$p$-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
23.6.0.1	$6$	$x^{6} + x^{4} + 9 x^{3} + 9 x^{2} + x + 5$	$23$	$1$	$6$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]$	$[\ ]^{6}$	$t^{6} + t^{4} + 9 t^{3} + 9 t^{2} + t + 5$	$x - 23$	$[0]$	$[]$
23.6.3.1	$6$	$x^{6} + 1058 x^{2} - 219006$	$23$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]_{2}^{3}$	$t^{3} + 2 t + 18$	$x^{2} + 23 t$	$[0]$	$[1]$
23.6.3.2	$6$	$x^{6} + 73 x^{4} + 36 x^{3} + 1591 x^{2} - 2412 x + 10467$	$23$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]$	$[\ ]_{2}^{3}$	$t^{3} + 2 t + 18$	$x^{2} + 23$	$[0]$	$[1]$
23.6.4.1	$6$	$x^{6} + 63 x^{5} + 1338 x^{4} + 9937 x^{3} + 8139 x^{2} + 31314 x + 206412$	$23$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]$	$[\ ]_{3}^{2}$	$t^{2} + 21 t + 5$	$x^{3} + 23$	$[0]$	$[1]$
23.6.4.2	$6$	$x^{6} - 483 x^{3} + 2645$	$23$	$3$	$2$	$4$	$S_3\times C_3$ (as 6T5)	$6$	$3$	$[\ ]$	$[\ ]_{3}^{6}$	$t^{2} + 21 t + 5$	$x^{3} + 23 t$	$[0]$	$[1]$
23.6.5.1	$6$	$x^{6} + 115$	$23$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t + 18$	$x^{6} + 115$	$[0]$	$[2]$
23.6.5.2	$6$	$x^{6} + 23$	$23$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t + 18$	$x^{6} + 23$	$[0]$	$[2]$