| 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 |
| 18.6.160...376.1 |
$x^{18} + 3 x^{16} - 27 x^{14} - 113 x^{12} + 15 x^{10} + 465 x^{8} + 366 x^{6} - 102 x^{4} - 39 x^{2} - 1$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$25.1331561847$ |
$31.66579252742446$ |
|
|
? |
$A_4 \times C_3$ (as 18T8) |
$[2]$ |
$2$ |
$11$ |
$238252.895142$ |
| 18.6.544...089.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 36 x^{15} + 101 x^{14} - 229 x^{13} + 498 x^{12} - 765 x^{11} + 930 x^{10} - 345 x^{9} - 1994 x^{8} + 7647 x^{7} - 18390 x^{6} + 33475 x^{5} - 47255 x^{4} + 49166 x^{3} - 37440 x^{2} + 18499 x - 3991$ |
$18$ |
[6,6] |
$7^{12}\cdot 13^{14}$ |
$2$ |
$26.9028988317$ |
$31.02307339173177$ |
|
|
|
$A_4 \times C_3$ (as 18T8) |
trivial |
$2$ |
$11$ |
$1529227.92476$ |
| 18.18.655...096.1 |
$x^{18} - 30 x^{16} + 369 x^{14} - 2407 x^{12} + 8964 x^{10} - 19056 x^{8} + 21848 x^{6} - 11904 x^{4} + 2208 x^{2} - 64$ |
$18$ |
[18,0] |
$2^{24}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$39.8963985669$ |
$63.33158505484892$ |
|
|
|
$A_4 \times C_3$ (as 18T8) |
trivial |
$2$ |
$17$ |
$423212183.857$ |
| 18.18.578...409.1 |
$x^{18} - 42 x^{16} - 28 x^{15} + 630 x^{14} + 714 x^{13} - 4107 x^{12} - 5880 x^{11} + 12159 x^{10} + 20818 x^{9} - 13965 x^{8} - 32634 x^{7} - 435 x^{6} + 19026 x^{5} + 7182 x^{4} - 1512 x^{3} - 945 x^{2} + 27$ |
$18$ |
[18,0] |
$3^{24}\cdot 7^{12}\cdot 23^{6}$ |
$3$ |
$45.0266508798$ |
$75.93190300685129$ |
|
|
|
$A_4 \times C_3$ (as 18T8) |
trivial |
$2$ |
$17$ |
$1768913822.57$ |
