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 |
18.6.608...904.1 |
$x^{18} - 4 x^{17} + 4 x^{16} + 2 x^{15} - 21 x^{14} + 110 x^{13} - 211 x^{12} - 48 x^{11} + 635 x^{10} - 600 x^{9} - 216 x^{8} + 538 x^{7} - 180 x^{6} + 98 x^{5} - 177 x^{4} + 46 x^{3} + 25 x^{2} - 2 x - 1$ |
$18$ |
[6,6] |
$2^{42}\cdot 7^{12}$ |
$2$ |
$18.4417451682$ |
$24.616776431006123$ |
|
|
? |
$C_3^2:C_{12}$ (as 18T44) |
trivial |
$2$ |
$11$ |
$36150.1579213$ |
18.6.608...904.2 |
$x^{18} - 4 x^{17} + 2 x^{16} + 10 x^{15} - 27 x^{14} + 70 x^{13} - 103 x^{12} + 12 x^{11} + 98 x^{10} - 76 x^{9} + 106 x^{8} - 208 x^{7} + 336 x^{5} - 152 x^{4} - 176 x^{3} + 104 x^{2} + 16 x - 8$ |
$18$ |
[6,6] |
$2^{42}\cdot 7^{12}$ |
$2$ |
$18.4417451682$ |
$24.616776431006123$ |
|
|
? |
$C_3^2:C_{12}$ (as 18T44) |
trivial |
$2$ |
$11$ |
$26652.5198107$ |
18.18.890...625.1 |
$x^{18} - 42 x^{16} - 21 x^{15} + 639 x^{14} + 477 x^{13} - 4557 x^{12} - 3465 x^{11} + 17562 x^{10} + 10481 x^{9} - 40194 x^{8} - 12870 x^{7} + 55341 x^{6} - 41745 x^{4} + 13068 x^{3} + 11979 x^{2} - 7986 x + 1331$ |
$18$ |
[18,0] |
$3^{30}\cdot 5^{12}\cdot 11^{6}$ |
$3$ |
$40.5800884349$ |
$118.99821203205568$ |
|
|
? |
$C_3^2:C_{12}$ (as 18T44) |
trivial |
$2$ |
$17$ |
$473091347.54$ |
18.18.187...521.1 |
$x^{18} - 45 x^{16} - x^{15} + 756 x^{14} + 57 x^{13} - 5953 x^{12} - 1089 x^{11} + 23253 x^{10} + 8945 x^{9} - 46602 x^{8} - 30060 x^{7} + 42927 x^{6} + 43173 x^{5} - 7479 x^{4} - 21483 x^{3} - 8262 x^{2} - 972 x - 27$ |
$18$ |
[18,0] |
$3^{24}\cdot 13^{16}$ |
$2$ |
$42.2993351867$ |
$100.43012088175487$ |
|
|
? |
$C_3^2:C_{12}$ (as 18T44) |
trivial |
$2$ |
$17$ |
$637998345.319$ |