$p$-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 (8 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
13.15.0.1	$15$	x^15 - 4x + 6	$13$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$15$	$1$	$[\ ]^{15}$
13.15.10.1	$15$	x^15 + 79092x^6 - 228488x^3 + 80199288	$13$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]_{3}^{5}$
13.15.10.2	$15$	x^15 - 57122x^3 + 2227758	$13$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]_{3}^{5}$
13.15.10.3	$15$	x^15 - 676x^9 + 114244x^3 - 13366548	$13$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]_{3}^{5}$
13.15.12.1	$15$	x^15 - 338x^5 + 13182	$13$	$5$	$3$	$12$	$F_5\times C_3$ (as 15T8)	$12$	$5$	$[\ ]_{5}^{12}$
13.15.14.1	$15$	x^15 - 13	$13$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]_{15}^{4}$
13.15.14.2	$15$	x^15 + 26	$13$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]_{15}^{4}$
13.15.14.3	$15$	x^15 - 52	$13$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]_{15}^{4}$