$p$-adic field search results

Note: Search results may be incomplete due to uncomputed quantities: galois_label (239087 objects)

Results (4 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
5.2.10.26a7.5	$20$	$( x^{2} + 4 x + 2 )^{10} + 10 ( x^{2} + 4 x + 2 )^{5} + \left(5 x + 15\right) ( x^{2} + 4 x + 2 )^{4} + 5$	$5$	$2$	$10$	$26$	$D_5^2$ (as 20T28)	not computed	not computed	$[\frac{3}{2}]$	$[\frac{1}{2}]$	not computed	not computed	not computed	not computed	$10$	$t^{2} + 4 t + 2$	$x^{10} + \left(5 t + 15\right) x^{4} + 5$	$[4, 0]$	$[1, 1]$	$z^5 + 2,2 z^4 + (t + 1)$	undefined
5.2.10.26a17.5	$20$	$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{5} + \left(20 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + 5$	$5$	$2$	$10$	$26$	$D_5^2$ (as 20T28)	not computed	not computed	$[\frac{3}{2}]$	$[\frac{1}{2}]$	not computed	not computed	not computed	not computed	$10$	$t^{2} + 4 t + 2$	$x^{10} + \left(20 t + 10\right) x^{4} + 5$	$[4, 0]$	$[1, 1]$	$z^5 + 2,2 z^4 + (4 t + 4)$	undefined
5.2.10.34a2.75	$20$	$( x^{2} + 4 x + 2 )^{10} + 5 ( x^{2} + 4 x + 2 )^{9} + 5 ( x^{2} + 4 x + 2 )^{8} + 5$	$5$	$2$	$10$	$34$	$D_5^2$ (as 20T28)	not computed	not computed	$[2]$	$[1]$	not computed	not computed	not computed	not computed	$10$	$t^{2} + 4 t + 2$	$x^{10} + 5 x^{9} + 5 x^{8} + 5$	$[8, 0]$	$[1, 1]$	$z^5 + 2,2 z^4 + 2$	undefined
5.2.10.34a2.96	$20$	$( x^{2} + 4 x + 2 )^{10} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{9} + 5 ( x^{2} + 4 x + 2 )^{8} + 25 x + 5$	$5$	$2$	$10$	$34$	$D_5^2$ (as 20T28)	not computed	not computed	$[2]$	$[1]$	not computed	not computed	not computed	not computed	$10$	$t^{2} + 4 t + 2$	$x^{10} + \left(5 t + 10\right) x^{9} + 5 x^{8} + 5$	$[8, 0]$	$[1, 1]$	$z^5 + 2,2 z^4 + 2$	undefined

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