| 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 |
| 5.10.1.0a1.1 |
$10$ |
$x^{10} + 3 x^{5} + 3 x^{4} + 2 x^{3} + 4 x^{2} + x + 2$ |
$5$ |
$10$ |
$1$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{10} + 3 t^{5} + 3 t^{4} + 2 t^{3} + 4 t^{2} + t + 2$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.5.2.5a1.1 |
$10$ |
$( x^{5} + 4 x + 3 )^{2} + 5 x$ |
$5$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + 4 t + 3$ |
$x^{2} + 5 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.5.2.5a1.2 |
$10$ |
$( x^{5} + 4 x + 3 )^{2} + 5$ |
$5$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + 4 t + 3$ |
$x^{2} + 5$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.2.5.10a1.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 20 ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t + 1)$ |
undefined |
| 5.2.5.10a2.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 15 ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 15 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 2)$ |
undefined |
| 5.2.5.10a3.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 10 ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t + 3)$ |
undefined |
| 5.2.5.10a4.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t + 4)$ |
undefined |
| 5.2.5.10a5.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 20 x ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t + 2)$ |
undefined |
| 5.2.5.10a6.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 3 t$ |
undefined |
| 5.2.5.10a7.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 15 x ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (3 t + 4)$ |
undefined |
| 5.2.5.10a8.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(15 x + 20\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
undefined |
| 5.2.5.10a9.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(15 x + 15\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 5\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (4 t + 1)$ |
undefined |
| 5.2.5.10a10.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 10 x ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 t x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t + 1)$ |
undefined |
| 5.2.5.10a11.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 20\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.2.5.10a12.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 x ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 t x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 3)$ |
undefined |
| 5.2.5.10a13.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 15\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 2 t$ |
undefined |
| 5.2.5.10a14.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5$ |
$5$ |
$2$ |
$5$ |
$10$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 10\right) x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.2.5.12a1.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 10 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$D_{10}$ (as 10T3) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 5.2.5.12a2.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 20 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$F_5$ (as 10T4) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 5.2.5.12a3.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$F_5$ (as 10T4) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 4$ |
undefined |
| 5.2.5.12a4.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 15 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$D_{10}$ (as 10T3) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 2$ |
undefined |
| 5.2.5.12a5.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 10 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 t x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (2 t + 3)$ |
undefined |
| 5.2.5.12a6.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t + 2)$ |
undefined |
| 5.2.5.12a7.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 20 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (4 t + 1)$ |
undefined |
| 5.2.5.12a8.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$D_5^2$ (as 10T9) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (4 t + 4)$ |
undefined |
| 5.2.5.12a9.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(20 x + 20\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$D_5^2$ (as 10T9) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (4 t + 2)$ |
undefined |
| 5.2.5.12a10.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 t x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (t + 4)$ |
undefined |
| 5.2.5.12a11.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (t + 2)$ |
undefined |
| 5.2.5.12a12.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 15 x ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 15\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (3 t + 2)$ |
undefined |
| 5.2.5.12a13.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(15 x + 20\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_4$ (as 10T10) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (3 t + 3)$ |
undefined |
| 5.2.5.12a14.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(15 x + 5\right) ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$5$ |
$12$ |
$C_5^2 : C_8$ (as 10T18) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 20\right) x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (3 t + 1)$ |
undefined |
| 5.2.5.14a1.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 15 ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 15 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (4 t + 3)$ |
undefined |
| 5.2.5.14a2.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (3 t + 1)$ |
undefined |
| 5.2.5.14a3.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 20 ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 20 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 4)$ |
undefined |
| 5.2.5.14a4.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 10 ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4}]_{4}^{2}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (t + 2)$ |
undefined |
| 5.2.5.14a5.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 15 x ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 15\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 1)$ |
undefined |
| 5.2.5.14a6.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(15 x + 20\right) ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 10\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 4 t$ |
undefined |
| 5.2.5.14a7.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 x ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 t x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (4 t + 2)$ |
undefined |
| 5.2.5.14a8.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 15\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 3 t$ |
undefined |
| 5.2.5.14a9.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(5 x + 5\right) ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 5\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 3)$ |
undefined |
| 5.2.5.14a10.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 20 x ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 20\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (t + 3)$ |
undefined |
| 5.2.5.14a11.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(5 t + 10\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.2.5.14a12.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 10 x ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 t x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + (3 t + 4)$ |
undefined |
| 5.2.5.14a13.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(10 x + 5\right) ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$(C_5^2 : C_4) : C_2$ (as 10T17) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 5\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + t$ |
undefined |
| 5.2.5.14a14.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$5$ |
$14$ |
$C_5^2 : C_8$ (as 10T18) |
$2$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}, \frac{7}{4}]_{4}^{2}$ |
$[\frac{3}{4},\frac{3}{4}]_{4}^{2}$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$1$ |
$t^{2} + 4 t + 2$ |
$x^{5} + \left(10 t + 20\right) x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 3$ |
undefined |
| 5.2.5.16a1.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$5$ |
$16$ |
$D_5$ (as 10T2) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 x^{4} + 5$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.2.5.16a1.2 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 ( x^{2} + 4 x + 2 )^{4} + 25 x + 5$ |
$5$ |
$2$ |
$5$ |
$16$ |
$D_5\times C_5$ (as 10T6) |
$10$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{10}$ |
$[1]^{10}$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 x^{4} + 25 t + 5$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.2.5.16a1.3 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 5 ( x^{2} + 4 x + 2 )^{4} + 50 x + 5$ |
$5$ |
$2$ |
$5$ |
$16$ |
$D_5\times C_5$ (as 10T6) |
$10$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{10}$ |
$[1]^{10}$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$5$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 5 x^{4} + 50 t + 5$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.2.5.16a2.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 10 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$5$ |
$16$ |
$F_5$ (as 10T4) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2]$ |
$z^4 + 3$ |
undefined |
| 5.2.5.16a3.1 |
$10$ |
$( x^{2} + 4 x + 2 )^{5} + 15 ( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$5$ |
$16$ |
$F_5$ (as 10T4) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x^{5} + 15 x^{4} + 5$ |
$[4, 0]$ |
$[2]$ |
$z^4 + 2$ |
undefined |
