$p$-adic field search results

Results (6 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
17.10.0.1	$10$	x^10 + 13x^5 + 6x^4 + 5x^3 + 9x^2 + 12x + 3	$17$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]$	$[\ ]^{10}$	$[0]$	$[]$
17.10.5.1	$10$	x^10 + 765x^9 + 234175x^8 + 35867790x^7 + 2751847887x^6 + 85060199629x^5 + 46781658675x^4 + 10404827560x^3 + 4386754121x^2 + 122151890859x + 1178806975473	$17$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$[0]$	$[1]$
17.10.5.2	$10$	x^10 + 83521x^2 - 19877998	$17$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$[0]$	$[1]$
17.10.8.1	$10$	x^10 + 80x^9 + 2575x^8 + 41920x^7 + 350810x^6 + 1298690x^5 + 1053790x^4 + 419780x^3 + 741365x^2 + 5317450x + 16794084	$17$	$5$	$2$	$8$	$F_5$ (as 10T4)	$4$	$5$	$[\ ]$	$[\ ]_{5}^{4}$	$[0]$	$[2]$
17.10.9.1	$10$	x^10 + 17	$17$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]_{10}^{4}$	$[0]$	$[4]$
17.10.9.2	$10$	x^10 + 51	$17$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]_{10}^{4}$	$[0]$	$[4]$