$p$-adic field search results

The results below are complete, since the LMFDB contains all p-adic fields of degree at most 23 and residue characteristic at most 199

Results (6 matches)

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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
3.10.1.0a1.1	$10$	$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{4} + x + 2$	$3$	$10$	$1$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]$	$[\ ]$	$[\ ]^{10}$	$[\ ]^{10}$	$[\ ]$	$[\ ]$	$10$	$t^{10} + 2 t^{6} + 2 t^{5} + 2 t^{4} + t + 2$	$x - 3$	$[0]$	$[\ ]$		undefined
3.5.2.5a1.1	$10$	$( x^{5} + 2 x + 1 )^{2} + 3 x$	$3$	$5$	$2$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{5}$	$[\ ]_{2}^{5}$	$[\ ]$	$[\ ]$	$10$	$t^{5} + 2 t + 1$	$x^{2} + 3 t$	$[0]$	$[1]$	$z + 2$	undefined
3.5.2.5a1.2	$10$	$( x^{5} + 2 x + 1 )^{2} + 3$	$3$	$5$	$2$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]$	$[\ ]_{2}^{5}$	$[\ ]_{2}^{5}$	$[\ ]$	$[\ ]$	$10$	$t^{5} + 2 t + 1$	$x^{2} + 3$	$[0]$	$[1]$	$z + 2$	$[1]$
3.2.5.8a1.1	$10$	$( x^{2} + 2 x + 2 )^{5} + 3$	$3$	$2$	$5$	$8$	$F_5$ (as 10T4)	$4$	$5$	$[\ ]$	$[\ ]$	$[\ ]_{5}^{4}$	$[\ ]_{5}^{4}$	$[\ ]^{2}$	$[\ ]^{2}$	$2$	$t^{2} + 2 t + 2$	$x^{5} + 3$	$[0]$	$[2]$	$z^4 + 2 z^3 + z^2 + z + 2$	undefined
3.1.10.9a1.1	$10$	$x^{10} + 3$	$3$	$1$	$10$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]$	$[\ ]_{10}^{4}$	$[\ ]_{10}^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$2$	$t + 1$	$x^{10} + 3$	$[0]$	$[4]$	$z^9 + z^8 + 1$	$[5]$
3.1.10.9a1.2	$10$	$x^{10} + 6$	$3$	$1$	$10$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]$	$[\ ]_{10}^{4}$	$[\ ]_{10}^{4}$	$[\ ]^{4}$	$[\ ]^{4}$	$2$	$t + 1$	$x^{10} + 6$	$[0]$	$[4]$	$z^9 + z^8 + 1$	undefined

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