$p$-adic field search results

Results (8 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
19.10.0.1	$10$	x^10 + 18x^5 + 13x^4 + 17x^3 + 3x^2 + 4x + 2	$19$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]$	$[\ ]^{10}$	$[0]$	$[]$
19.10.5.1	$10$	x^10 + 651605x^2 - 42093683	$19$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$[0]$	$[1]$
19.10.5.2	$10$	x^10 + 95x^8 + 3620x^6 + 34x^5 + 67640x^4 - 6460x^3 + 633580x^2 + 61540x + 2545453	$19$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$[0]$	$[1]$
19.10.8.1	$10$	x^10 + 90x^9 + 3250x^8 + 59040x^7 + 544360x^6 + 2125046x^5 + 1090430x^4 + 296960x^3 + 1113560x^2 + 9728680x + 34800945	$19$	$5$	$2$	$8$	$D_5$ (as 10T2)	$2$	$5$	$[\ ]$	$[\ ]_{5}^{2}$	$[0]$	$[1]$
19.10.8.2	$10$	x^10 - 5396x^5 - 21660	$19$	$5$	$2$	$8$	$D_5\times C_5$ (as 10T6)	$10$	$5$	$[\ ]$	$[\ ]_{5}^{10}$	$[0]$	$[1]$
19.10.8.3	$10$	x^10 - 5510x^5 - 1650131	$19$	$5$	$2$	$8$	$D_5\times C_5$ (as 10T6)	$10$	$5$	$[\ ]$	$[\ ]_{5}^{10}$	$[0]$	$[1]$
19.10.9.1	$10$	x^10 + 38	$19$	$10$	$1$	$9$	$D_{10}$ (as 10T3)	$2$	$10$	$[\ ]$	$[\ ]_{10}^{2}$	$[0]$	$[2]$
19.10.9.2	$10$	x^10 + 19	$19$	$10$	$1$	$9$	$D_{10}$ (as 10T3)	$2$	$10$	$[\ ]$	$[\ ]_{10}^{2}$	$[0]$	$[2]$