$p$-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
3.10.0.1	$10$	$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{4} + x + 2$	$3$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]$	$[\ ]^{10}$	$t^{10} + 2 t^{6} + 2 t^{5} + 2 t^{4} + t + 2$	$x - 3$	$[0]$	$[]$
3.10.5.1	$10$	$x^{10} + 162 x^{2} - 243$	$3$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$t^{5} + 2 t + 1$	$x^{2} + 3 t$	$[0]$	$[1]$
3.10.5.2	$10$	$x^{10} + 15 x^{8} + 94 x^{6} + 2 x^{5} + 210 x^{4} - 60 x^{3} + 229 x^{2} + 94 x + 364$	$3$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$t^{5} + 2 t + 1$	$x^{2} + 3$	$[0]$	$[1]$
3.10.8.1	$10$	$x^{10} + 10 x^{9} + 50 x^{8} + 160 x^{7} + 360 x^{6} + 598 x^{5} + 750 x^{4} + 640 x^{3} + 280 x^{2} + 40 x + 17$	$3$	$5$	$2$	$8$	$F_5$ (as 10T4)	$4$	$5$	$[\ ]$	$[\ ]_{5}^{4}$	$t^{2} + 2 t + 2$	$x^{5} + 3$	$[0]$	$[2]$
3.10.9.1	$10$	$x^{10} + 6$	$3$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]_{10}^{4}$	$t + 1$	$x^{10} + 6$	$[0]$	$[4]$
3.10.9.2	$10$	$x^{10} + 3$	$3$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]_{10}^{4}$	$t + 1$	$x^{10} + 3$	$[0]$	$[4]$