Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.15.19.1 |
$15$ |
$x^{15} + 3 x^{8} + 3 x^{7} + 3 x^{5} + 3$ |
$3$ |
$15$ |
$1$ |
$19$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[3/2]$ |
$[11/10, 11/10, 11/10, 11/10, 3/2]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{8} + 3 x^{7} + 3 x^{5} + 3$ |
$[5, 0]$ |
$[1, 4]$ |
3.15.19.2 |
$15$ |
$x^{15} + 6 x^{8} + 6 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$19$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[3/2]$ |
$[11/10, 11/10, 11/10, 11/10, 3/2]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{8} + 6 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$[5, 0]$ |
$[1, 4]$ |
3.15.19.3 |
$15$ |
$x^{15} + 6 x^{8} + 6 x^{7} + 6 x^{5} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$19$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[3/2]$ |
$[11/10, 11/10, 11/10, 11/10, 3/2]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{8} + 6 x^{7} + 6 x^{5} + 3 x^{3} + 3$ |
$[5, 0]$ |
$[1, 4]$ |
3.15.19.4 |
$15$ |
$x^{15} + 3 x^{8} + 3 x^{5} + 3$ |
$3$ |
$15$ |
$1$ |
$19$ |
$F_5 \times S_3$ (as 15T11) |
$4$ |
$10$ |
$[3/2]$ |
$[3/2]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{8} + 3 x^{5} + 3$ |
$[5, 0]$ |
$[1, 4]$ |
3.15.19.5 |
$15$ |
$x^{15} + 6 x^{5} + 3$ |
$3$ |
$15$ |
$1$ |
$19$ |
$F_5 \times S_3$ (as 15T11) |
$4$ |
$10$ |
$[3/2]$ |
$[3/2]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{5} + 3$ |
$[5, 0]$ |
$[1, 4]$ |
3.15.19.6 |
$15$ |
$x^{15} + 6 x^{8} + 6 x^{7} + 6 x^{5} + 3$ |
$3$ |
$15$ |
$1$ |
$19$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[3/2]$ |
$[11/10, 11/10, 11/10, 11/10, 3/2]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{8} + 6 x^{7} + 6 x^{5} + 3$ |
$[5, 0]$ |
$[1, 4]$ |