$p$-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
17.14.0.1	$14$	x^14 + x^8 + 11x^7 + x^6 + 8x^5 + 16x^4 + 13x^3 + 9x^2 + 3x + 3	$17$	$1$	$14$	$0$	$C_{14}$ (as 14T1)	$14$	$1$	$[\ ]$	$[\ ]^{14}$	$[0]$	$[]$
17.14.7.1	$14$	x^14 + 1071x^13 + 491708x^12 + 125464437x^11 + 19221135969x^10 + 1769192651898x^9 + 90773424099277x^8 + 2022717194718445x^7 + 1543148215595651x^6 + 511298184911304x^5 + 94664842882197x^4 + 31823467716383x^3 + 1100435035211950x^2 + 24803053432496659x + 29942903574449667	$17$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]$	$[\ ]_{2}^{7}$	$[0]$	$[1]$
17.14.7.2	$14$	x^14 + 289650828x^2 - 5744741422	$17$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]$	$[\ ]_{2}^{7}$	$[0]$	$[1]$
17.14.12.1	$14$	x^14 + 112x^13 + 5397x^12 + 145376x^11 + 2374589x^10 + 23755536x^9 + 138569137x^8 + 408357986x^7 + 415709315x^6 + 213889074x^5 + 66465343x^4 + 48952246x^3 + 353976063x^2 + 1858653398x + 4197785820	$17$	$7$	$2$	$12$	$F_7$ (as 14T4)	$6$	$7$	$[\ ]$	$[\ ]_{7}^{6}$	$[0]$	$[3]$
17.14.13.1	$14$	x^14 + 17	$17$	$14$	$1$	$13$	$F_7 \times C_2$ (as 14T7)	$6$	$14$	$[\ ]$	$[\ ]_{14}^{6}$	$[0]$	$[6]$
17.14.13.2	$14$	x^14 + 51	$17$	$14$	$1$	$13$	$F_7 \times C_2$ (as 14T7)	$6$	$14$	$[\ ]$	$[\ ]_{14}^{6}$	$[0]$	$[6]$