$p$-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
5.10.12.10	$10$	$x^{10} + 20 x^{7} - 200 x^{6} + 10 x^{5} + 100 x^{4} + 100 x^{2} + 25$	$5$	$5$	$2$	$12$	$D_{10}$ (as 10T3)	$2$	$2$	$[3/2]$	$[3/2]_{2}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(10 t + 20\right) x^{3} + 10 x^{2} + 5$	$[2, 0]$	$[1]$
5.10.12.7	$10$	$x^{10} - 50 x^{8} + 30 x^{7} + 175 x^{6} - 740 x^{5} + 225 x^{4} - 250 x^{3} + 150 x^{2} + 25$	$5$	$5$	$2$	$12$	$D_{10}$ (as 10T3)	$2$	$2$	$[3/2]$	$[3/2]_{2}^{2}$	$t^{2} + 4 t + 2$	$x^{5} + \left(15 t + 5\right) x^{3} + 15 x^{2} + 5$	$[2, 0]$	$[1]$
5.10.13.2	$10$	$x^{10} + 10 x^{4} + 5$	$5$	$10$	$1$	$13$	$D_{10}$ (as 10T3)	$2$	$2$	$[3/2]$	$[3/2]_{2}^{2}$	$t + 3$	$x^{10} + 10 x^{4} + 5$	$[4, 0]$	$[2, 1]$
5.10.13.8	$10$	$x^{10} + 20 x^{4} + 10$	$5$	$10$	$1$	$13$	$D_{10}$ (as 10T3)	$2$	$2$	$[3/2]$	$[3/2]_{2}^{2}$	$t + 3$	$x^{10} + 20 x^{4} + 10$	$[4, 0]$	$[2, 1]$
5.10.17.30	$10$	$x^{10} + 10 x^{8} + 10$	$5$	$10$	$1$	$17$	$D_{10}$ (as 10T3)	$2$	$2$	$[2]$	$[2]_{2}^{2}$	$t + 3$	$x^{10} + 10 x^{8} + 10$	$[8, 0]$	$[2, 1]$
5.10.17.6	$10$	$x^{10} + 5 x^{8} + 5$	$5$	$10$	$1$	$17$	$D_{10}$ (as 10T3)	$2$	$2$	$[2]$	$[2]_{2}^{2}$	$t + 3$	$x^{10} + 5 x^{8} + 5$	$[8, 0]$	$[2, 1]$