| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.15.26.115 |
$15$ |
$x^{15} + 20 x^{14} + 20 x^{13} + 5 x^{12} + 10 x^{5} + 80$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 20 x^{13} + 5 x^{12} + 10 x^{5} + 80$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.120 |
$15$ |
$x^{15} + 20 x^{14} + 5 x^{13} + 5 x^{12} + 20 x^{5} + 80$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 5 x^{13} + 5 x^{12} + 20 x^{5} + 80$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.122 |
$15$ |
$x^{15} + 5 x^{14} + 15 x^{13} + 5 x^{12} + 15 x^{10} + 15 x^{5} + 105$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 15 x^{13} + 5 x^{12} + 15 x^{10} + 15 x^{5} + 105$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.127 |
$15$ |
$x^{15} + 5 x^{14} + 20 x^{13} + 5 x^{12} + 15 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 20 x^{13} + 5 x^{12} + 15 x^{5} + 5$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.128 |
$15$ |
$x^{15} + 10 x^{13} + 5 x^{12} + 5 x^{10} + 105$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{13} + 5 x^{12} + 5 x^{10} + 105$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.141 |
$15$ |
$x^{15} + 15 x^{13} + 5 x^{12} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{13} + 5 x^{12} + 5$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.150 |
$15$ |
$x^{15} + 10 x^{14} + 5 x^{12} + 5 x^{10} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 5 x^{12} + 5 x^{10} + 5$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.19 |
$15$ |
$x^{15} + 15 x^{14} + 5 x^{12} + 20 x^{10} + 15 x^{5} + 55$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 5 x^{12} + 20 x^{10} + 15 x^{5} + 55$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.24 |
$15$ |
$x^{15} + 15 x^{13} + 5 x^{12} + 5 x^{10} + 20 x^{5} + 105$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{13} + 5 x^{12} + 5 x^{10} + 20 x^{5} + 105$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.25 |
$15$ |
$x^{15} + 15 x^{14} + 10 x^{13} + 5 x^{12} + 10 x^{10} + 80$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 10 x^{13} + 5 x^{12} + 10 x^{10} + 80$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.35 |
$15$ |
$x^{15} + 15 x^{14} + 10 x^{13} + 5 x^{12} + 5 x^{10} + 15 x^{5} + 30$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 10 x^{13} + 5 x^{12} + 5 x^{10} + 15 x^{5} + 30$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.40 |
$15$ |
$x^{15} + 5 x^{14} + 5 x^{13} + 5 x^{12} + 15 x^{10} + 15 x^{5} + 30$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 5 x^{13} + 5 x^{12} + 15 x^{10} + 15 x^{5} + 30$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.41 |
$15$ |
$x^{15} + 5 x^{14} + 20 x^{13} + 5 x^{12} + 15 x^{10} + 105$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 20 x^{13} + 5 x^{12} + 15 x^{10} + 105$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.43 |
$15$ |
$x^{15} + 10 x^{14} + 10 x^{13} + 5 x^{12} + 5 x^{10} + 5 x^{5} + 80$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 10 x^{13} + 5 x^{12} + 5 x^{10} + 5 x^{5} + 80$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.46 |
$15$ |
$x^{15} + 10 x^{13} + 5 x^{12} + 15 x^{10} + 20 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{13} + 5 x^{12} + 15 x^{10} + 20 x^{5} + 5$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.49 |
$15$ |
$x^{15} + 15 x^{14} + 5 x^{13} + 5 x^{12} + 15 x^{10} + 55$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 5 x^{13} + 5 x^{12} + 15 x^{10} + 55$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.58 |
$15$ |
$x^{15} + 5 x^{14} + 20 x^{13} + 5 x^{12} + 55$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 20 x^{13} + 5 x^{12} + 55$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.59 |
$15$ |
$x^{15} + 20 x^{14} + 10 x^{13} + 5 x^{12} + 20 x^{10} + 5 x^{5} + 80$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 10 x^{13} + 5 x^{12} + 20 x^{10} + 5 x^{5} + 80$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.6 |
$15$ |
$x^{15} + 10 x^{14} + 15 x^{13} + 5 x^{12} + 20 x^{10} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 15 x^{13} + 5 x^{12} + 20 x^{10} + 5$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.68 |
$15$ |
$x^{15} + 10 x^{14} + 20 x^{13} + 5 x^{12} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 20 x^{13} + 5 x^{12} + 5$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.75 |
$15$ |
$x^{15} + 20 x^{14} + 20 x^{13} + 5 x^{12} + 20 x^{5} + 30$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 20 x^{13} + 5 x^{12} + 20 x^{5} + 30$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.9 |
$15$ |
$x^{15} + 15 x^{14} + 5 x^{13} + 5 x^{12} + 80$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 5 x^{13} + 5 x^{12} + 80$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.90 |
$15$ |
$x^{15} + 5 x^{14} + 10 x^{13} + 5 x^{12} + 10 x^{10} + 20 x^{5} + 5$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[5/3, 5/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 10 x^{13} + 5 x^{12} + 10 x^{10} + 20 x^{5} + 5$ |
$[12, 0]$ |
$[2, 2]$ |
| 5.15.26.92 |
$15$ |
$x^{15} + 20 x^{13} + 5 x^{12} + 15 x^{10} + 20 x^{5} + 30$ |
$5$ |
$15$ |
$1$ |
$26$ |
$C_5^2:D_{15}$ (as 15T31) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t + 3$ |
$x^{15} + 20 x^{13} + 5 x^{12} + 15 x^{10} + 20 x^{5} + 30$ |
$[12, 0]$ |
$[2, 2]$ |
