| 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 |
| 18.2.192...344.1 |
$x^{18} + 288 x^{12} - 9216 x^{9} - 15552 x^{8} + 65664 x^{6} - 497664 x^{3} + 653184 x^{2} - 746496$ |
$18$ |
[2,8] |
$2^{60}\cdot 3^{34}$ |
$2$ |
$80.2901659541319$ |
|
|
|
? |
$A_{18}$ (as 18T982) |
trivial |
$2$ |
$9$ |
$112597278235.35344$ |
| 18.2.243...576.1 |
$x^{18} - 8 x^{17} + 37 x^{16} - 144 x^{15} + 480 x^{14} - 960 x^{13} + 1800 x^{12} - 2304 x^{11} - 2466 x^{10} + 25712 x^{9} - 38242 x^{8} + 203984 x^{7} - 157224 x^{6} + 604416 x^{5} - 535056 x^{4} + 669792 x^{3} - 1099311 x^{2} + 576120 x - 299763$ |
$18$ |
[2,8] |
$2^{54}\cdot 3^{38}$ |
$2$ |
$81.34782940150222$ |
|
|
|
|
$A_{18}$ (as 18T982) |
trivial |
$2$ |
$9$ |
$208003889751.14267$ |
| 18.2.269...000.1 |
$x^{18} - 3 x^{17} + 21 x^{16} - 198 x^{15} + 180 x^{14} - 1092 x^{13} + 23611 x^{12} + 97293 x^{11} + 593271 x^{10} + 1360730 x^{9} + 2502192 x^{8} - 1915326 x^{7} - 31691898 x^{6} - 54019896 x^{5} - 111814770 x^{4} + 209720586 x^{3} + 565097442 x^{2} + 377540976 x - 1059046848$ |
$18$ |
[2,8] |
$2^{26}\cdot 3^{18}\cdot 5^{16}\cdot 7^{14}$ |
$4$ |
$155.07704098$ |
$2368.5438573897973$ |
|
|
|
$A_{18}$ (as 18T982) |
trivial |
$2$ |
$9$ |
$175948770443000$ |
| 18.2.354...224.1 |
$x^{18} - 147456 x - 278528$ |
$18$ |
[2,8] |
$2^{24}\cdot 3^{36}\cdot 17^{18}$ |
$3$ |
$385.535841268$ |
|
|
|
? |
$A_{18}$ (as 18T982) |
trivial |
$2$ |
$9$ |
$25651792895400000$ |
