| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.15.18.10 |
$15$ |
$x^{15} - 105 x^{13} + 30 x^{12} + 4575 x^{11} - 2085 x^{10} + 58925 x^{9} + 44700 x^{8} - 10200 x^{7} + 23875 x^{6} - 10425 x^{5} + 1500 x^{4} - 2625 x^{3} + 750 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$D_5\times C_3$ (as 15T3) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(20 t^{2} + 10 t + 5\right) x^{3} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.15.18.42 |
$15$ |
$x^{15} + 45 x^{12} - 75 x^{11} + 15 x^{10} + 2050 x^{9} - 1125 x^{8} + 450 x^{7} + 3000 x^{6} + 75 x^{5} + 3375 x^{4} + 1125 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$D_5\times C_3$ (as 15T3) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 10\right) x^{3} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.15.24.70 |
$15$ |
$x^{15} + 15 x^{14} + 75 x^{13} + 125 x^{12} - 135 x^{10} - 1350 x^{9} - 3375 x^{8} + 73575 x^{5} + 367875 x^{4} + 496375$ |
$5$ |
$5$ |
$3$ |
$24$ |
$D_5\times C_3$ (as 15T3) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 5 x^{4} + 50 t^{2} + 100 t + 55$ |
$[4, 0]$ |
$[2]$ |
