| $x^{10} + 5 a_{3} x^{3} + 5 d_{0}$ |
| Label |
Packet size |
Polynomial |
Galois group |
Galois degree |
$\#\Aut(K/\Q_p)$ |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 5.1.10.12a1.1 |
4 |
$x^{10} + 5 x^{3} + 5$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$400$ |
$1$ |
$[\frac{11}{8}, \frac{11}{8}]_{8}^{2}$ |
$[\frac{3}{8},\frac{3}{8}]_{8}^{2}$ |
$[\frac{11}{8}]^{2}_{4}$ |
$[\frac{3}{8}]^{2}_{4}$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 2$ |
undefined |
| 5.1.10.12a1.2 |
4 |
$x^{10} + 10 x^{3} + 5$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$400$ |
$1$ |
$[\frac{11}{8}, \frac{11}{8}]_{8}^{2}$ |
$[\frac{3}{8},\frac{3}{8}]_{8}^{2}$ |
$[\frac{11}{8}]^{2}_{4}$ |
$[\frac{3}{8}]^{2}_{4}$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 4$ |
undefined |
| 5.1.10.12a1.3 |
4 |
$x^{10} + 5 x^{3} + 10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$400$ |
$1$ |
$[\frac{11}{8}, \frac{11}{8}]_{8}^{2}$ |
$[\frac{3}{8},\frac{3}{8}]_{8}^{2}$ |
$[\frac{11}{8}]^{2}_{4}$ |
$[\frac{3}{8}]^{2}_{4}$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 1$ |
undefined |
| 5.1.10.12a1.4 |
4 |
$x^{10} + 10 x^{3} + 10$ |
$(C_5^2 : C_8):C_2$ (as 10T28) |
$400$ |
$1$ |
$[\frac{11}{8}, \frac{11}{8}]_{8}^{2}$ |
$[\frac{3}{8},\frac{3}{8}]_{8}^{2}$ |
$[\frac{11}{8}]^{2}_{4}$ |
$[\frac{3}{8}]^{2}_{4}$ |
$[3, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z + 2$ |
undefined |
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