| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.15.10.1 |
$15$ |
$x^{15} + 25 x^{12} + 12 x^{11} + 9 x^{10} + 250 x^{9} - 900 x^{8} - 1302 x^{7} + 1322 x^{6} - 1773 x^{5} + 11325 x^{4} + 4989 x^{3} + 16494 x^{2} - 717 x + 2572$ |
$5$ |
$3$ |
$5$ |
$10$ |
$S_3 \times C_5$ (as 15T4) |
$10$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{10}$ |
$t^{5} + 4 t + 3$ |
$x^{3} + 5$ |
$[0]$ |
$[2]$ |
| 5.15.26.148 |
$15$ |
$x^{15} + 5 x^{14} + 20 x^{12} + 20 x^{10} + 80$ |
$5$ |
$15$ |
$1$ |
$26$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 20 x^{12} + 20 x^{10} + 80$ |
$[12, 0]$ |
$[1, 2]$ |
| 5.15.26.174 |
$15$ |
$x^{15} + 15 x^{14} + 20 x^{12} + 10 x^{10} + 30$ |
$5$ |
$15$ |
$1$ |
$26$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 20 x^{12} + 10 x^{10} + 30$ |
$[12, 0]$ |
$[1, 2]$ |
| 5.15.26.177 |
$15$ |
$x^{15} + 15 x^{14} + 20 x^{12} + 10 x^{10} + 105$ |
$5$ |
$15$ |
$1$ |
$26$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 20 x^{12} + 10 x^{10} + 105$ |
$[12, 0]$ |
$[1, 2]$ |
| 5.15.26.199 |
$15$ |
$x^{15} + 20 x^{12} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{12} + 5$ |
$[12, 0]$ |
$[1, 2]$ |
| 5.15.26.82 |
$15$ |
$x^{15} + 20 x^{12} + 55$ |
$5$ |
$15$ |
$1$ |
$26$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{12} + 55$ |
$[12, 0]$ |
$[1, 2]$ |
