| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 18.6.366...625.1 |
$x^{18} - 12 x^{15} + 36 x^{14} - 33 x^{12} + 117 x^{11} - 171 x^{10} - 2 x^{9} + 135 x^{8} - 81 x^{7} - 30 x^{6} + 36 x^{5} + 81 x^{4} - 393 x^{3} + 531 x^{2} - 270 x + 44$ |
$18$ |
[6,6] |
$3^{36}\cdot 5^{12}$ |
$2$ |
$26.3161596439$ |
$35.412341444574025$ |
|
|
|
$\He_3:C_4$ (as 18T49) |
trivial |
trivial |
$2$ |
$11$ |
$1783677.91642$ |
| 18.6.366...625.2 |
$x^{18} - 12 x^{15} + 9 x^{14} + 54 x^{13} - 18 x^{12} + 72 x^{11} - 261 x^{10} - 14 x^{9} + 135 x^{8} - 270 x^{7} + 840 x^{6} - 1116 x^{5} + 1269 x^{4} - 1026 x^{3} + 576 x^{2} - 252 x + 49$ |
$18$ |
[6,6] |
$3^{36}\cdot 5^{12}$ |
$2$ |
$26.3161596439$ |
$35.412341444574025$ |
|
|
|
$\He_3:C_4$ (as 18T49) |
trivial |
trivial |
$2$ |
$11$ |
$1592430.98785$ |
| 18.18.160...625.1 |
$x^{18} - 6 x^{17} - 18 x^{16} + 141 x^{15} + 108 x^{14} - 1227 x^{13} - 438 x^{12} + 5220 x^{11} + 1956 x^{10} - 11198 x^{9} - 5475 x^{8} + 11283 x^{7} + 6315 x^{6} - 5184 x^{5} - 3051 x^{4} + 930 x^{3} + 552 x^{2} - 24 x - 16$ |
$18$ |
[18,0] |
$3^{26}\cdot 5^{12}\cdot 11^{10}$ |
$3$ |
$54.1634900255$ |
$93.22094273535318$ |
|
|
|
$\He_3:C_4$ (as 18T49) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$14711932756.8$ |
| 18.18.130...625.1 |
$x^{18} - 3 x^{17} - 63 x^{16} + 147 x^{15} + 1245 x^{14} - 1968 x^{13} - 9306 x^{12} + 9264 x^{11} + 28194 x^{10} - 15305 x^{9} - 31773 x^{8} + 6729 x^{7} + 13914 x^{6} - 786 x^{5} - 2355 x^{4} + 57 x^{3} + 144 x^{2} - 6 x - 1$ |
$18$ |
[18,0] |
$3^{30}\cdot 5^{12}\cdot 11^{10}$ |
$3$ |
$69.14067034$ |
$118.99821203205568$ |
|
|
? |
$\He_3:C_4$ (as 18T49) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$39669265431.8$ |
