$p$-adic field search results

Results (15 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
2.10.10.15	$10$	$x^{10} + 2 x + 2$	$2$	$10$	$1$	$10$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[6/5]$	$[6/5, 6/5, 6/5, 6/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x + 2$	$[1, 0]$	$[1, 4]$
2.10.12.1	$10$	$x^{10} + 2 x^{6} + 2 x^{3} + 2$	$2$	$10$	$1$	$12$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[8/5]$	$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{6} + 2 x^{3} + 2$	$[3, 0]$	$[1, 4]$
2.10.12.2	$10$	$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$	$2$	$10$	$1$	$12$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[8/5]$	$[8/5, 8/5, 8/5, 8/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$	$[3, 0]$	$[1, 4]$
2.10.16.1	$10$	$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$[7, 0]$	$[1, 4]$
2.10.16.2	$10$	$x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{3} + 4 x^{2} + 6$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{3} + 4 x^{2} + 6$	$[7, 0]$	$[1, 4]$
2.10.16.3	$10$	$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 6$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 6$	$[7, 0]$	$[1, 4]$
2.10.16.4	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 2$	$[7, 0]$	$[1, 4]$
2.10.18.1	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.2	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.3	$10$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.4	$10$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.5	$10$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.6	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.7	$10$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.8	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$[9, 0]$	$[1, 4]$