| 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 |
| 13.1.57655000561921.1 |
$x^{13} - 3 x^{12} + 7 x^{11} - 10 x^{10} + 15 x^{9} - 17 x^{8} + 19 x^{7} - 18 x^{6} + 15 x^{5} - 12 x^{4} + 6 x^{3} - 3 x^{2} + 2 x - 1$ |
$13$ |
[1,6] |
$7^{4}\cdot 83^{2}\cdot 1867^{2}$ |
$3$ |
$11.4426317504$ |
$1867.194834176372$ |
|
|
? |
$A_{13}$ (as 13T8) |
trivial |
$2$ |
$6$ |
$43.4347813984$ |
| 13.1.1414971204906609.1 |
$x^{13} - x^{12} + x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + 4 x^{5} - 5 x^{4} + 4 x^{3} - 2 x + 1$ |
$13$ |
[1,6] |
$3^{6}\cdot 7^{2}\cdot 29^{2}\cdot 6863^{2}$ |
$4$ |
$14.6366646729$ |
$5305.167415671284$ |
|
|
? |
$A_{13}$ (as 13T8) |
trivial |
$2$ |
$6$ |
$307.196082794$ |
| 13.5.5749519947196921.1 |
$x^{13} - 2 x^{12} - 3 x^{11} + 7 x^{10} + 5 x^{9} - 16 x^{8} - 6 x^{7} + 18 x^{6} + 2 x^{5} - 16 x^{4} - 4 x^{3} + 7 x^{2} + x - 1$ |
$13$ |
[5,4] |
$7^{4}\cdot 241^{2}\cdot 6421^{2}$ |
$3$ |
$16.3034438732$ |
$27143.05132536518$ |
|
|
? |
$A_{13}$ (as 13T8) |
trivial |
$2$ |
$8$ |
$838.358604129$ |
| 13.5.274918279650903001.1 |
$x^{13} - 3 x^{11} - 2 x^{10} + 2 x^{9} + 4 x^{8} - 2 x^{7} - 3 x^{6} - x^{5} + 3 x^{4} - 4 x^{2} + 1$ |
$13$ |
[5,4] |
$47^{2}\cdot 89^{2}\cdot 163^{2}\cdot 769^{2}$ |
$4$ |
$21.9521570645$ |
$101667.42283652654$ |
|
|
? |
$A_{13}$ (as 13T8) |
trivial |
$2$ |
$8$ |
$12272.0363797$ |
| 13.13.308...625.1 |
$x^{13} - 2 x^{12} - 306 x^{11} + 737 x^{10} + 35420 x^{9} - 94473 x^{8} - 1919784 x^{7} + 5276958 x^{6} + 48766779 x^{5} - 126847180 x^{4} - 502327474 x^{3} + 1061716068 x^{2} + 1350962689 x - 1362894158$ |
$13$ |
[13,0] |
$3^{28}\cdot 5^{18}\cdot 29^{12}$ |
$3$ |
$2214.91082149$ |
$16854.804228764082$ |
|
|
? |
$A_{13}$ (as 13T8) |
trivial |
$2$ |
$12$ |
$4344433704670000000$ |
