| 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 |
| 18.0.295...643.2 |
$x^{18} - 9 x^{15} + 36 x^{12} - 53 x^{9} + 27 x^{6} + 1$ |
$18$ |
[0,9] |
$-\,3^{45}$ |
$1$ |
$15.5884572681$ |
$19.898946404249138$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
trivial |
$18$ |
$8$ |
$23143.3269777$ |
| 18.0.121...728.3 |
$x^{18} + 108 x^{12} - 424 x^{9} + 576 x^{6} - 288 x^{3} + 64$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{45}$ |
$2$ |
$24.74513346597485$ |
$31.5876084551639$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
trivial |
$18$ |
$8$ |
$957708.9948188227$ |
| 18.0.121...728.4 |
$x^{18} - 8 x^{9} + 64$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{45}$ |
$2$ |
$24.74513346597485$ |
$26.84306578592094$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
trivial |
$18$ |
$8$ |
$1817377.5854392452$ |
| 18.0.121...728.5 |
$x^{18} - 18 x^{15} + 144 x^{12} - 424 x^{9} + 432 x^{6} + 64$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{45}$ |
$2$ |
$24.74513346597485$ |
$31.5876084551639$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
trivial |
$18$ |
$8$ |
$1452047.2367816924$ |
| 18.0.258...864.1 |
$x^{18} + 27 x^{14} + 207 x^{10} - 4 x^{9} + 126 x^{7} + 414 x^{6} + 108 x^{5} - 420 x^{3} + 81 x^{2} - 36 x + 53$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{44}$ |
$2$ |
$29.3309679999$ |
$34.51525023937336$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
trivial |
$4$ |
$8$ |
$1803849.29799$ |
| 18.0.577...375.2 |
$x^{18} + 18 x^{16} + 135 x^{14} + 546 x^{12} + 1287 x^{10} - 4 x^{9} + 1782 x^{8} - 36 x^{7} + 1386 x^{6} - 108 x^{5} + 540 x^{4} - 120 x^{3} + 81 x^{2} - 36 x + 19$ |
$18$ |
[0,9] |
$-\,3^{45}\cdot 5^{9}$ |
$2$ |
$34.85685011586675$ |
$37.812070079830384$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
$[2]$ |
$2$ |
$8$ |
$2650610.008812996$ |
| 18.18.787...000.1 |
$x^{18} - 36 x^{16} + 540 x^{14} - 4368 x^{12} + 20592 x^{10} - 72 x^{9} - 57024 x^{8} + 1296 x^{7} + 88704 x^{6} - 7776 x^{5} - 69120 x^{4} + 17280 x^{3} + 20736 x^{2} - 10368 x + 1216$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{44}\cdot 5^{9}$ |
$3$ |
$52.055673091$ |
$61.25657302264647$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
trivial |
$2$ |
$17$ |
$5504906840.3$ |
| 18.18.427...848.1 |
$x^{18} - 72 x^{16} + 2160 x^{14} - 34944 x^{12} + 329472 x^{10} - 1728 x^{9} - 1824768 x^{8} + 62208 x^{7} + 5677056 x^{6} - 746496 x^{5} - 8847360 x^{4} + 3317760 x^{3} + 5308416 x^{2} - 3981312 x + 733184$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{44}\cdot 13^{9}$ |
$3$ |
$83.9372507441$ |
$83.93725074408307$ |
|
|
? |
$C_9\times S_3$ (as 18T16) |
$[3]$ |
$2$ |
$17$ |
$241280047092$ |
