| 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 |
| 5.2.10.26a1.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_{10}.D_{10}$ (as 20T58) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 20\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + 1$ |
undefined |
| 5.2.10.26a1.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2}]_{2}^{4}$ |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{4} + 5$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + 1$ |
undefined |
| 5.2.10.26a2.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{5} + 10 x ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5^2:C_{20}$ (as 20T126) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{5} + \left(10 t + 15\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 2$ |
undefined |
| 5.2.10.26a2.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{5} + 10 x ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5:F_5$ (as 20T27) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 15\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 2$ |
undefined |
| 5.2.10.26a2.3 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{5} + 10 x ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5^2:C_{20}$ (as 20T126) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{5} + \left(10 t + 15\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 2$ |
undefined |
| 5.2.10.26a2.4 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$D_{10}$ (as 20T4) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$20$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 2$ |
undefined |
| 5.2.10.26a2.5 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{5} + 10 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times D_{10}$ (as 20T24) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 t x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 2$ |
undefined |
| 5.2.10.26a2.6 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{5} + 10 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times D_{10}$ (as 20T24) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 t x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 2$ |
undefined |
| 5.2.10.26a3.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$D_{10}$ (as 20T4) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$20$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 15 x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 3$ |
undefined |
| 5.2.10.26a3.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{5} + 15 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times D_{10}$ (as 20T24) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{5} + 15 x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 3$ |
undefined |
| 5.2.10.26a3.3 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{5} + 15 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times D_{10}$ (as 20T24) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{5} + 15 x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + 3$ |
undefined |
| 5.2.10.26a4.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2}]_{2}^{4}$ |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 20 x^{4} + 5$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + 4$ |
undefined |
| 5.2.10.26a5.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 15\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + t$ |
undefined |
| 5.2.10.26a5.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 5\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + t$ |
undefined |
| 5.2.10.26a6.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(15 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T113) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 15\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + (t + 2)$ |
undefined |
| 5.2.10.26a7.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$F_5$ (as 20T5) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$20$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 15\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (t + 3)$ |
undefined |
| 5.2.10.26a7.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{5} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times F_5$ (as 20T29) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{5} + \left(20 t + 15\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (t + 3)$ |
undefined |
| 5.2.10.26a7.3 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{5} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times D_5^2$ (as 20T124) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{5} + \left(20 t + 20\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (t + 3)$ |
undefined |
| 5.2.10.26a7.4 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{5} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times D_5^2$ (as 20T124) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{5} + \left(5 t + 15\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (t + 3)$ |
undefined |
| 5.2.10.26a7.5 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{5} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$D_5^2$ (as 20T28) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 15\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (t + 3)$ |
undefined |
| 5.2.10.26a8.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 10\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + 2 t$ |
undefined |
| 5.2.10.26a9.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(15 x + 5\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_4\times D_5$ (as 20T6) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 5\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + (2 t + 1)$ |
undefined |
| 5.2.10.26a9.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_{10}:F_5$ (as 20T52) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 15\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + (2 t + 1)$ |
undefined |
| 5.2.10.26a10.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 5\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_{10}.D_{10}$ (as 20T58) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 5\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + (2 t + 2)$ |
undefined |
| 5.2.10.26a10.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_{10}:F_5$ (as 20T52) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 10\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + (2 t + 2)$ |
undefined |
| 5.2.10.26a11.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 x ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 15\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + 3 t$ |
undefined |
| 5.2.10.26a12.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 20\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T113) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 20\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + (3 t + 1)$ |
undefined |
| 5.2.10.26a12.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(15 x + 5\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 20\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + (3 t + 1)$ |
undefined |
| 5.2.10.26a13.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T113) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + (3 t + 2)$ |
undefined |
| 5.2.10.26a14.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_4\times D_5$ (as 20T6) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 20\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + (3 t + 4)$ |
undefined |
| 5.2.10.26a15.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 x ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 20 t x^{4} + 5$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + 4 t$ |
undefined |
| 5.2.10.26a16.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T113) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + (4 t + 1)$ |
undefined |
| 5.2.10.26a17.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{5} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times F_5$ (as 20T29) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{5} + \left(5 t + 10\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 2)$ |
undefined |
| 5.2.10.26a17.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{5} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$F_5$ (as 20T5) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$20$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 10\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 2)$ |
undefined |
| 5.2.10.26a17.3 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 ( x^{2} + 4 x + 2 )^{5} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5\times D_5^2$ (as 20T124) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{5} + \left(5 t + 5\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 2)$ |
undefined |
| 5.2.10.26a17.4 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{5} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
not computed |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{5} + \left(5 t + 5\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 2)$ |
undefined |
| 5.2.10.26a17.5 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{5} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$D_5^2$ (as 20T28) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 10\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 2)$ |
undefined |
| 5.2.10.26a18.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T113) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 5\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + (4 t + 3)$ |
undefined |
| 5.2.10.26a18.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 10\right) x^{4} + 5$ |
$[4, 0]$ |
$[1, 4]$ |
$z^5 + 2,2 z^4 + (4 t + 3)$ |
undefined |
| 5.2.10.26a19.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 x ( x^{2} + 4 x + 2 )^{5} + \left(15 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5^2:C_{20}$ (as 20T126) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{5} + 15 t x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 4)$ |
undefined |
| 5.2.10.26a19.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{5} + \left(15 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5^2:C_{20}$ (as 20T126) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{5} + 15 t x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 4)$ |
undefined |
| 5.2.10.26a19.3 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 x ( x^{2} + 4 x + 2 )^{5} + \left(15 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5:F_5$ (as 20T27) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 10\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 4)$ |
undefined |
