$p$-adic field search results

Results (8 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
13.15.0.1	$15$	$x^{15} + 2 x^{7} + 12 x^{6} + 2 x^{5} + 11 x^{4} + 10 x^{3} + 11 x^{2} + 8 x + 11$	$13$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$15$	$1$	$[\ ]$	$[\ ]^{15}$	$t^{15} + 2 t^{7} + 12 t^{6} + 2 t^{5} + 11 t^{4} + 10 t^{3} + 11 t^{2} + 8 t + 11$	$x - 13$	$[0]$	$[]$
13.15.10.1	$15$	$x^{15} + 65 x^{12} + 12 x^{11} + 33 x^{10} + 1690 x^{9} - 2340 x^{8} - 12822 x^{7} + 22234 x^{6} - 11805 x^{5} + 254085 x^{4} + 160029 x^{3} + 311358 x^{2} - 328605 x + 351148$	$13$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + 4 t + 11$	$x^{3} + 13$	$[0]$	$[1]$
13.15.10.2	$15$	$x^{15} + 1352 x^{9} + 456976 x^{3} + 44926453$	$13$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + 4 t + 11$	$x^{3} + 13 t^{2}$	$[0]$	$[1]$
13.15.10.3	$15$	$x^{15} + 114244 x^{3} - 4084223$	$13$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + 4 t + 11$	$x^{3} + 13 t$	$[0]$	$[1]$
13.15.12.1	$15$	$x^{15} + 10 x^{13} + 55 x^{12} + 40 x^{11} + 479 x^{10} + 1290 x^{9} + 930 x^{8} - 5530 x^{7} + 16110 x^{6} + 19349 x^{5} + 267515 x^{4} + 64685 x^{3} + 204430 x^{2} - 112095 x + 176534$	$13$	$5$	$3$	$12$	$F_5\times C_3$ (as 15T8)	$12$	$5$	$[\ ]$	$[\ ]_{5}^{12}$	$t^{3} + 2 t + 11$	$x^{5} + 13$	$[0]$	$[4]$
13.15.14.1	$15$	$x^{15} + 13$	$13$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 11$	$x^{15} + 13$	$[0]$	$[4]$
13.15.14.2	$15$	$x^{15} + 26$	$13$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 11$	$x^{15} + 26$	$[0]$	$[4]$
13.15.14.3	$15$	$x^{15} + 52$	$13$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 11$	$x^{15} + 52$	$[0]$	$[4]$