Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
7.15.0.1 |
$15$ |
$x^{15} + 5 x^{6} + 6 x^{5} + 6 x^{4} + 4 x^{3} + x^{2} + 2 x + 4$ |
$7$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]^{15}$ |
$t^{15} + 5 t^{6} + 6 t^{5} + 6 t^{4} + 4 t^{3} + t^{2} + 2 t + 4$ |
$x - 7$ |
$[0]$ |
$[]$ |
7.15.10.1 |
$15$ |
$x^{15} + 35 x^{12} + 3 x^{11} + 12 x^{10} + 490 x^{9} - 315 x^{8} - 2517 x^{7} + 3454 x^{6} - 834 x^{5} + 26565 x^{4} + 12846 x^{3} + 13662 x^{2} - 19944 x + 16290$ |
$7$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$t^{5} + t + 4$ |
$x^{3} + 7$ |
$[0]$ |
$[1]$ |
7.15.10.2 |
$15$ |
$x^{15} + 2401 x^{3} - 67228$ |
$7$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$t^{5} + t + 4$ |
$x^{3} + 7 t$ |
$[0]$ |
$[1]$ |
7.15.10.3 |
$15$ |
$x^{15} + 98 x^{9} + 2401 x^{3} + 268912$ |
$7$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$t^{5} + t + 4$ |
$x^{3} + 7 t^{2}$ |
$[0]$ |
$[1]$ |
7.15.12.1 |
$15$ |
$x^{15} + 30 x^{14} + 360 x^{13} + 2180 x^{12} + 6960 x^{11} + 12117 x^{10} + 17860 x^{9} + 33840 x^{8} + 45000 x^{7} + 90640 x^{6} - 100029 x^{5} - 595410 x^{4} - 585880 x^{3} + 441960 x^{2} + 576240 x + 404231$ |
$7$ |
$5$ |
$3$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{5} + 7$ |
$[0]$ |
$[4]$ |
7.15.14.1 |
$15$ |
$x^{15} + 7$ |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 4$ |
$x^{15} + 7$ |
$[0]$ |
$[4]$ |
7.15.14.2 |
$15$ |
$x^{15} + 14$ |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 4$ |
$x^{15} + 14$ |
$[0]$ |
$[4]$ |
7.15.14.3 |
$15$ |
$x^{15} + 21$ |
$7$ |
$15$ |
$1$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$t + 4$ |
$x^{15} + 21$ |
$[0]$ |
$[4]$ |