| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.13.12.1 |
$13$ |
$x^{13} + 5$ |
$5$ |
$13$ |
$1$ |
$12$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$13$ |
$[\ ]$ |
$[\ ]_{13}^{4}$ |
$t + 3$ |
$x^{13} + 5$ |
$[0]$ |
$[4]$ |
| 13.13.15.1 |
$13$ |
$x^{13} + 52 x^{3} + 13$ |
$13$ |
$13$ |
$1$ |
$15$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 11$ |
$x^{13} + 52 x^{3} + 13$ |
$[3, 0]$ |
$[1]$ |
| 13.13.15.2 |
$13$ |
$x^{13} + 117 x^{3} + 13$ |
$13$ |
$13$ |
$1$ |
$15$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 11$ |
$x^{13} + 117 x^{3} + 13$ |
$[3, 0]$ |
$[1]$ |
| 13.13.15.7 |
$13$ |
$x^{13} + 78 x^{3} + 13$ |
$13$ |
$13$ |
$1$ |
$15$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 11$ |
$x^{13} + 78 x^{3} + 13$ |
$[3, 0]$ |
$[1]$ |
| 13.13.15.8 |
$13$ |
$x^{13} + 91 x^{3} + 13$ |
$13$ |
$13$ |
$1$ |
$15$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 11$ |
$x^{13} + 91 x^{3} + 13$ |
$[3, 0]$ |
$[1]$ |
| 13.13.18.7 |
$13$ |
$x^{13} + 39 x^{6} + 13$ |
$13$ |
$13$ |
$1$ |
$18$ |
$C_{13}:C_4$ (as 13T4) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 11$ |
$x^{13} + 39 x^{6} + 13$ |
$[6, 0]$ |
$[2]$ |
| 13.13.18.8 |
$13$ |
$x^{13} + 130 x^{6} + 13$ |
$13$ |
$13$ |
$1$ |
$18$ |
$C_{13}:C_4$ (as 13T4) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 11$ |
$x^{13} + 130 x^{6} + 13$ |
$[6, 0]$ |
$[2]$ |
| 13.13.21.1 |
$13$ |
$x^{13} + 39 x^{9} + 13$ |
$13$ |
$13$ |
$1$ |
$21$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 11$ |
$x^{13} + 39 x^{9} + 13$ |
$[9, 0]$ |
$[1]$ |
| 13.13.21.2 |
$13$ |
$x^{13} + 130 x^{9} + 13$ |
$13$ |
$13$ |
$1$ |
$21$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 11$ |
$x^{13} + 130 x^{9} + 13$ |
$[9, 0]$ |
$[1]$ |
| 13.13.21.7 |
$13$ |
$x^{13} + 26 x^{9} + 13$ |
$13$ |
$13$ |
$1$ |
$21$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 11$ |
$x^{13} + 26 x^{9} + 13$ |
$[9, 0]$ |
$[1]$ |
| 13.13.21.8 |
$13$ |
$x^{13} + 143 x^{9} + 13$ |
$13$ |
$13$ |
$1$ |
$21$ |
$C_{13}:C_4$ (as 13T4) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 11$ |
$x^{13} + 143 x^{9} + 13$ |
$[9, 0]$ |
$[1]$ |
| 13.13.24.19 |
$13$ |
$x^{13} + 65 x^{12} + 13$ |
$13$ |
$13$ |
$1$ |
$24$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t + 11$ |
$x^{13} + 65 x^{12} + 13$ |
$[12, 0]$ |
$[4]$ |
| 13.13.24.20 |
$13$ |
$x^{13} + 104 x^{12} + 13$ |
$13$ |
$13$ |
$1$ |
$24$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t + 11$ |
$x^{13} + 104 x^{12} + 13$ |
$[12, 0]$ |
$[4]$ |
| 31.13.12.1 |
$13$ |
$x^{13} + 31$ |
$31$ |
$13$ |
$1$ |
$12$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$13$ |
$[\ ]$ |
$[\ ]_{13}^{4}$ |
$t + 28$ |
$x^{13} + 31$ |
$[0]$ |
$[4]$ |
| 47.13.12.1 |
$13$ |
$x^{13} + 47$ |
$47$ |
$13$ |
$1$ |
$12$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$13$ |
$[\ ]$ |
$[\ ]_{13}^{4}$ |
$t + 42$ |
$x^{13} + 47$ |
$[0]$ |
$[4]$ |
| 73.13.12.1 |
$13$ |
$x^{13} + 73$ |
$73$ |
$13$ |
$1$ |
$12$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$13$ |
$[\ ]$ |
$[\ ]_{13}^{4}$ |
$t + 68$ |
$x^{13} + 73$ |
$[0]$ |
$[4]$ |
| 83.13.12.1 |
$13$ |
$x^{13} + 83$ |
$83$ |
$13$ |
$1$ |
$12$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$13$ |
$[\ ]$ |
$[\ ]_{13}^{4}$ |
$t + 81$ |
$x^{13} + 83$ |
$[0]$ |
$[4]$ |
| 109.13.12.1 |
$13$ |
$x^{13} + 109$ |
$109$ |
$13$ |
$1$ |
$12$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$13$ |
$[\ ]$ |
$[\ ]_{13}^{4}$ |
$t + 103$ |
$x^{13} + 109$ |
$[0]$ |
$[4]$ |
| 151.13.12.1 |
$13$ |
$x^{13} + 151$ |
$151$ |
$13$ |
$1$ |
$12$ |
$C_{13}:C_4$ (as 13T4) |
$4$ |
$13$ |
$[\ ]$ |
$[\ ]_{13}^{4}$ |
$t + 145$ |
$x^{13} + 151$ |
$[0]$ |
$[4]$ |
