$p$-adic field search results

Results (8 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
3.12.13.1	$12$	$x^{12} + 3 x^{2} + 3$	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{2} + 3$	$[2, 0]$	$[2, 2]$
3.12.13.4	$12$	$x^{12} + 6 x^{2} + 6$	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{2} + 6$	$[2, 0]$	$[2, 2]$
3.12.21.26	$12$	$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 15$	$3$	$12$	$1$	$21$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[9/4]$	$[9/4, 9/4]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 15$	$[10, 0]$	$[2, 2]$
3.12.21.27	$12$	$x^{12} + 3 x^{10} + 6 x^{9} + 9 x^{3} + 18 x + 24$	$3$	$12$	$1$	$21$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[9/4]$	$[9/4, 9/4]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{10} + 6 x^{9} + 9 x^{3} + 18 x + 24$	$[10, 0]$	$[2, 2]$
3.12.21.4	$12$	$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 6$	$3$	$12$	$1$	$21$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[9/4]$	$[9/4, 9/4]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 6$	$[10, 0]$	$[2, 2]$
3.12.21.46	$12$	$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 12 x^{3} + 12$	$3$	$12$	$1$	$21$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[9/4]$	$[9/4, 9/4]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 12 x^{3} + 12$	$[10, 0]$	$[2, 2]$
3.12.21.7	$12$	$x^{12} + 6 x^{10} + 3 x^{9} + 18 x^{2} + 18 x + 21$	$3$	$12$	$1$	$21$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[9/4]$	$[9/4, 9/4]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{10} + 3 x^{9} + 18 x^{2} + 18 x + 21$	$[10, 0]$	$[2, 2]$
3.12.21.74	$12$	$x^{12} + 6 x^{10} + 6 x^{9} + 9 x^{3} + 9 x + 12$	$3$	$12$	$1$	$21$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[9/4]$	$[9/4, 9/4]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{10} + 6 x^{9} + 9 x^{3} + 9 x + 12$	$[10, 0]$	$[2, 2]$