$p$-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
7.10.0.1	$10$	$x^{10} + x^{6} + x^{5} + 4 x^{4} + x^{3} + 2 x^{2} + 3 x + 3$	$7$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]$	$[\ ]^{10}$	$t^{10} + t^{6} + t^{5} + 4 t^{4} + t^{3} + 2 t^{2} + 3 t + 3$	$x - 7$	$[0]$	$[]$
7.10.5.1	$10$	$x^{10} + 2401 x^{2} - 67228$	$7$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$t^{5} + t + 4$	$x^{2} + 7 t$	$[0]$	$[1]$
7.10.5.2	$10$	$x^{10} + 35 x^{8} + 492 x^{6} + 8 x^{5} + 3360 x^{4} - 560 x^{3} + 11516 x^{2} + 1968 x + 17516$	$7$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]$	$[\ ]_{2}^{5}$	$t^{5} + t + 4$	$x^{2} + 7$	$[0]$	$[1]$
7.10.8.1	$10$	$x^{10} + 30 x^{9} + 375 x^{8} + 2520 x^{7} + 9810 x^{6} + 22370 x^{5} + 29640 x^{4} + 24780 x^{3} + 21465 x^{2} + 33300 x + 33934$	$7$	$5$	$2$	$8$	$F_5$ (as 10T4)	$4$	$5$	$[\ ]$	$[\ ]_{5}^{4}$	$t^{2} + 6 t + 3$	$x^{5} + 7$	$[0]$	$[2]$
7.10.9.1	$10$	$x^{10} + 21$	$7$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]_{10}^{4}$	$t + 4$	$x^{10} + 21$	$[0]$	$[4]$
7.10.9.2	$10$	$x^{10} + 7$	$7$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$4$	$10$	$[\ ]$	$[\ ]_{10}^{4}$	$t + 4$	$x^{10} + 7$	$[0]$	$[4]$