| 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 |
| 5.2.10.20a1.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 10\right) x + 5 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 1$ |
undefined |
| 5.2.10.20a1.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T115) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 1$ |
undefined |
| 5.2.10.20a2.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T115) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 2$ |
undefined |
| 5.2.10.20a3.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 10\right) x + 5 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + t$ |
undefined |
| 5.2.10.20a3.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T107) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + t$ |
undefined |
| 5.2.10.20a4.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 15\right) x + 5 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (t + 3)$ |
undefined |
| 5.2.10.20a4.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T107) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (t + 3)$ |
undefined |
| 5.2.10.20a5.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 5\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 20\right) x + 5 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 2 t$ |
undefined |
| 5.2.10.20a5.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T107) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 2 t$ |
undefined |
| 5.2.10.20a6.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 5\right) x + 5 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (2 t + 2)$ |
undefined |
| 5.2.10.20a6.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 10\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T107) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (2 t + 2)$ |
undefined |
| 5.2.10.20a7.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T115) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (3 t + 1)$ |
undefined |
| 5.2.10.20a8.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 20 x + 5 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (4 t + 1)$ |
undefined |
| 5.2.10.20a9.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$10$ |
$20$ |
$C_5^2:\OD_{16}$ (as 20T115) |
$2$ |
$8$ |
$[\frac{9}{8}]$ |
$[\frac{1}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (4 t + 3)$ |
undefined |
| 5.2.10.22a1.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_8$ (as 20T56) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 t x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 1$ |
undefined |
| 5.2.10.22a1.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times F_5$ (as 20T13) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 1$ |
undefined |
| 5.2.10.22a2.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times F_5$ (as 20T13) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 2$ |
undefined |
| 5.2.10.22a3.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times F_5$ (as 20T13) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 3$ |
undefined |
| 5.2.10.22a4.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times F_5$ (as 20T13) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 4$ |
undefined |
| 5.2.10.22a5.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 20\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 5\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + t$ |
undefined |
| 5.2.10.22a5.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 t x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + t$ |
undefined |
| 5.2.10.22a6.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_4^2$ (as 20T91) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 5\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + (t + 2)$ |
undefined |
| 5.2.10.22a7.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_8$ (as 20T56) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 5\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (t + 3)$ |
undefined |
| 5.2.10.22a7.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$D_5:F_5$ (as 20T54) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (t + 3)$ |
undefined |
| 5.2.10.22a8.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 x ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 10\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + 2 t$ |
undefined |
| 5.2.10.22a8.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + 2 t$ |
undefined |
| 5.2.10.22a9.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_8$ (as 20T56) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 10\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (2 t + 1)$ |
undefined |
| 5.2.10.22a9.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$D_5:F_5$ (as 20T54) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (2 t + 1)$ |
undefined |
| 5.2.10.22a10.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_8$ (as 20T56) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 10\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (2 t + 2)$ |
undefined |
| 5.2.10.22a10.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 20\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$D_5:F_5$ (as 20T54) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (2 t + 2)$ |
undefined |
| 5.2.10.22a11.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 15\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + 3 t$ |
undefined |
| 5.2.10.22a11.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 t x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + 3 t$ |
undefined |
| 5.2.10.22a12.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_4^2$ (as 20T91) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 15\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + (3 t + 1)$ |
undefined |
| 5.2.10.22a12.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + (3 t + 1)$ |
undefined |
| 5.2.10.22a13.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_4\times F_5$ (as 20T20) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 20\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + 4 t$ |
undefined |
| 5.2.10.22a13.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 15 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + 4 t$ |
undefined |
| 5.2.10.22a14.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_4^2$ (as 20T91) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 10\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + (4 t + 1)$ |
undefined |
| 5.2.10.22a15.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_8$ (as 20T56) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 5 t x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (4 t + 2)$ |
undefined |
| 5.2.10.22a15.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(15 x + 20\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$D_5:F_5$ (as 20T54) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (4 t + 2)$ |
undefined |
| 5.2.10.22a16.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(15 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_4^2$ (as 20T91) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 15 x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + (4 t + 3)$ |
undefined |
| 5.2.10.22a16.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(15 x + 5\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_2\times C_5^2:C_8$ (as 20T110) |
not computed |
not computed |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^2 + (4 t + 3)$ |
undefined |
| 5.2.10.22a17.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$22$ |
$C_5^2:C_8$ (as 20T56) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(20 t + 5\right) x^{2} + 5 t$ |
$[2, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + (4 t + 4)$ |
undefined |
| 5.2.10.24a1.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{3} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 20 t x^{3} + 5 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 1$ |
undefined |
| 5.2.10.24a1.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^2:\OD_{16}$ (as 20T115) |
$2$ |
$8$ |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 1$ |
undefined |
| 5.2.10.24a2.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^2:\OD_{16}$ (as 20T115) |
$2$ |
$8$ |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 20 x^{3} + 5$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 2$ |
undefined |
| 5.2.10.24a3.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{3} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 5\right) x^{3} + 5 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + t$ |
undefined |
| 5.2.10.24a3.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 10 x ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^2:\OD_{16}$ (as 20T107) |
$2$ |
$8$ |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 10\right) x^{3} + 5$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + t$ |
undefined |
| 5.2.10.24a4.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 )^{3} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^4.\OD_{32}$ (as 20T504) |
not computed |
not computed |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 5\right) x^{3} + 5 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (t + 3)$ |
undefined |
| 5.2.10.24a4.2 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^2:\OD_{16}$ (as 20T107) |
$2$ |
$8$ |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 15\right) x^{3} + 5$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + (t + 3)$ |
undefined |
| 5.2.10.24a5.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 5 x ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$10$ |
$24$ |
$C_5^2:\OD_{16}$ (as 20T107) |
$2$ |
$8$ |
$[\frac{11}{8}]$ |
$[\frac{3}{8}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(5 t + 20\right) x^{3} + 5$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 2 t$ |
undefined |
