Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.15.22.1 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{8} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.10 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.11 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.12 |
$15$ |
$x^{15} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.13 |
$15$ |
$x^{15} + 6 x^{12} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.14 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.15 |
$15$ |
$x^{15} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.16 |
$15$ |
$x^{15} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.17 |
$15$ |
$x^{15} + 3 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.18 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.19 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 6 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 6 x^{8} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.2 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.20 |
$15$ |
$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.21 |
$15$ |
$x^{15} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.22 |
$15$ |
$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.23 |
$15$ |
$x^{15} + 3 x^{12} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.24 |
$15$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.25 |
$15$ |
$x^{15} + 3 x^{11} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.26 |
$15$ |
$x^{15} + 6 x^{11} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.27 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.28 |
$15$ |
$x^{15} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.29 |
$15$ |
$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.3 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{10} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{10} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.30 |
$15$ |
$x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.31 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.32 |
$15$ |
$x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.33 |
$15$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T41) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.34 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.35 |
$15$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.36 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.4 |
$15$ |
$x^{15} + 3 x^{11} + 6 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 6 x^{8} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.5 |
$15$ |
$x^{15} + 6 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 6 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.6 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.7 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$ |
$[8, 0]$ |
$[2, 4]$ |
3.15.22.8 |
$15$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3\wr F_5$ (as 15T56) |
$12$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$ |
$[8, 0]$ |
$[1, 4]$ |
3.15.22.9 |
$15$ |
$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$ |
$3$ |
$15$ |
$1$ |
$22$ |
$C_3^4:F_5$ (as 15T42) |
$4$ |
$5$ |
$[9/5]$ |
$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$ |
$[8, 0]$ |
$[2, 4]$ |