| 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 |
| 18.6.113...641.1 |
$x^{18} - 6 x^{17} + 30 x^{16} - 117 x^{15} + 309 x^{14} - 627 x^{13} + 930 x^{12} - 627 x^{11} - 510 x^{10} - 974 x^{9} + 6243 x^{8} - 2055 x^{7} - 11115 x^{6} + 10734 x^{5} - 696 x^{4} + 168 x^{3} - 1344 x^{2} - 192 x + 64$ |
$18$ |
[6,6] |
$3^{32}\cdot 19^{10}$ |
$2$ |
$36.1938040759$ |
$82.00561024067765$ |
|
|
|
$C_3^2:A_4$ (as 18T48) |
$[2]$ |
$2$ |
$11$ |
$22453155.9774$ |
| 18.6.121...169.1 |
$x^{18} - 3 x^{17} + 15 x^{16} - 50 x^{15} + 45 x^{14} - 204 x^{13} + 140 x^{12} + 210 x^{11} + 1962 x^{10} - 166 x^{9} - 1536 x^{8} - 7242 x^{7} - 1448 x^{6} + 28032 x^{5} + 44793 x^{4} + 20953 x^{3} - 12165 x^{2} - 14862 x - 3691$ |
$18$ |
[6,6] |
$3^{24}\cdot 73^{10}$ |
$2$ |
$46.9181673181$ |
$154.5007966313496$ |
|
|
|
$C_3^2:A_4$ (as 18T48) |
trivial |
$2$ |
$11$ |
$208631462.937$ |
| 18.18.297...304.1 |
$x^{18} - 54 x^{16} + 1143 x^{14} - 12240 x^{12} + 71820 x^{10} - 233244 x^{8} + 397746 x^{6} - 302157 x^{4} + 58482 x^{2} - 3249$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{32}\cdot 19^{10}$ |
$3$ |
$72.3876081518$ |
$231.9468923860966$ |
|
|
|
$C_3^2:A_4$ (as 18T48) |
trivial |
$2$ |
$17$ |
$211204307630$ |
| 18.18.318...336.1 |
$x^{18} - 63 x^{16} + 1221 x^{14} - 9772 x^{12} + 38544 x^{10} - 84315 x^{8} + 107675 x^{6} - 79935 x^{4} + 31974 x^{2} - 5329$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{24}\cdot 73^{10}$ |
$3$ |
$93.8363346363$ |
$436.99424398700404$ |
|
|
|
$C_3^2:A_4$ (as 18T48) |
trivial |
$2$ |
$17$ |
$1494891798290$ |
