Note: Search results may be incomplete due to uncomputed quantities: galois_label (239087 objects), Hidden content (1054941 objects)
| 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 |
| 5.1.15.18a2.2 |
$15$ |
$x^{15} + 5 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 5 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a2.3 |
$15$ |
$x^{15} + 10 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 10 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a2.4 |
$15$ |
$x^{15} + 15 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 15 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
| 5.1.15.18a2.5 |
$15$ |
$x^{15} + 20 x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$C_5\wr S_3$ (as 15T32) |
$10$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{10}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{10}$ |
$[\frac{4}{3}]^{10}$ |
$[\frac{1}{3}]^{10}$ |
$5$ |
$t + 3$ |
$x^{15} + 20 x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[2, 1]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 2$ |
undefined |
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