| 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 |
| 18.0.944...443.1 |
$x^{18} - 3 x^{17} + 24 x^{16} - 57 x^{15} + 339 x^{14} - 750 x^{13} + 2691 x^{12} - 4620 x^{11} + 12813 x^{10} - 19451 x^{9} + 38334 x^{8} - 40263 x^{7} + 55569 x^{6} - 41604 x^{5} + 50556 x^{4} - 25632 x^{3} + 19056 x^{2} + 1056 x + 64$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 19^{8}$ |
$2$ |
$27.7368561442$ |
$53.36109106637179$ |
✓ |
|
? |
$C_2\times \He_3$ (as 18T15) |
$[3]$ |
$18$ |
$8$ |
$958684.150365$ |
| 18.0.614...947.1 |
$x^{18} - 3 x^{17} + 27 x^{16} - 26 x^{15} + 321 x^{14} - 123 x^{13} + 2645 x^{12} + 1020 x^{11} + 13374 x^{10} + 10200 x^{9} + 51657 x^{8} + 49845 x^{7} + 115629 x^{6} + 89958 x^{5} + 147603 x^{4} + 114065 x^{3} + 107682 x^{2} + 43053 x + 16129$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 73^{8}$ |
$2$ |
$34.9804486614$ |
$90.76055065978505$ |
✓ |
|
? |
$C_2\times \He_3$ (as 18T15) |
$[21]$ |
$18$ |
$8$ |
$1105667.84512$ |
| 18.18.247...792.1 |
$x^{18} - 54 x^{16} + 1089 x^{14} - 10116 x^{12} + 43200 x^{10} - 74196 x^{8} + 58644 x^{6} - 21627 x^{4} + 3078 x^{2} - 27$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{33}\cdot 19^{8}$ |
$3$ |
$55.4737122883$ |
$106.72218213274358$ |
|
|
|
$C_2\times \He_3$ (as 18T15) |
trivial |
$2$ |
$17$ |
$11273350288.2$ |
| 18.18.614...125.1 |
$x^{18} - 3 x^{17} - 45 x^{16} + 108 x^{15} + 792 x^{14} - 1416 x^{13} - 7026 x^{12} + 8616 x^{11} + 33624 x^{10} - 25698 x^{9} - 85104 x^{8} + 37308 x^{7} + 103944 x^{6} - 26562 x^{5} - 48483 x^{4} + 12969 x^{3} + 6732 x^{2} - 2397 x + 181$ |
$18$ |
[18,0] |
$3^{32}\cdot 5^{9}\cdot 19^{8}$ |
$3$ |
$58.3492797886$ |
$112.25429501711845$ |
|
|
? |
$C_2\times \He_3$ (as 18T15) |
trivial |
$2$ |
$17$ |
$12294031262.8$ |
