$p$-adic field search results

Results (16 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
2.10.16.1	$10$	$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$[7, 0]$	$[1, 4]$
2.10.16.10	$10$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[7, 0]$	$[1, 4]$
2.10.16.11	$10$	$x^{10} + 2 x^{9} + 2 x^{7} + 4 x^{3} + 6$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{7} + 4 x^{3} + 6$	$[7, 0]$	$[1, 4]$
2.10.16.12	$10$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$	$[7, 0]$	$[1, 4]$
2.10.16.13	$10$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 4 x^{3} + 4 x + 6$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 4 x^{3} + 4 x + 6$	$[7, 0]$	$[1, 4]$
2.10.16.14	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 4 x + 2$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 4 x + 2$	$[7, 0]$	$[1, 4]$
2.10.16.15	$10$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{2} + 2$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{2} + 2$	$[7, 0]$	$[1, 4]$
2.10.16.16	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x^{2} + 2$	$[7, 0]$	$[1, 4]$
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)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 2$	$[7, 0]$	$[1, 4]$
2.10.16.5	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x^{2} + 2$	$[7, 0]$	$[1, 4]$
2.10.16.6	$10$	$x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x + 2$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{8} + 2 x^{7} + 4 x^{4} + 4 x + 2$	$[7, 0]$	$[1, 4]$
2.10.16.7	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 6$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 6$	$[7, 0]$	$[1, 4]$
2.10.16.8	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 6$	$2$	$10$	$1$	$16$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[12/5]$	$[12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{7} + 2 x^{4} + 4 x^{2} + 4 x + 6$	$[7, 0]$	$[1, 4]$
2.10.16.9	$10$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 6$	$2$	$10$	$1$	$16$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[12/5]$	$[2, 12/5, 12/5, 12/5, 12/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{8} + 2 x^{7} + 2 x^{6} + 6 x^{4} + 6$	$[7, 0]$	$[1, 4]$