| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.15.17.1 |
$15$ |
$x^{15} + 5 x^{4} + 15 x^{3} + 5$ |
$5$ |
$15$ |
$1$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[5/4]$ |
$[5/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{4} + 15 x^{3} + 5$ |
$[3, 0]$ |
$[1, 2]$ |
| 5.15.17.2 |
$15$ |
$x^{15} + 10 x^{3} + 5$ |
$5$ |
$15$ |
$1$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[5/4]$ |
$[5/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[1, 2]$ |
| 5.15.17.3 |
$15$ |
$x^{15} + 5 x^{3} + 5$ |
$5$ |
$15$ |
$1$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[5/4]$ |
$[5/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{3} + 5$ |
$[3, 0]$ |
$[1, 2]$ |
| 5.15.17.4 |
$15$ |
$x^{15} + 15 x^{4} + 20 x^{3} + 5$ |
$5$ |
$15$ |
$1$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[5/4]$ |
$[5/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{4} + 20 x^{3} + 5$ |
$[3, 0]$ |
$[1, 2]$ |
| 5.15.23.13 |
$15$ |
$x^{15} + 15 x^{12} + 10 x^{11} + 15 x^{10} + 5 x^{9} + 10 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$23$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[7/4]$ |
$[7/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{12} + 10 x^{11} + 15 x^{10} + 5 x^{9} + 10 x^{5} + 5$ |
$[9, 0]$ |
$[1, 2]$ |
| 5.15.23.5 |
$15$ |
$x^{15} + 10 x^{12} + 5 x^{11} + 10 x^{10} + 20 x^{9} + 5$ |
$5$ |
$15$ |
$1$ |
$23$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[7/4]$ |
$[7/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{12} + 5 x^{11} + 10 x^{10} + 20 x^{9} + 5$ |
$[9, 0]$ |
$[1, 2]$ |
| 5.15.23.8 |
$15$ |
$x^{15} + 5 x^{12} + 15 x^{11} + 20 x^{10} + 15 x^{9} + 15 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$23$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[7/4]$ |
$[7/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{12} + 15 x^{11} + 20 x^{10} + 15 x^{9} + 15 x^{5} + 5$ |
$[9, 0]$ |
$[1, 2]$ |
| 5.15.23.9 |
$15$ |
$x^{15} + 5 x^{12} + 20 x^{11} + 10 x^{10} + 10 x^{9} + 10 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$23$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[7/4]$ |
$[7/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{12} + 20 x^{11} + 10 x^{10} + 10 x^{9} + 10 x^{5} + 5$ |
$[9, 0]$ |
$[1, 2]$ |
| 5.15.29.114 |
$15$ |
$x^{15} + 20 x^{10} + 50 x^{4} + 25 x^{3} + 100 x^{2} + 80$ |
$5$ |
$15$ |
$1$ |
$29$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[9/4]$ |
$[9/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{10} + 50 x^{4} + 25 x^{3} + 100 x^{2} + 80$ |
$[15, 0]$ |
$[1, 2]$ |
| 5.15.29.124 |
$15$ |
$x^{15} + 10 x^{10} + 20 x^{5} + 100 x^{3} + 100 x^{2} + 100 x + 105$ |
$5$ |
$15$ |
$1$ |
$29$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[9/4]$ |
$[9/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{10} + 20 x^{5} + 100 x^{3} + 100 x^{2} + 100 x + 105$ |
$[15, 0]$ |
$[1, 2]$ |
| 5.15.29.6 |
$15$ |
$x^{15} + 15 x^{10} + 75 x^{2} + 55$ |
$5$ |
$15$ |
$1$ |
$29$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[9/4]$ |
$[9/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{10} + 75 x^{2} + 55$ |
$[15, 0]$ |
$[1, 2]$ |
| 5.15.29.7 |
$15$ |
$x^{15} + 15 x^{10} + 5 x^{5} + 50 x^{3} + 25 x + 55$ |
$5$ |
$15$ |
$1$ |
$29$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[9/4]$ |
$[9/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{10} + 5 x^{5} + 50 x^{3} + 25 x + 55$ |
$[15, 0]$ |
$[1, 2]$ |
| 5.15.29.74 |
$15$ |
$x^{15} + 20 x^{10} + 15 x^{5} + 100 x^{4} + 50 x^{2} + 75 x + 80$ |
$5$ |
$15$ |
$1$ |
$29$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[9/4]$ |
$[9/4]_{12}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{10} + 15 x^{5} + 100 x^{4} + 50 x^{2} + 75 x + 80$ |
$[15, 0]$ |
$[1, 2]$ |
