| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 5.1.15.15a1.1 |
$15$ |
$x^{15} + 5 x + 5$ |
$5$ |
$1$ |
$15$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[\frac{13}{12}]$ |
$[\frac{1}{12}]$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x + 5$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 4$ |
undefined |
| 5.1.15.15a1.2 |
$15$ |
$x^{15} + 10 x + 5$ |
$5$ |
$1$ |
$15$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[\frac{13}{12}]$ |
$[\frac{1}{12}]$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x + 5$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.15a1.3 |
$15$ |
$x^{15} + 15 x + 5$ |
$5$ |
$1$ |
$15$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[\frac{13}{12}]$ |
$[\frac{1}{12}]$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x + 5$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 2$ |
undefined |
| 5.1.15.15a1.4 |
$15$ |
$x^{15} + 20 x + 5$ |
$5$ |
$1$ |
$15$ |
$15$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[\frac{13}{12}]$ |
$[\frac{1}{12}]$ |
$[\frac{13}{12}, \frac{13}{12}]_{12}^{2}$ |
$[\frac{1}{12},\frac{1}{12}]_{12}^{2}$ |
$[\frac{13}{12}]^{2}_{4}$ |
$[\frac{1}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x + 5$ |
$[1, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
| 5.1.15.16a1.1 |
$15$ |
$x^{15} + 10 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$16$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}, \frac{7}{6}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6}]_{6}^{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.16a1.2 |
$15$ |
$x^{15} + 15 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$16$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}, \frac{7}{6}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6}]_{6}^{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.16a2.1 |
$15$ |
$x^{15} + 5 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$16$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}, \frac{7}{6}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6}]_{6}^{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 3$ |
undefined |
| 5.1.15.16a2.2 |
$15$ |
$x^{15} + 20 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$16$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}, \frac{7}{6}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6}]_{6}^{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 2$ |
undefined |
| 5.1.15.17a1.1 |
$15$ |
$x^{15} + 5 x^{3} + 5$ |
$5$ |
$1$ |
$15$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{12}^{2}$ |
$[\frac{1}{4}]_{12}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{3} + 5$ |
$[3, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 2$ |
undefined |
| 5.1.15.17a1.2 |
$15$ |
$x^{15} + 10 x^{3} + 5$ |
$5$ |
$1$ |
$15$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{12}^{2}$ |
$[\frac{1}{4}]_{12}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 4$ |
undefined |
| 5.1.15.17a1.3 |
$15$ |
$x^{15} + 15 x^{3} + 5$ |
$5$ |
$1$ |
$15$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{12}^{2}$ |
$[\frac{1}{4}]_{12}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{3} + 5$ |
$[3, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
| 5.1.15.17a1.4 |
$15$ |
$x^{15} + 20 x^{3} + 5$ |
$5$ |
$1$ |
$15$ |
$17$ |
$F_5 \times S_3$ (as 15T11) |
$2$ |
$12$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{12}^{2}$ |
$[\frac{1}{4}]_{12}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{3} + 5$ |
$[3, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.18a1.1 |
$15$ |
$x^{15} + 5 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{4}$ |
$[\frac{4}{3}]^{4}$ |
$[\frac{1}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{4} + 5$ |
$[4, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 1$ |
undefined |
| 5.1.15.18a2.1 |
$15$ |
$x^{15} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$(C_5^2 : C_3):C_2$ (as 15T13) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$5$ |
$t + 3$ |
$x^{15} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a2.2 |
$15$ |
$x^{15} + 5 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 5 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a2.3 |
$15$ |
$x^{15} + 10 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 10 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a2.4 |
$15$ |
$x^{15} + 15 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 15 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a2.5 |
$15$ |
$x^{15} + 20 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 20 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a3.1 |
$15$ |
$x^{15} + 15 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$(C_5^2 : C_3):C_2$ (as 15T14) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{4} + 5$ |
$[4, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 3$ |
undefined |
| 5.1.15.18a4.1 |
$15$ |
$x^{15} + 20 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{4}$ |
$[\frac{4}{3}]^{4}$ |
$[\frac{1}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{4} + 5$ |
$[4, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 4$ |
undefined |
| 5.1.15.20a1.1 |
$15$ |
$x^{15} + 5 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_{15} : C_4$ (as 15T6) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{2}]_{6}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.20a1.2 |
$15$ |
$x^{15} + 5 x^{7} + 5 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{7} + 5 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.20a1.3 |
$15$ |
$x^{15} + 10 x^{7} + 5 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{7} + 5 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.20a1.4 |
$15$ |
$x^{15} + 15 x^{7} + 5 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{7} + 5 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.20a1.5 |
$15$ |
$x^{15} + 20 x^{7} + 5 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{7} + 5 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.20a1.6 |
$15$ |
$x^{15} + 20 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_{15} : C_4$ (as 15T6) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{2}]_{6}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.20a1.7 |
$15$ |
$x^{15} + 5 x^{7} + 20 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{7} + 20 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.20a1.8 |
$15$ |
$x^{15} + 10 x^{7} + 20 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{7} + 20 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.20a1.9 |
$15$ |
$x^{15} + 15 x^{7} + 20 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{7} + 20 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.20a1.10 |
$15$ |
$x^{15} + 20 x^{7} + 20 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5\wr C_3:C_4$ (as 15T37) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{7} + 20 x^{6} + 5$ |
$[6, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.20a2.1 |
$15$ |
$x^{15} + 10 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$D_5\times S_3$ (as 15T7) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{2}]_{6}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 3$ |
undefined |
| 5.1.15.20a2.2 |
$15$ |
$x^{15} + 5 x^{7} + 10 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{7} + 10 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 3$ |
undefined |
| 5.1.15.20a2.3 |
$15$ |
$x^{15} + 10 x^{7} + 10 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{7} + 10 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 3$ |
undefined |
| 5.1.15.20a2.4 |
$15$ |
$x^{15} + 15 x^{7} + 10 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{7} + 10 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 3$ |
undefined |
| 5.1.15.20a2.5 |
$15$ |
$x^{15} + 20 x^{7} + 10 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{7} + 10 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 3$ |
undefined |
| 5.1.15.20a2.6 |
$15$ |
$x^{15} + 15 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$D_5\times S_3$ (as 15T7) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{2}]_{6}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 2$ |
undefined |
| 5.1.15.20a2.7 |
$15$ |
$x^{15} + 5 x^{7} + 15 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{7} + 15 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 2$ |
undefined |
| 5.1.15.20a2.8 |
$15$ |
$x^{15} + 10 x^{7} + 15 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{7} + 15 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 2$ |
undefined |
| 5.1.15.20a2.9 |
$15$ |
$x^{15} + 15 x^{7} + 15 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{7} + 15 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 2$ |
undefined |
| 5.1.15.20a2.10 |
$15$ |
$x^{15} + 20 x^{7} + 15 x^{6} + 5$ |
$5$ |
$1$ |
$15$ |
$20$ |
$C_5^3:D_6$ (as 15T40) |
$2$ |
$6$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{7}{6}, \frac{7}{6}, \frac{3}{2}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6},\frac{1}{2}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6},\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{7} + 15 x^{6} + 5$ |
$[6, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 2$ |
undefined |
| 5.1.15.21a1.1 |
$15$ |
$x^{15} + 5 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{19}{12}]^{2}_{4}$ |
$[\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.21a1.2 |
$15$ |
$x^{15} + 5 x^{8} + 5 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{8} + 5 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.21a1.3 |
$15$ |
$x^{15} + 10 x^{8} + 5 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{8} + 5 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.21a1.4 |
$15$ |
$x^{15} + 15 x^{8} + 5 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{8} + 5 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.21a1.5 |
$15$ |
$x^{15} + 20 x^{8} + 5 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{8} + 5 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 3$ |
undefined |
| 5.1.15.21a1.6 |
$15$ |
$x^{15} + 10 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{19}{12}]^{2}_{4}$ |
$[\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
| 5.1.15.21a1.7 |
$15$ |
$x^{15} + 5 x^{8} + 10 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{8} + 10 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
| 5.1.15.21a1.8 |
$15$ |
$x^{15} + 10 x^{8} + 10 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{8} + 10 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
| 5.1.15.21a1.9 |
$15$ |
$x^{15} + 15 x^{8} + 10 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{8} + 10 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
| 5.1.15.21a1.10 |
$15$ |
$x^{15} + 20 x^{8} + 10 x^{7} + 5$ |
$5$ |
$1$ |
$15$ |
$21$ |
$C_5^3:(C_4\times S_3)$ (as 15T49) |
$2$ |
$12$ |
$[\frac{19}{12}]$ |
$[\frac{7}{12}]$ |
$[\frac{5}{4}, \frac{19}{12}, \frac{19}{12}]_{12}^{2}$ |
$[\frac{1}{4},\frac{7}{12},\frac{7}{12}]_{12}^{2}$ |
$[\frac{5}{4},\frac{19}{12}]^{2}_{4}$ |
$[\frac{1}{4},\frac{7}{12}]^{2}_{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{8} + 10 x^{7} + 5$ |
$[7, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z + 1$ |
undefined |
