| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 23.10.0.1 |
$10$ |
$x^{10} + 17 x^{5} + 5 x^{4} + 15 x^{3} + 6 x^{2} + x + 5$ |
$23$ |
$1$ |
$10$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]^{10}$ |
$t^{10} + 17 t^{5} + 5 t^{4} + 15 t^{3} + 6 t^{2} + t + 5$ |
$x - 23$ |
$[0]$ |
$[\ ]$ |
| 23.10.5.1 |
$10$ |
$x^{10} - 3335 x^{9} + 21724972 x^{8} + 32175051716 x^{7} + 187094353927946 x^{6} + 562900511451090140 x^{5} + 3155504389465566 x^{4} - 101811190699272 x^{3} - 1679305412607 x^{2} - 10291712457 x - 115854174$ |
$23$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 3 t + 18$ |
$x^{2} + \left(345 t^{4} + 161 t^{3} + 253 t^{2} + 414 t + 161\right) x + 23 t$ |
$[0]$ |
$[1]$ |
| 23.10.5.2 |
$10$ |
$x^{10} + 115 x^{8} + 5296 x^{6} + 36 x^{5} + 120980 x^{4} - 8280 x^{3} + 1383344 x^{2} + 95328 x + 6509876$ |
$23$ |
$2$ |
$5$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$t^{5} + 3 t + 18$ |
$x^{2} + 23$ |
$[0]$ |
$[1]$ |
| 23.10.8.1 |
$10$ |
$x^{10} + 105 x^{9} + 4435 x^{8} + 94710 x^{7} + 1038805 x^{6} + 5025997 x^{5} + 5196440 x^{4} + 2466880 x^{3} + 2611955 x^{2} + 21422390 x + 88673277$ |
$23$ |
$5$ |
$2$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$t^{2} + 21 t + 5$ |
$x^{5} + 23$ |
$[0]$ |
$[2]$ |
| 23.10.9.1 |
$10$ |
$x^{10} + 115$ |
$23$ |
$10$ |
$1$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$t + 18$ |
$x^{10} + 115$ |
$[0]$ |
$[4]$ |
| 23.10.9.2 |
$10$ |
$x^{10} + 23$ |
$23$ |
$10$ |
$1$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$t + 18$ |
$x^{10} + 23$ |
$[0]$ |
$[4]$ |
