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 |
11.9.7530807227563.1 |
$x^{11} - x^{10} - 6 x^{9} + 5 x^{8} + 10 x^{7} - 8 x^{6} + 5 x^{4} - 10 x^{3} - 2 x^{2} + 4 x + 1$ |
$11$ |
[9,1] |
$-\,29\cdot 131\cdot 5399\cdot 367163$ |
$4$ |
$14.8122815114$ |
$2744231.6278993287$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$9$ |
$302.713730235$ |
11.9.8674315276967.1 |
$x^{11} - x^{10} - 7 x^{9} + 3 x^{8} + 19 x^{7} + 3 x^{6} - 24 x^{5} - 12 x^{4} + 13 x^{3} + 7 x^{2} - 2 x - 1$ |
$11$ |
[9,1] |
$-\,8674315276967$ |
$1$ |
$15.0038668109$ |
$2945219.0541565833$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$9$ |
$312.159083126$ |
11.9.8692675390643.1 |
$x^{11} - 3 x^{10} - x^{9} + 6 x^{8} + x^{7} + 4 x^{6} - 8 x^{5} - 14 x^{4} + 9 x^{3} + 7 x^{2} - 2 x - 1$ |
$11$ |
[9,1] |
$-\,151\cdot 2311\cdot 24910163$ |
$3$ |
$15.006751063$ |
$2948334.3417331423$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$9$ |
$330.73377624737765$ |
11.9.10298992926983.1 |
$x^{11} - 3 x^{10} - 3 x^{9} + 16 x^{8} - 6 x^{7} - 26 x^{6} + 27 x^{5} + 11 x^{4} - 24 x^{3} + 2 x^{2} + 5 x - 1$ |
$11$ |
[9,1] |
$-\,10298992926983$ |
$1$ |
$15.2398727873$ |
$3209204.4071674524$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$9$ |
$346.83130282469835$ |
11.9.17524013040643.1 |
$x^{11} - 3 x^{10} - x^{9} + 7 x^{8} - 2 x^{7} + 4 x^{6} - 2 x^{5} - 16 x^{4} + 4 x^{3} + 9 x^{2} - x - 1$ |
$11$ |
[9,1] |
$-\,17524013040643$ |
$1$ |
$15.9943534117$ |
$4186169.256091182$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$9$ |
$460.0899562934776$ |
11.9.31015897276291.1 |
$x^{11} - 3 x^{10} - x^{9} + 7 x^{8} - 8 x^{7} + 6 x^{6} + 13 x^{5} - 17 x^{4} - 7 x^{3} + 8 x^{2} + x - 1$ |
$11$ |
[9,1] |
$-\,31015897276291$ |
$1$ |
$16.846421715$ |
$5569191.797405706$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$9$ |
$759.0484978493934$ |