| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 11.15.0.1 |
$15$ |
$x^{15} + 10 x^{6} + 7 x^{5} + 5 x^{3} + 9$ |
$11$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]^{15}$ |
$t^{15} + 10 t^{6} + 7 t^{5} + 5 t^{3} + 9$ |
$x - 11$ |
$[0]$ |
$[]$ |
| 11.15.10.1 |
$15$ |
$x^{15} + 85 x^{12} + 27 x^{10} - 140 x^{9} - 8370 x^{7} - 19350 x^{6} + 243 x^{5} + 134865 x^{4} + 4455 x^{3} + 29160 x^{2} - 467775 x + 1121310$ |
$11$ |
$3$ |
$5$ |
$10$ |
$S_3 \times C_5$ (as 15T4) |
$10$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{10}$ |
$t^{5} + 10 t^{2} + 9$ |
$x^{3} + 11$ |
$[0]$ |
$[2]$ |
| 11.15.12.1 |
$15$ |
$x^{15} + 10 x^{13} + 45 x^{12} + 40 x^{11} + 393 x^{10} + 890 x^{9} + 750 x^{8} - 3970 x^{7} + 9610 x^{6} + 13085 x^{5} + 151045 x^{4} + 26525 x^{3} + 116170 x^{2} - 53795 x + 67662$ |
$11$ |
$5$ |
$3$ |
$12$ |
$C_{15}$ (as 15T1) |
$3$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{3}$ |
$t^{3} + 2 t + 9$ |
$x^{5} + 11$ |
$[0]$ |
$[1]$ |
| 11.15.12.2 |
$15$ |
$x^{15} + 66 x^{10} + 21054 x^{5} - 8290799$ |
$11$ |
$5$ |
$3$ |
$12$ |
$C_{15}$ (as 15T1) |
$3$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{3}$ |
$t^{3} + 2 t + 9$ |
$x^{5} + 99 t + 22$ |
$[0]$ |
$[1]$ |
| 11.15.12.3 |
$15$ |
$x^{15} + 242 x^{5} - 11979$ |
$11$ |
$5$ |
$3$ |
$12$ |
$C_{15}$ (as 15T1) |
$3$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{3}$ |
$t^{3} + 2 t + 9$ |
$x^{5} + 11 t$ |
$[0]$ |
$[1]$ |
| 11.15.12.4 |
$15$ |
$x^{15} - 396 x^{10} + 98978 x^{5} + 74617191$ |
$11$ |
$5$ |
$3$ |
$12$ |
$C_{15}$ (as 15T1) |
$3$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{3}$ |
$t^{3} + 2 t + 9$ |
$x^{5} + 99 t^{2} + 22 t$ |
$[0]$ |
$[1]$ |
| 11.15.12.5 |
$15$ |
$x^{15} - 44 x^{10} + 484 x^{5} + 107811$ |
$11$ |
$5$ |
$3$ |
$12$ |
$C_{15}$ (as 15T1) |
$3$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{3}$ |
$t^{3} + 2 t + 9$ |
$x^{5} + 11 t^{2}$ |
$[0]$ |
$[1]$ |
| 11.15.14.1 |
$15$ |
$x^{15} + 11$ |
$11$ |
$15$ |
$1$ |
$14$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 9$ |
$x^{15} + 11$ |
$[0]$ |
$[2]$ |
| 11.15.14.2 |
$15$ |
$x^{15} + 33$ |
$11$ |
$15$ |
$1$ |
$14$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 9$ |
$x^{15} + 33$ |
$[0]$ |
$[2]$ |
| 11.15.14.3 |
$15$ |
$x^{15} + 22$ |
$11$ |
$15$ |
$1$ |
$14$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 9$ |
$x^{15} + 22$ |
$[0]$ |
$[2]$ |
| 11.15.14.4 |
$15$ |
$x^{15} + 55$ |
$11$ |
$15$ |
$1$ |
$14$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 9$ |
$x^{15} + 55$ |
$[0]$ |
$[2]$ |
| 11.15.14.5 |
$15$ |
$x^{15} + 44$ |
$11$ |
$15$ |
$1$ |
$14$ |
$S_3 \times C_5$ (as 15T4) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 9$ |
$x^{15} + 44$ |
$[0]$ |
$[2]$ |
