$p$-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
19.15.0.1	$15$	$x^{15} + x^{7} + 10 x^{6} + 11 x^{5} + 13 x^{4} + 15 x^{3} + 14 x^{2} + 17$	$19$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$15$	$1$	$[\ ]$	$[\ ]^{15}$	$t^{15} + t^{7} + 10 t^{6} + 11 t^{5} + 13 t^{4} + 15 t^{3} + 14 t^{2} + 17$	$x - 19$	$[0]$	$[]$
19.15.10.1	$15$	$x^{15} + 95 x^{12} + 15 x^{11} + 51 x^{10} + 3610 x^{9} - 4275 x^{8} - 28995 x^{7} + 69100 x^{6} - 31623 x^{5} + 835620 x^{4} + 700180 x^{3} + 1194855 x^{2} - 1636410 x + 2391332$	$19$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + 5 t + 17$	$x^{3} + 19$	$[0]$	$[1]$
19.15.10.2	$15$	$x^{15} + 651605 x^{3} - 42093683$	$19$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + 5 t + 17$	$x^{3} + 19 t$	$[0]$	$[1]$
19.15.10.3	$15$	$x^{15} + 3610 x^{9} + 3258025 x^{3} + 715592611$	$19$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + 5 t + 17$	$x^{3} + 19 t^{2}$	$[0]$	$[1]$
19.15.12.1	$15$	$x^{15} + 20 x^{13} + 85 x^{12} + 160 x^{11} + 1417 x^{10} + 3530 x^{9} + 7020 x^{8} + 6890 x^{7} + 76970 x^{6} + 160207 x^{5} + 1168245 x^{4} + 470325 x^{3} + 1653430 x^{2} + 224615 x + 1762712$	$19$	$5$	$3$	$12$	$D_5\times C_3$ (as 15T3)	$6$	$5$	$[\ ]$	$[\ ]_{5}^{6}$	$t^{3} + 4 t + 17$	$x^{5} + 19$	$[0]$	$[2]$
19.15.14.1	$15$	$x^{15} + 19$	$19$	$15$	$1$	$14$	$D_5\times C_3$ (as 15T3)	$2$	$15$	$[\ ]$	$[\ ]_{15}^{2}$	$t + 17$	$x^{15} + 19$	$[0]$	$[2]$
19.15.14.2	$15$	$x^{15} + 76$	$19$	$15$	$1$	$14$	$D_5\times C_3$ (as 15T3)	$2$	$15$	$[\ ]$	$[\ ]_{15}^{2}$	$t + 17$	$x^{15} + 76$	$[0]$	$[2]$
19.15.14.3	$15$	$x^{15} + 38$	$19$	$15$	$1$	$14$	$D_5\times C_3$ (as 15T3)	$2$	$15$	$[\ ]$	$[\ ]_{15}^{2}$	$t + 17$	$x^{15} + 38$	$[0]$	$[2]$