| 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 |
| 18.0.319...743.1 |
$x^{18} - 5 x^{17} + 15 x^{16} - 36 x^{15} + 75 x^{14} - 137 x^{13} + 221 x^{12} - 312 x^{11} + 384 x^{10} - 411 x^{9} + 384 x^{8} - 312 x^{7} + 221 x^{6} - 137 x^{5} + 75 x^{4} - 36 x^{3} + 15 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,11^{6}\cdot 23^{9}$ |
$2$ |
$10.6658338256$ |
$34.833107461122644$ |
|
|
? |
$C_3^3:S_4$ (as 18T221) |
trivial |
$2$ |
$8$ |
$39.4992656122$ |
| 18.0.126...199.1 |
$x^{18} - x^{17} - 2 x^{16} + x^{15} + 6 x^{14} - 11 x^{13} + 5 x^{12} - 2 x^{11} + x^{10} + 13 x^{9} - 2 x^{8} - 28 x^{7} + 14 x^{6} + 27 x^{5} - 19 x^{4} + x^{3} + 8 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,3^{14}\cdot 31^{9}$ |
$2$ |
$13.0850430599$ |
$60.4212463767511$ |
|
|
? |
$C_3^3:S_4$ (as 18T221) |
trivial |
$2$ |
$8$ |
$350.327705995$ |
| 18.6.532...000.1 |
$x^{18} - 5 x^{17} + 7 x^{16} + 6 x^{15} - 14 x^{14} - 26 x^{13} + 20 x^{12} + 72 x^{11} + 7 x^{10} - 107 x^{9} - 79 x^{8} + 172 x^{7} - 122 x^{6} + 210 x^{5} - 226 x^{4} + 94 x^{3} - 7 x^{2} - 5 x + 1$ |
$18$ |
[6,6] |
$2^{16}\cdot 5^{4}\cdot 37^{9}$ |
$3$ |
$16.1068178761$ |
$81.22945030822322$ |
|
|
? |
$C_3^3:S_4$ (as 18T221) |
trivial |
$2$ |
$11$ |
$7920.70304722$ |
| 18.6.716...936.1 |
$x^{18} - 5 x^{17} + 15 x^{16} - 30 x^{15} + 48 x^{14} - 76 x^{13} + 80 x^{12} + 8 x^{11} - 169 x^{10} + 257 x^{9} - 169 x^{8} + 8 x^{7} + 80 x^{6} - 76 x^{5} + 48 x^{4} - 30 x^{3} + 15 x^{2} - 5 x + 1$ |
$18$ |
[6,6] |
$2^{16}\cdot 101^{9}$ |
$2$ |
$18.6098513985$ |
$58.996092611880485$ |
|
|
? |
$C_3^3:S_4$ (as 18T221) |
trivial |
$2$ |
$11$ |
$41754.4199743$ |
| 18.18.285...161.1 |
$x^{18} - 9 x^{17} + 10 x^{16} + 124 x^{15} - 380 x^{14} - 224 x^{13} + 2242 x^{12} - 2246 x^{11} - 2595 x^{10} + 6155 x^{9} - 2595 x^{8} - 2246 x^{7} + 2242 x^{6} - 224 x^{5} - 380 x^{4} + 124 x^{3} + 10 x^{2} - 9 x + 1$ |
$18$ |
[18,0] |
$3^{9}\cdot 53^{4}\cdot 107^{9}$ |
$3$ |
$43.2937227542$ |
$1070.0301643596565$ |
|
|
? |
$C_3^3:S_4$ (as 18T221) |
trivial |
$2$ |
$17$ |
$2577975005.9$ |
| 18.18.388...976.2 |
$x^{18} - 45 x^{16} - 6 x^{15} + 774 x^{14} + 234 x^{13} - 6555 x^{12} - 3420 x^{11} + 29034 x^{10} + 23344 x^{9} - 64449 x^{8} - 76284 x^{7} + 53727 x^{6} + 111114 x^{5} + 21204 x^{4} - 49452 x^{3} - 37620 x^{2} - 10512 x - 1052$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{25}\cdot 47^{9}$ |
$3$ |
$50.0499908106$ |
$205.02706746888765$ |
|
|
|
$C_3^3:S_4$ (as 18T221) |
trivial |
$2$ |
$17$ |
$10900954227.8$ |
