$p$-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
3.10.0.1	$10$	x^10 - x^3 - x + 2	$3$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]^{10}$
3.10.5.1	$10$	x^10 - 18x^6 + 81x^2 - 243	$3$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]_{2}^{5}$
3.10.5.2	$10$	x^10 - 81x^2 + 243	$3$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]_{2}^{5}$
3.10.8.1	$10$	x^10 - 3x^5 + 18	$3$	$5$	$2$	$8$	$F_5$ (as 10T4)	$4$	$5$	$[\ ]_{5}^{4}$
3.10.9.1	$10$	x^10 - 3	$3$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]_{10}^{4}$
3.10.9.2	$10$	x^10 + 3	$3$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]_{10}^{4}$