$p$-adic field search results

Results (6 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
3.6.7.1	$6$	$x^{6} + 6 x^{2} + 6$	$3$	$6$	$1$	$7$	$S_3$ (as 6T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$t + 1$	$x^{6} + 6 x^{2} + 6$	$[2, 0]$	$[1, 1]$
3.6.7.4	$6$	$x^{6} + 3 x^{2} + 3$	$3$	$6$	$1$	$7$	$S_3$ (as 6T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$t + 1$	$x^{6} + 3 x^{2} + 3$	$[2, 0]$	$[1, 1]$
3.6.8.5	$6$	$x^{6} + 12 x^{5} + 57 x^{4} + 146 x^{3} + 240 x^{2} + 204 x + 65$	$3$	$3$	$2$	$8$	$S_3$ (as 6T2)	$2$	$1$	$[2]$	$[2]^{2}$	$t^{2} + 2 t + 2$	$x^{3} + 3 x^{2} + 3$	$[2, 0]$	$[1]$
3.6.11.7	$6$	$x^{6} + 9 x^{2} + 12$	$3$	$6$	$1$	$11$	$S_3$ (as 6T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$	$t + 1$	$x^{6} + 9 x^{2} + 12$	$[6, 0]$	$[1, 1]$
3.6.11.8	$6$	$x^{6} + 18 x^{2} + 21$	$3$	$6$	$1$	$11$	$S_3$ (as 6T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$	$t + 1$	$x^{6} + 18 x^{2} + 21$	$[6, 0]$	$[1, 1]$
3.6.11.9	$6$	$x^{6} + 3$	$3$	$6$	$1$	$11$	$S_3$ (as 6T2)	$1$	$2$	$[5/2]$	$[5/2]_{2}$	$t + 1$	$x^{6} + 3$	$[6, 0]$	$[1, 1]$