| 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 |
| 18.0.129...896.1 |
$x^{18} - 9 x^{17} + 41 x^{16} - 124 x^{15} + 276 x^{14} - 476 x^{13} + 646 x^{12} - 678 x^{11} + 517 x^{10} - 231 x^{9} - 15 x^{8} + 98 x^{7} - 48 x^{6} - 18 x^{5} + 36 x^{4} - 22 x^{3} + 9 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 11^{9}\cdot 17^{4}$ |
$3$ |
$11.5268768841$ |
$40.60484358442798$ |
|
|
? |
$C_3^3:S_3$ (as 18T88) |
trivial |
$2$ |
$8$ |
$113.075873428$ |
| 18.0.164...375.1 |
$x^{18} + 2 x^{16} - x^{15} - 5 x^{14} - 5 x^{12} + 10 x^{11} - 11 x^{10} + 19 x^{9} - 8 x^{8} - 17 x^{7} + 46 x^{6} - 57 x^{5} + 52 x^{4} - 37 x^{3} + 14 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,5^{4}\cdot 11^{4}\cdot 23^{9}$ |
$3$ |
$11.6845282344$ |
$69.35946123538706$ |
|
|
? |
$C_3^3:S_3$ (as 18T88) |
trivial |
$2$ |
$8$ |
$102.074554739$ |
| 18.18.403...000.1 |
$x^{18} - 3 x^{17} - 33 x^{16} + 106 x^{15} + 365 x^{14} - 1333 x^{13} - 1544 x^{12} + 7717 x^{11} + 893 x^{10} - 21464 x^{9} + 9947 x^{8} + 25981 x^{7} - 22611 x^{6} - 8420 x^{5} + 13270 x^{4} - 1416 x^{3} - 1968 x^{2} + 512 x - 4$ |
$18$ |
[18,0] |
$2^{12}\cdot 5^{4}\cdot 37^{9}\cdot 59^{4}$ |
$4$ |
$34.1693614362$ |
$427.8933494155845$ |
|
|
|
$C_3^3:S_3$ (as 18T88) |
trivial |
$2$ |
$17$ |
$156226776.16$ |
| 18.18.277...000.1 |
$x^{18} - 3 x^{17} - 43 x^{16} + 144 x^{15} + 618 x^{14} - 2454 x^{13} - 3140 x^{12} + 18208 x^{11} + 757 x^{10} - 60741 x^{9} + 28339 x^{8} + 101212 x^{7} - 73600 x^{6} - 86246 x^{5} + 77066 x^{4} + 34932 x^{3} - 36045 x^{2} - 5051 x + 6047$ |
$18$ |
[18,0] |
$2^{16}\cdot 5^{8}\cdot 17^{4}\cdot 37^{9}$ |
$4$ |
$43.2284346273$ |
$217.75210610577363$ |
|
|
? |
$C_3^3:S_3$ (as 18T88) |
trivial |
$2$ |
$17$ |
$957797101.545$ |
