Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
19.15.0.1 |
$15$ |
$x^{15} + x^{7} + 10 x^{6} + 11 x^{5} + 13 x^{4} + 15 x^{3} + 14 x^{2} + 17$ |
$19$ |
$1$ |
$15$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]^{15}$ |
$t^{15} + t^{7} + 10 t^{6} + 11 t^{5} + 13 t^{4} + 15 t^{3} + 14 t^{2} + 17$ |
$x - 19$ |
$[0]$ |
$[\ ]$ |
19.15.10.1 |
$15$ |
$x^{15} + 95 x^{12} + 15 x^{11} + 51 x^{10} + 3610 x^{9} - 4275 x^{8} - 28995 x^{7} + 69100 x^{6} - 31623 x^{5} + 835620 x^{4} + 700180 x^{3} + 1194855 x^{2} - 1636410 x + 2391332$ |
$19$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$t^{5} + 5 t + 17$ |
$x^{3} + 19$ |
$[0]$ |
$[1]$ |
19.15.10.2 |
$15$ |
$x^{15} + 651605 x^{3} - 42093683$ |
$19$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$t^{5} + 5 t + 17$ |
$x^{3} + 19 t$ |
$[0]$ |
$[1]$ |
19.15.10.3 |
$15$ |
$x^{15} + 3610 x^{9} + 3258025 x^{3} + 715592611$ |
$19$ |
$3$ |
$5$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$t^{5} + 5 t + 17$ |
$x^{3} + 19 t^{2}$ |
$[0]$ |
$[1]$ |
19.15.12.1 |
$15$ |
$x^{15} + 20 x^{13} + 85 x^{12} + 160 x^{11} + 1417 x^{10} + 3530 x^{9} + 7020 x^{8} + 6890 x^{7} + 76970 x^{6} + 160207 x^{5} + 1168245 x^{4} + 470325 x^{3} + 1653430 x^{2} + 224615 x + 1762712$ |
$19$ |
$5$ |
$3$ |
$12$ |
$D_5\times C_3$ (as 15T3) |
$6$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{6}$ |
$t^{3} + 4 t + 17$ |
$x^{5} + 19$ |
$[0]$ |
$[2]$ |
19.15.14.1 |
$15$ |
$x^{15} + 19$ |
$19$ |
$15$ |
$1$ |
$14$ |
$D_5\times C_3$ (as 15T3) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 17$ |
$x^{15} + 19$ |
$[0]$ |
$[2]$ |
19.15.14.2 |
$15$ |
$x^{15} + 76$ |
$19$ |
$15$ |
$1$ |
$14$ |
$D_5\times C_3$ (as 15T3) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 17$ |
$x^{15} + 76$ |
$[0]$ |
$[2]$ |
19.15.14.3 |
$15$ |
$x^{15} + 38$ |
$19$ |
$15$ |
$1$ |
$14$ |
$D_5\times C_3$ (as 15T3) |
$2$ |
$15$ |
$[\ ]$ |
$[\ ]_{15}^{2}$ |
$t + 17$ |
$x^{15} + 38$ |
$[0]$ |
$[2]$ |