$p$-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 (6 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
13.10.0.1	$10$	x^10 + 2x^2 - 2x + 2	$13$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]^{10}$
13.10.5.1	$10$	x^10 - 676x^6 + 114244x^2 - 13366548	$13$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]_{2}^{5}$
13.10.5.2	$10$	x^10 - 57122x^2 + 2227758	$13$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]_{2}^{5}$
13.10.8.1	$10$	x^10 - 13x^5 + 338	$13$	$5$	$2$	$8$	$F_5$ (as 10T4)	$4$	$5$	$[\ ]_{5}^{4}$
13.10.9.1	$10$	x^10 - 13	$13$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]_{10}^{4}$
13.10.9.2	$10$	x^10 + 26	$13$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]_{10}^{4}$