$p$-adic field search results

Results (22 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
3.9.16.1	$9$	$x^{9} + 3 x^{8} + 3 x^{6} + 3$	$3$	$9$	$1$	$16$	$C_3^2:C_3$ (as 9T7)	$3$	$1$	$[2, 2]$	$[2, 2]^{3}$	$t + 1$	$x^{9} + 3 x^{8} + 3 x^{6} + 3$	$[8, 6, 0]$	$[3]$
3.9.16.10	$9$	$x^{9} + 3 x^{8} + 3 x^{3} + 21$	$3$	$9$	$1$	$16$	$(C_9:C_3):C_2$ (as 9T10)	$1$	$2$	$[3/2, 13/6]$	$[3/2, 2, 13/6]_{2}$	$t + 1$	$x^{9} + 3 x^{8} + 3 x^{3} + 21$	$[8, 3, 0]$	$[1, 1]$
3.9.16.11	$9$	$x^{9} + 3 x^{8} + 6 x^{3} + 21$	$3$	$9$	$1$	$16$	$(C_9:C_3):C_2$ (as 9T10)	$1$	$2$	$[3/2, 13/6]$	$[3/2, 2, 13/6]_{2}$	$t + 1$	$x^{9} + 3 x^{8} + 6 x^{3} + 21$	$[8, 3, 0]$	$[1, 1]$
3.9.16.12	$9$	$x^{9} + 6 x^{8} + 3$	$3$	$9$	$1$	$16$	$S_3\times C_3$ (as 9T4)	$2$	$1$	$[2, 2]$	$[2, 2]^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 3$	$[8, 8, 0]$	$[2]$
3.9.16.13	$9$	$x^{9} + 6 x^{8} + 12$	$3$	$9$	$1$	$16$	$S_3\times C_3$ (as 9T4)	$2$	$1$	$[2, 2]$	$[2, 2]^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 12$	$[8, 8, 0]$	$[2]$
3.9.16.14	$9$	$x^{9} + 6 x^{8} + 21$	$3$	$9$	$1$	$16$	$S_3\times C_3$ (as 9T4)	$2$	$1$	$[2, 2]$	$[2, 2]^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 21$	$[8, 8, 0]$	$[2]$
3.9.16.15	$9$	$x^{9} + 6 x^{8} + 6 x^{6} + 21$	$3$	$9$	$1$	$16$	$C_3^2:C_8$ (as 9T15)	$8$	$1$	$[2, 2]$	$[2, 2]^{8}$	$t + 1$	$x^{9} + 6 x^{8} + 6 x^{6} + 21$	$[8, 6, 0]$	$[8]$
3.9.16.16	$9$	$x^{9} + 6 x^{8} + 3 x^{6} + 3$	$3$	$9$	$1$	$16$	$C_3^2:C_8$ (as 9T15)	$8$	$1$	$[2, 2]$	$[2, 2]^{8}$	$t + 1$	$x^{9} + 6 x^{8} + 3 x^{6} + 3$	$[8, 6, 0]$	$[8]$
3.9.16.17	$9$	$x^{9} + 6 x^{8} + 3 x^{3} + 3$	$3$	$9$	$1$	$16$	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$2$	$2$	$[3/2, 13/6]$	$[3/2, 3/2, 2, 13/6]_{2}^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 3 x^{3} + 3$	$[8, 3, 0]$	$[1, 1]$
3.9.16.18	$9$	$x^{9} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 9 x^{2} + 18 x + 3$	$3$	$9$	$1$	$16$	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$2$	$2$	$[3/2, 13/6]$	$[3/2, 3/2, 2, 13/6]_{2}^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 9 x^{2} + 18 x + 3$	$[8, 3, 0]$	$[1, 1]$
3.9.16.19	$9$	$x^{9} + 6 x^{8} + 6 x^{3} + 3$	$3$	$9$	$1$	$16$	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$2$	$2$	$[3/2, 13/6]$	$[3/2, 3/2, 2, 13/6]_{2}^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 6 x^{3} + 3$	$[8, 3, 0]$	$[1, 1]$
3.9.16.2	$9$	$x^{9} + 3 x^{8} + 3 x^{6} + 21$	$3$	$9$	$1$	$16$	$C_3^2:C_3$ (as 9T7)	$3$	$1$	$[2, 2]$	$[2, 2]^{3}$	$t + 1$	$x^{9} + 3 x^{8} + 3 x^{6} + 21$	$[8, 6, 0]$	$[3]$
3.9.16.20	$9$	$x^{9} + 6 x^{8} + 3 x^{3} + 9 x + 21$	$3$	$9$	$1$	$16$	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$2$	$2$	$[3/2, 13/6]$	$[3/2, 3/2, 2, 13/6]_{2}^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 3 x^{3} + 9 x + 21$	$[8, 3, 0]$	$[1, 1]$
3.9.16.21	$9$	$x^{9} + 6 x^{8} + 6 x^{3} + 21$	$3$	$9$	$1$	$16$	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$2$	$2$	$[3/2, 13/6]$	$[3/2, 3/2, 2, 13/6]_{2}^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 6 x^{3} + 21$	$[8, 3, 0]$	$[1, 1]$
3.9.16.22	$9$	$x^{9} + 6 x^{8} + 3 x^{3} + 21$	$3$	$9$	$1$	$16$	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$2$	$2$	$[3/2, 13/6]$	$[3/2, 3/2, 2, 13/6]_{2}^{2}$	$t + 1$	$x^{9} + 6 x^{8} + 3 x^{3} + 21$	$[8, 3, 0]$	$[1, 1]$
3.9.16.3	$9$	$x^{9} + 3 x^{8} + 3 x^{6} + 12$	$3$	$9$	$1$	$16$	$C_3^2:C_3$ (as 9T7)	$3$	$1$	$[2, 2]$	$[2, 2]^{3}$	$t + 1$	$x^{9} + 3 x^{8} + 3 x^{6} + 12$	$[8, 6, 0]$	$[3]$
3.9.16.4	$9$	$x^{9} + 3 x^{8} + 3$	$3$	$9$	$1$	$16$	$C_3^2:C_4$ (as 9T9)	$4$	$1$	$[2, 2]$	$[2, 2]^{4}$	$t + 1$	$x^{9} + 3 x^{8} + 3$	$[8, 8, 0]$	$[4]$
3.9.16.5	$9$	$x^{9} + 3 x^{8} + 6 x^{6} + 3$	$3$	$9$	$1$	$16$	$C_3^2 : C_6$ (as 9T11)	$6$	$1$	$[2, 2]$	$[2, 2]^{6}$	$t + 1$	$x^{9} + 3 x^{8} + 6 x^{6} + 3$	$[8, 6, 0]$	$[6]$
3.9.16.6	$9$	$x^{9} + 3 x^{8} + 3 x^{3} + 18 x + 21$	$3$	$9$	$1$	$16$	$(C_9:C_3):C_2$ (as 9T10)	$1$	$2$	$[3/2, 13/6]$	$[3/2, 2, 13/6]_{2}$	$t + 1$	$x^{9} + 3 x^{8} + 3 x^{3} + 18 x + 21$	$[8, 3, 0]$	$[1, 1]$
3.9.16.7	$9$	$x^{9} + 3 x^{8} + 3 x^{3} + 3$	$3$	$9$	$1$	$16$	$(C_9:C_3):C_2$ (as 9T10)	$1$	$2$	$[3/2, 13/6]$	$[3/2, 2, 13/6]_{2}$	$t + 1$	$x^{9} + 3 x^{8} + 3 x^{3} + 3$	$[8, 3, 0]$	$[1, 1]$
3.9.16.8	$9$	$x^{9} + 3 x^{8} + 6 x^{3} + 3$	$3$	$9$	$1$	$16$	$(C_9:C_3):C_2$ (as 9T10)	$1$	$2$	$[3/2, 13/6]$	$[3/2, 2, 13/6]_{2}$	$t + 1$	$x^{9} + 3 x^{8} + 6 x^{3} + 3$	$[8, 3, 0]$	$[1, 1]$
3.9.16.9	$9$	$x^{9} + 3 x^{8} + 6 x^{3} + 18 x + 3$	$3$	$9$	$1$	$16$	$(C_9:C_3):C_2$ (as 9T10)	$1$	$2$	$[3/2, 13/6]$	$[3/2, 2, 13/6]_{2}$	$t + 1$	$x^{9} + 3 x^{8} + 6 x^{3} + 18 x + 3$	$[8, 3, 0]$	$[1, 1]$