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 |
11.7.610429790897.1 |
$x^{11} - x^{10} - 4 x^{9} + x^{8} + 5 x^{7} + 7 x^{6} - 7 x^{5} - 5 x^{4} + 7 x^{3} - 3 x^{2} - x + 1$ |
$11$ |
[7,2] |
$610429790897$ |
$1$ |
$11.7874924921$ |
$781300.0645699449$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$8$ |
$49.9574794147$ |
11.7.808524990121.1 |
$x^{11} - 2 x^{10} - x^{9} + 4 x^{8} - x^{7} - 5 x^{6} - x^{5} + 8 x^{4} + 3 x^{3} - 5 x^{2} - x + 1$ |
$11$ |
[7,2] |
$43\cdot 547\cdot 34374601$ |
$3$ |
$12.0925414904$ |
$899180.1766726177$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$8$ |
$59.1581764769$ |
11.7.835929782249.1 |
$x^{11} - x^{10} - x^{9} - 3 x^{7} + 4 x^{6} + 2 x^{5} + x^{4} + 4 x^{3} - 6 x^{2} - 3 x + 1$ |
$11$ |
[7,2] |
$56509\cdot 14792861$ |
$2$ |
$12.1292407976$ |
$914291.956788968$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$8$ |
$60.09604192925153$ |
11.7.1135258109569.1 |
$x^{11} - 2 x^{10} - x^{9} + 5 x^{8} - 3 x^{7} - 2 x^{6} - 3 x^{5} + 3 x^{4} + 11 x^{3} - 5 x^{2} - 4 x + 1$ |
$11$ |
[7,2] |
$71\cdot 73\cdot 219034943$ |
$3$ |
$12.4714713129$ |
$1065484.9175699297$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$8$ |
$72.38649544528622$ |
11.7.1619043113033.1 |
$x^{11} - x^{10} - x^{9} + x^{8} + 3 x^{6} - 7 x^{5} - 7 x^{4} + 8 x^{3} + 5 x^{2} - 2 x - 1$ |
$11$ |
[7,2] |
$1619043113033$ |
$1$ |
$12.8804958805$ |
$1272416.2499092033$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$8$ |
$91.94897355015553$ |
11.7.1792166448977.1 |
$x^{11} - x^{10} - x^{9} + x^{8} - 3 x^{7} - 5 x^{6} + 11 x^{5} + 11 x^{4} - 9 x^{3} - 8 x^{2} + x + 1$ |
$11$ |
[7,2] |
$1792166448977$ |
$1$ |
$13.0000039928$ |
$1338718.2111919594$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$8$ |
$98.96130237811647$ |
11.7.2308712232653.1 |
$x^{11} - 2 x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 4 x^{6} + x^{5} - 6 x^{4} + 6 x^{3} + 2 x^{2} - 3 x - 1$ |
$11$ |
[7,2] |
$349\cdot 6615221297$ |
$2$ |
$13.3027892087$ |
$1519444.7119434783$ |
|
|
✓ |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$8$ |
$116.6813224133741$ |
11.7.630...384.1 |
$x^{11} - 3 x^{10} - 36 x^{9} + 60 x^{8} + 213 x^{7} - 9 x^{6} - 114 x^{5} - 180 x^{4} - 108 x^{3} + 6 x^{2} + 36 x + 54$ |
$11$ |
[7,2] |
$2^{12}\cdot 3^{14}\cdot 7^{2}\cdot 23^{2}\cdot 137^{8}$ |
$5$ |
$777.788029448$ |
$12681.160459728126$ |
|
|
|
$A_{11}$ (as 11T7) |
trivial |
$2$ |
$8$ |
$21261383857900$ |