$p$-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
7.8.0.1	$8$	x^8 + 4x^3 + 6x^2 + 2x + 3	$7$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$[0]$	$[]$
7.8.4.1	$8$	x^8 + 38x^6 + 8x^5 + 395x^4 - 72x^3 + 1026x^2 - 872x + 401	$7$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$[0]$	$[1]$
7.8.4.2	$8$	x^8 + 245x^4 - 1372x^2 + 7203	$7$	$2$	$4$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$[0]$	$[1]$
7.8.6.1	$8$	x^8 + 14x^4 - 245	$7$	$4$	$2$	$6$	$Q_8$ (as 8T5)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
7.8.6.2	$8$	x^8 + 24x^7 + 228x^6 + 1080x^5 + 2660x^4 + 3408x^3 + 3312x^2 + 5184x + 6304	$7$	$4$	$2$	$6$	$D_4$ (as 8T4)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$[0]$	$[1]$
7.8.6.3	$8$	x^8 - 154x^4 - 1421	$7$	$4$	$2$	$6$	$C_8:C_2$ (as 8T7)	$4$	$4$	$[\ ]$	$[\ ]_{4}^{4}$	$[0]$	$[1]$
7.8.7.1	$8$	x^8 + 7	$7$	$8$	$1$	$7$	$D_{8}$ (as 8T6)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$
7.8.7.2	$8$	x^8 + 21	$7$	$8$	$1$	$7$	$D_{8}$ (as 8T6)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$[0]$	$[2]$