$p$-adic field search results

Degree	Residue characteristic	Galois group	Galois unramified degree
Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree
Residue field degree	Top slope	Wild inertia subgroup

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Results (5 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
23.4.0.1	$4$	x^4 - x + 11	$23$	$1$	$4$	$0$	$C_4$ (as 4T1)	$4$	$1$	$[\ ]^{4}$
23.4.2.1	$4$	x^4 + 299x^2 + 25921	$23$	$2$	$2$	$2$	$C_2^2$ (as 4T2)	$2$	$2$	$[\ ]_{2}^{2}$
23.4.2.2	$4$	x^4 - 23x^2 + 3703	$23$	$2$	$2$	$2$	$C_4$ (as 4T1)	$2$	$2$	$[\ ]_{2}^{2}$
23.4.3.1	$4$	x^4 + 46	$23$	$4$	$1$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]_{4}^{2}$
23.4.3.2	$4$	x^4 - 23	$23$	$4$	$1$	$3$	$D_{4}$ (as 4T3)	$2$	$4$	$[\ ]_{4}^{2}$