Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
5.15.20.12 |
$15$ |
$x^{15} + 20 x^{8} + 20 x^{7} + 20 x^{6} + 10 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$20$ |
$C_{15} : C_4$ (as 15T6) |
$2$ |
$6$ |
$[3/2]$ |
$[3/2]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{8} + 20 x^{7} + 20 x^{6} + 10 x^{5} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
5.15.20.16 |
$15$ |
$x^{15} + 15 x^{8} + 5 x^{7} + 5 x^{6} + 10 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$20$ |
$C_{15} : C_4$ (as 15T6) |
$2$ |
$6$ |
$[3/2]$ |
$[3/2]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{8} + 5 x^{7} + 5 x^{6} + 10 x^{5} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
5.15.26.70 |
$15$ |
$x^{15} + 20 x^{14} + 15 x^{12} + 15 x^{10} + 55$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_{15} : C_4$ (as 15T6) |
$4$ |
$3$ |
$[2]$ |
$[2]_{3}^{4}$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 15 x^{12} + 15 x^{10} + 55$ |
$[12, 0]$ |
$[4, 2]$ |
5.15.26.79 |
$15$ |
$x^{15} + 15 x^{14} + 20 x^{13} + 10 x^{12} + 20 x^{10} + 10 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_{15} : C_4$ (as 15T6) |
$4$ |
$3$ |
$[2]$ |
$[2]_{3}^{4}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 20 x^{13} + 10 x^{12} + 20 x^{10} + 10 x^{5} + 5$ |
$[12, 0]$ |
$[4, 2]$ |