$p$-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 (9 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
13.14.0.1	$14$	x^14 - x + 2	$13$	$1$	$14$	$0$	$C_{14}$ (as 14T1)	$14$	$1$	$[\ ]^{14}$
13.14.7.1	$14$	x^14 - 43940x^8 + 482680900x^2 - 250994068	$13$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]_{2}^{7}$
13.14.7.2	$14$	x^14 - 48268090x^2 + 125497034	$13$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]_{2}^{7}$
13.14.12.1	$14$	x^14 + 169x^7 + 21632	$13$	$7$	$2$	$12$	$D_{7}$ (as 14T2)	$2$	$7$	$[\ ]_{7}^{2}$
13.14.12.2	$14$	x^14 - 13x^7 + 338	$13$	$7$	$2$	$12$	$C_7 \wr C_2$ (as 14T8)	$14$	$7$	$[\ ]_{7}^{14}$
13.14.12.3	$14$	x^14 + 39x^7 + 676	$13$	$7$	$2$	$12$	$C_7 \wr C_2$ (as 14T8)	$14$	$7$	$[\ ]_{7}^{14}$
13.14.12.4	$14$	x^14 + 65x^7 + 1352	$13$	$7$	$2$	$12$	$C_7 \wr C_2$ (as 14T8)	$14$	$7$	$[\ ]_{7}^{14}$
13.14.13.1	$14$	x^14 - 13	$13$	$14$	$1$	$13$	$D_{14}$ (as 14T3)	$2$	$14$	$[\ ]_{14}^{2}$
13.14.13.2	$14$	x^14 + 26	$13$	$14$	$1$	$13$	$D_{14}$ (as 14T3)	$2$	$14$	$[\ ]_{14}^{2}$