3438952$ |
| 18.2.476...777.1 |
$x^{18} - 2 x^{17} + 17 x^{15} - 17 x^{14} + 51 x^{13} + 119 x^{12} - 476 x^{11} + 493 x^{10} + 1632 x^{9} - 3638 x^{8} - 3502 x^{7} + 6936 x^{6} + 1972 x^{5} - 3451 x^{4} + 3264 x^{3} + 17 x^{2} - 750 x + 225$ |
$18$ |
[2,8] |
$7^{8}\cdot 17^{17}$ |
$2$ |
$34.489728596$ |
$38.427282044851594$ |
|
|
|
$D_{18}$ (as 18T13) |
trivial |
$2$ |
$9$ |
$10997947.525$ |
| 18.0.333...439.1 |
$x^{18} - 4 x^{17} + 17 x^{16} - 51 x^{15} + 170 x^{14} - 408 x^{13} + 918 x^{12} - 1445 x^{11} + 1870 x^{10} - 1887 x^{9} + 3672 x^{8} - 5797 x^{7} + 8058 x^{6} - 8143 x^{5} + 9044 x^{4} - 6851 x^{3} + 5916 x^{2} - 2826 x + 1971$ |
$18$ |
[0,9] |
$-\,7^{9}\cdot 17^{17}$ |
$2$ |
$38.4272820449$ |
$38.427282044851594$ |
|
|
|
$D_{18}$ (as 18T13) |
$[10]$ |
$2$ |
$8$ |
$5250337.35027$ |
| 18.0.519...963.1 |
$x^{18} - 3 x^{17} + 19 x^{16} - 46 x^{15} + 209 x^{14} - 457 x^{13} + 1289 x^{12} - 2046 x^{11} + 4263 x^{10} - 5541 x^{9} + 9392 x^{8} - 9256 x^{7} + 11934 x^{6} - 8321 x^{5} + 9457 x^{4} - 4564 x^{3} + 3678 x^{2} + 60 x + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 1129^{8}$ |
$2$ |
$39.383425757$ |
$58.19793810780585$ |
✓ |
|
? |
$D_{18}$ (as 18T13) |
$[2, 38]$ |
$6$ |
$8$ |
$290542.983381$ |
| 18.0.691...184.1 |
$x^{18} + 29 x^{16} + 338 x^{14} + 2070 x^{12} + 7345 x^{10} + 15603 x^{8} + 19532 x^{6} + 13258 x^{4} + 3756 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 1129^{8}$ |
$2$ |
$45.4760629249$ |
$67.20119046564577$ |
✓ |
|
? |
$D_{18}$ (as 18T13) |
$[178]$ |
$4$ |
$8$ |
$290542.983381$ |
| 18.18.354...208.1 |
$x^{18} - 6 x^{17} - 29 x^{16} + 232 x^{15} + 122 x^{14} - 2972 x^{13} + 2218 x^{12} + 15816 x^{11} - 21375 x^{10} - 33384 x^{9} + 61321 x^{8} + 17204 x^{7} - 59508 x^{6} + 13790 x^{5} + 7002 x^{4} - 1052 x^{3} - 340 x^{2} - 8 x + 1$ |
$18$ |
[18,0] |
$2^{27}\cdot 1129^{8}$ |
$2$ |
$64.3128649517$ |
$95.03683496413377$ |
|
|
? |
$D_{18}$ (as 18T13) |
trivial |
$2$ |
$17$ |
$26253722476.4$ |
| 18.18.136...672.1 |
$x^{18} - 6 x^{17} - 38 x^{16} + 280 x^{15} + 350 x^{14} - 4460 x^{13} + 932 x^{12} + 30696 x^{11} - 23739 x^{10} - 93216 x^{9} + 86432 x^{8} + 120652 x^{7} - 101484 x^{6} - 59266 x^{5} + 34798 x^{4} + 12148 x^{3} - 3288 x^{2} - 564 x + 109$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{9}\cdot 1129^{8}$ |
$3$ |
$78.7668515141$ |
$116.3958762156117$ |
|
|
? |
$D_{18}$ (as 18T13) |
trivial |
$2$ |
$17$ |
$236007763005$ |
