| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.15.0.1 |
$15$ |
$x^{15} + 2 x^{8} + x^{5} + 2 x^{2} + x + 1$ |
$3$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]^{15}$ |
$t^{15} + 2 t^{8} + t^{5} + 2 t^{2} + t + 1$ |
$x - 3$ |
$[0]$ |
$[]$ |
| 3.15.20.100 |
$15$ |
$x^{15} + 30 x^{14} + 360 x^{13} + 2076 x^{12} + 4464 x^{11} - 10368 x^{10} - 65250 x^{9} + 23004 x^{8} + 791208 x^{7} + 1628370 x^{6} + 551448 x^{5} + 1654344 x^{4} + 245592 x^{3} + 1473552 x^{2} + 7850115$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_{15}$ (as 15T1) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 18 t^{4} + 18 t^{3} + 18 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.65 |
$15$ |
$x^{15} + 30 x^{14} + 360 x^{13} + 2175 x^{12} + 6840 x^{11} + 11016 x^{10} + 13050 x^{9} + 21060 x^{8} + 9720 x^{7} + 24084 x^{6} + 55728 x^{5} + 167184 x^{4} + 79137 x^{3} + 474822 x^{2} + 138024$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_{15}$ (as 15T1) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 9 t^{3} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.15.20.99 |
$15$ |
$x^{15} + 30 x^{14} + 360 x^{13} + 2220 x^{12} + 7920 x^{11} + 20736 x^{10} + 54576 x^{9} + 127008 x^{8} + 295488 x^{7} + 682614 x^{6} + 1099656 x^{5} + 3298968 x^{4} + 2128842 x^{3} + 12773052 x^{2} + 9410175$ |
$3$ |
$3$ |
$5$ |
$20$ |
$C_{15}$ (as 15T1) |
$5$ |
$1$ |
$[2]$ |
$[2]^{5}$ |
$t^{5} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 18 t^{3} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
