$p$-adic field search results

Results (7 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
17.6.0.1	$6$	$x^{6} + 2 x^{4} + 10 x^{2} + 3 x + 3$	$17$	$1$	$6$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]$	$[\ ]^{6}$	$t^{6} + 2 t^{4} + 10 t^{2} + 3 t + 3$	$x - 17$	$[0]$	$[]$
17.6.3.1	$6$	$x^{6} + 459 x^{5} + 70280 x^{4} + 3597823 x^{3} + 1271380 x^{2} + 4696159 x + 50437479$	$17$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]_{2}^{3}$	$t^{3} + t + 14$	$x^{2} + 153 x + 17$	$[0]$	$[1]$
17.6.3.2	$6$	$x^{6} + 289 x^{2} - 68782$	$17$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]_{2}^{3}$	$t^{3} + t + 14$	$x^{2} + 17 t$	$[0]$	$[1]$
17.6.4.1	$6$	$x^{6} + 48 x^{5} + 879 x^{4} + 7682 x^{3} + 44916 x^{2} + 265428 x + 127425$	$17$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$	$t^{2} + 16 t + 3$	$x^{3} + 51 x + 17$	$[0]$	$[1]$
17.6.4.2	$6$	$x^{6} + 204 x^{3} - 7225$	$17$	$3$	$2$	$4$	$S_3\times C_3$ (as 6T5)	$6$	$3$	$[\ ]$	$[\ ]_{3}^{6}$	$t^{2} + 16 t + 3$	$x^{3} + 17 t + 238$	$[0]$	$[1]$
17.6.5.1	$6$	$x^{6} + 17$	$17$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t + 14$	$x^{6} + 17$	$[0]$	$[2]$
17.6.5.2	$6$	$x^{6} + 51$	$17$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t + 14$	$x^{6} + 51$	$[0]$	$[2]$