$p$-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
2.12.16.27	$12$	$x^{12} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$	$2$	$12$	$1$	$16$	$C_4^2:S_3$ (as 12T64)	$2$	$3$	$[4/3, 5/3]$	$[4/3, 4/3, 5/3, 5/3]_{3}^{2}$	$t + 1$	$x^{12} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$	$[5, 2, 0]$	$[1, 1, 2]$
2.12.22.83	$12$	$x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 6$	$2$	$12$	$1$	$22$	$C_4^2:S_3$ (as 12T64)	$2$	$3$	$[4/3, 8/3]$	$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$	$t + 1$	$x^{12} + 2 x^{11} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 6$	$[11, 2, 0]$	$[1, 1, 2]$
2.12.32.225	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{2} + 2$	$2$	$12$	$1$	$32$	$C_4^2:S_3$ (as 12T64)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{7} + 8 x^{6} + 12 x^{2} + 2$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.268	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{6} + 12 x^{2} + 2$	$2$	$12$	$1$	$32$	$C_4^2:S_3$ (as 12T64)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{6} + 12 x^{2} + 2$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.330	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$2$	$12$	$1$	$32$	$C_4^2:S_3$ (as 12T64)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.57	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{4} + 4 x^{2} + 2$	$2$	$12$	$1$	$32$	$C_4^2:S_3$ (as 12T64)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{4} + 4 x^{2} + 2$	$[21, 10, 0]$	$[1, 1, 2]$