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 |
18.0.258...864.2 |
$x^{18} + 18 x^{16} - 18 x^{15} + 135 x^{14} - 270 x^{13} + 699 x^{12} - 1620 x^{11} + 3123 x^{10} - 5760 x^{9} + 10044 x^{8} - 15390 x^{7} + 21528 x^{6} - 28674 x^{5} + 34641 x^{4} - 33822 x^{3} + 32643 x^{2} - 28566 x + 12301$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{44}$ |
$2$ |
$29.3309679999$ |
$34.51525023937336$ |
|
|
|
$C_3\times D_9$ (as 18T19) |
trivial |
$4$ |
$8$ |
$1082911.90412$ |
18.18.140...409.1 |
$x^{18} - 42 x^{16} - 4 x^{15} + 621 x^{14} + 69 x^{13} - 4331 x^{12} + 16005 x^{10} - 3117 x^{9} - 31995 x^{8} + 13491 x^{7} + 31560 x^{6} - 20790 x^{5} - 10521 x^{4} + 10989 x^{3} - 1728 x^{2} - 216 x + 9$ |
$18$ |
[18,0] |
$3^{27}\cdot 107^{9}$ |
$2$ |
$53.7494186015$ |
$68.61210071110087$ |
|
|
? |
$C_3\times D_9$ (as 18T19) |
trivial |
$2$ |
$17$ |
$14865346201.2$ |
18.18.530...509.1 |
$x^{18} - 3 x^{17} - 635 x^{16} + 637 x^{15} + 147470 x^{14} + 31278 x^{13} - 15388414 x^{12} - 4948990 x^{11} + 811072595 x^{10} - 33481138 x^{9} - 21732949914 x^{8} + 10719756413 x^{7} + 274397510025 x^{6} - 231330970625 x^{5} - 1350644250998 x^{4} + 1050009163838 x^{3} + 2453632857591 x^{2} - 1197940138849 x - 1164062910163$ |
$18$ |
[18,0] |
$7^{12}\cdot 19^{12}\cdot 229^{9}$ |
$3$ |
$394.292789518$ |
$394.2927895181429$ |
|
|
? |
$C_3\times D_9$ (as 18T19) |
$[3, 3]$ |
$2$ |
$17$ |
$39968959368600000$ |