$p$-adic field search results

Results (26 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
5.5.0.1	$5$	$x^{5} + 4 x + 3$	$5$	$1$	$5$	$0$	$C_5$ (as 5T1)	$5$	$1$	$[\ ]$	$[\ ]^{5}$	$t^{5} + 4 t + 3$	$x - 5$	$[0]$	$[]$
5.5.5.1	$5$	$x^{5} + 20 x + 5$	$5$	$5$	$1$	$5$	$F_5$ (as 5T3)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 3$	$x^{5} + 20 x + 5$	$[1, 0]$	$[1]$
5.5.5.2	$5$	$x^{5} + 5 x + 5$	$5$	$5$	$1$	$5$	$F_5$ (as 5T3)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 3$	$x^{5} + 5 x + 5$	$[1, 0]$	$[1]$
5.5.5.3	$5$	$x^{5} + 15 x + 5$	$5$	$5$	$1$	$5$	$F_5$ (as 5T3)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 3$	$x^{5} + 15 x + 5$	$[1, 0]$	$[1]$
5.5.5.4	$5$	$x^{5} + 10 x + 5$	$5$	$5$	$1$	$5$	$F_5$ (as 5T3)	$1$	$4$	$[5/4]$	$[5/4]_{4}$	$t + 3$	$x^{5} + 10 x + 5$	$[1, 0]$	$[1]$
5.5.6.1	$5$	$x^{5} + 10 x^{2} + 5$	$5$	$5$	$1$	$6$	$D_{5}$ (as 5T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$t + 3$	$x^{5} + 10 x^{2} + 5$	$[2, 0]$	$[1]$
5.5.6.2	$5$	$x^{5} + 15 x^{2} + 5$	$5$	$5$	$1$	$6$	$D_{5}$ (as 5T2)	$1$	$2$	$[3/2]$	$[3/2]_{2}$	$t + 3$	$x^{5} + 15 x^{2} + 5$	$[2, 0]$	$[1]$
5.5.6.3	$5$	$x^{5} + 5 x^{2} + 5$	$5$	$5$	$1$	$6$	$F_5$ (as 5T3)	$2$	$2$	$[3/2]$	$[3/2]_{2}^{2}$	$t + 3$	$x^{5} + 5 x^{2} + 5$	$[2, 0]$	$[2]$
5.5.6.4	$5$	$x^{5} + 20 x^{2} + 5$	$5$	$5$	$1$	$6$	$F_5$ (as 5T3)	$2$	$2$	$[3/2]$	$[3/2]_{2}^{2}$	$t + 3$	$x^{5} + 20 x^{2} + 5$	$[2, 0]$	$[2]$
5.5.7.1	$5$	$x^{5} + 15 x^{3} + 5$	$5$	$5$	$1$	$7$	$F_5$ (as 5T3)	$1$	$4$	$[7/4]$	$[7/4]_{4}$	$t + 3$	$x^{5} + 15 x^{3} + 5$	$[3, 0]$	$[1]$
5.5.7.2	$5$	$x^{5} + 10 x^{3} + 5$	$5$	$5$	$1$	$7$	$F_5$ (as 5T3)	$1$	$4$	$[7/4]$	$[7/4]_{4}$	$t + 3$	$x^{5} + 10 x^{3} + 5$	$[3, 0]$	$[1]$
5.5.7.3	$5$	$x^{5} + 20 x^{3} + 5$	$5$	$5$	$1$	$7$	$F_5$ (as 5T3)	$1$	$4$	$[7/4]$	$[7/4]_{4}$	$t + 3$	$x^{5} + 20 x^{3} + 5$	$[3, 0]$	$[1]$
5.5.7.4	$5$	$x^{5} + 5 x^{3} + 5$	$5$	$5$	$1$	$7$	$F_5$ (as 5T3)	$1$	$4$	$[7/4]$	$[7/4]_{4}$	$t + 3$	$x^{5} + 5 x^{3} + 5$	$[3, 0]$	$[1]$
5.5.8.1	$5$	$x^{5} + 20 x^{4} + 105$	$5$	$5$	$1$	$8$	$C_5$ (as 5T1)	$1$	$1$	$[2]$	$[2]$	$t + 3$	$x^{5} + 20 x^{4} + 105$	$[4, 0]$	$[1]$
5.5.8.2	$5$	$x^{5} + 20 x^{4} + 5$	$5$	$5$	$1$	$8$	$C_5$ (as 5T1)	$1$	$1$	$[2]$	$[2]$	$t + 3$	$x^{5} + 20 x^{4} + 5$	$[4, 0]$	$[1]$
5.5.8.3	$5$	$x^{5} + 20 x^{4} + 30$	$5$	$5$	$1$	$8$	$C_5$ (as 5T1)	$1$	$1$	$[2]$	$[2]$	$t + 3$	$x^{5} + 20 x^{4} + 30$	$[4, 0]$	$[1]$
5.5.8.4	$5$	$x^{5} + 20 x^{4} + 55$	$5$	$5$	$1$	$8$	$C_5$ (as 5T1)	$1$	$1$	$[2]$	$[2]$	$t + 3$	$x^{5} + 20 x^{4} + 55$	$[4, 0]$	$[1]$
5.5.8.5	$5$	$x^{5} + 20 x^{4} + 80$	$5$	$5$	$1$	$8$	$C_5$ (as 5T1)	$1$	$1$	$[2]$	$[2]$	$t + 3$	$x^{5} + 20 x^{4} + 80$	$[4, 0]$	$[1]$
5.5.8.6	$5$	$x^{5} + 5 x^{4} + 5$	$5$	$5$	$1$	$8$	$D_{5}$ (as 5T2)	$2$	$1$	$[2]$	$[2]^{2}$	$t + 3$	$x^{5} + 5 x^{4} + 5$	$[4, 0]$	$[2]$
5.5.8.7	$5$	$x^{5} + 10 x^{4} + 5$	$5$	$5$	$1$	$8$	$F_5$ (as 5T3)	$4$	$1$	$[2]$	$[2]^{4}$	$t + 3$	$x^{5} + 10 x^{4} + 5$	$[4, 0]$	$[4]$
5.5.8.8	$5$	$x^{5} + 15 x^{4} + 5$	$5$	$5$	$1$	$8$	$F_5$ (as 5T3)	$4$	$1$	$[2]$	$[2]^{4}$	$t + 3$	$x^{5} + 15 x^{4} + 5$	$[4, 0]$	$[4]$
5.5.9.1	$5$	$x^{5} + 5$	$5$	$5$	$1$	$9$	$F_5$ (as 5T3)	$1$	$4$	$[9/4]$	$[9/4]_{4}$	$t + 3$	$x^{5} + 5$	$[5, 0]$	$[1]$
5.5.9.2	$5$	$x^{5} + 100 x^{2} + 50 x + 5$	$5$	$5$	$1$	$9$	$F_5$ (as 5T3)	$1$	$4$	$[9/4]$	$[9/4]_{4}$	$t + 3$	$x^{5} + 100 x^{2} + 50 x + 5$	$[5, 0]$	$[1]$
5.5.9.3	$5$	$x^{5} + 100 x^{2} + 75 x + 5$	$5$	$5$	$1$	$9$	$F_5$ (as 5T3)	$1$	$4$	$[9/4]$	$[9/4]_{4}$	$t + 3$	$x^{5} + 100 x^{2} + 75 x + 5$	$[5, 0]$	$[1]$
5.5.9.4	$5$	$x^{5} + 25 x^{2} + 25 x + 5$	$5$	$5$	$1$	$9$	$F_5$ (as 5T3)	$1$	$4$	$[9/4]$	$[9/4]_{4}$	$t + 3$	$x^{5} + 25 x^{2} + 25 x + 5$	$[5, 0]$	$[1]$
5.5.9.5	$5$	$x^{5} + 25 x^{2} + 100 x + 5$	$5$	$5$	$1$	$9$	$F_5$ (as 5T3)	$1$	$4$	$[9/4]$	$[9/4]_{4}$	$t + 3$	$x^{5} + 25 x^{2} + 100 x + 5$	$[5, 0]$	$[1]$