| 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 |
| 18.6.458...249.1 |
$x^{18} - 2 x^{17} - 4 x^{16} + 12 x^{15} - 20 x^{14} + 28 x^{13} + 84 x^{12} - 232 x^{11} - 180 x^{10} + 900 x^{9} - 334 x^{8} - 1660 x^{7} + 2996 x^{6} - 2576 x^{5} + 1380 x^{4} - 492 x^{3} + 115 x^{2} - 16 x + 1$ |
$18$ |
[6,6] |
$7^{16}\cdot 13^{10}$ |
$2$ |
$23.4452936033$ |
$47.806217686235044$ |
|
|
? |
$C_3^2.A_4$ (as 18T47) |
trivial |
$2$ |
$11$ |
$299765.553553$ |
| 18.6.774...081.1 |
$x^{18} - x^{17} - 15 x^{16} + 26 x^{15} + 102 x^{14} - 154 x^{13} - 658 x^{12} + 1123 x^{11} + 1768 x^{10} - 3055 x^{9} - 5130 x^{8} + 7964 x^{7} + 3857 x^{6} - 7735 x^{5} - 6123 x^{4} + 4758 x^{3} + 2938 x^{2} - 312 x - 13$ |
$18$ |
[6,6] |
$7^{16}\cdot 13^{12}$ |
$2$ |
$31.1764857428$ |
$47.806217686235044$ |
|
|
? |
$C_3^2.A_4$ (as 18T47) |
trivial |
$2$ |
$11$ |
$2770505.95053$ |
| 18.18.120...856.1 |
$x^{18} - 39 x^{16} + 599 x^{14} - 4620 x^{12} + 19019 x^{10} - 41678 x^{8} + 46956 x^{6} - 23998 x^{4} + 3718 x^{2} - 169$ |
$18$ |
[18,0] |
$2^{18}\cdot 7^{16}\cdot 13^{10}$ |
$3$ |
$46.8905872065$ |
$135.21640283526824$ |
|
|
? |
$C_3^2.A_4$ (as 18T47) |
trivial |
$2$ |
$17$ |
$1751416910.41$ |
| 18.18.202...664.1 |
$x^{18} - 67 x^{16} + 1726 x^{14} - 22316 x^{12} + 159978 x^{10} - 660569 x^{8} + 1557465 x^{6} - 1946373 x^{4} + 1012817 x^{2} - 28561$ |
$18$ |
[18,0] |
$2^{18}\cdot 7^{16}\cdot 13^{12}$ |
$3$ |
$62.3529714856$ |
$135.21640283526824$ |
|
|
? |
$C_3^2.A_4$ (as 18T47) |
trivial |
$2$ |
$17$ |
$20486548774.7$ |
