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 |
22.2.344...000.1 |
$x^{22} - 22 x^{11} - 4$ |
$22$ |
[2,10] |
$2^{20}\cdot 5^{11}\cdot 11^{20}$ |
$3$ |
$37.1423396803$ |
$56.20127598128519$ |
|
|
? |
$D_{11}:F_{11}$ (as 22T15) |
trivial |
$2$ |
$11$ |
$432770899.224$ |
22.0.333...000.1 |
$x^{22} - 4 x^{11} + 5$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 5^{10}\cdot 11^{22}$ |
$3$ |
$45.7231685927$ |
|
|
|
✓ |
$D_{11}:F_{11}$ (as 22T15) |
trivial |
$4$ |
$10$ |
$9003752939.67$ |
22.2.416...000.1 |
$x^{22} - 14 x^{11} + 4$ |
$22$ |
[2,10] |
$2^{20}\cdot 5^{11}\cdot 11^{22}$ |
$3$ |
$46.1892935331$ |
$56.20127598128519$ |
|
|
? |
$D_{11}:F_{11}$ (as 22T15) |
trivial |
$2$ |
$11$ |
$4417709133.13$ |
22.0.341...000.1 |
$x^{22} - 128 x^{11} + 5120$ |
$22$ |
[0,11] |
$-\,2^{32}\cdot 5^{10}\cdot 11^{22}$ |
$3$ |
$62.6567891056$ |
|
|
|
? |
$D_{11}:F_{11}$ (as 22T15) |
trivial |
$4$ |
$10$ |
$293138871458$ |
22.22.144...832.1 |
$x^{22} - 110 x^{20} + 4961 x^{18} - 120010 x^{16} + 1717628 x^{14} - 15154920 x^{12} - 113976 x^{11} + 83059603 x^{10} + 2713744 x^{9} - 276604790 x^{8} - 23295712 x^{7} + 527297551 x^{6} + 84739424 x^{5} - 505302050 x^{4} - 110247720 x^{3} + 171802697 x^{2} + 14699696 x - 16203074$ |
$22$ |
[22,0] |
$2^{43}\cdot 11^{22}\cdot 17^{10}$ |
$3$ |
$154.548380728$ |
|
|
|
? |
$D_{11}:F_{11}$ (as 22T15) |
trivial |
$2$ |
$21$ |
$372931478202000000$ |
22.22.961...968.1 |
$x^{22} - 154 x^{20} + 9977 x^{18} - 356510 x^{16} + 7743164 x^{14} - 106106616 x^{12} - 569132 x^{11} + 920181163 x^{10} + 25806220 x^{9} - 4917829378 x^{8} - 418434192 x^{7} + 15202800943 x^{6} + 2845252564 x^{5} - 23934195670 x^{4} - 7007773300 x^{3} + 14018600321 x^{2} + 2956714508 x - 2857488932$ |
$22$ |
[22,0] |
$2^{43}\cdot 11^{22}\cdot 41^{10}$ |
$3$ |
$230.596688401$ |
|
|
|
? |
$D_{11}:F_{11}$ (as 22T15) |
trivial |
$2$ |
$21$ |
$30149249254500000000$ |