$p$-adic field search results

Results (4 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
2.15.0.1	$15$	$x^{15} + x^{5} + x^{4} + x^{2} + 1$	$2$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$15$	$1$	$[\ ]$	$[\ ]^{15}$	$t^{15} + t^{5} + t^{4} + t^{2} + 1$	$x - 2$	$[0]$	$[]$
2.15.10.1	$15$	$x^{15} + 13 x^{12} + 3 x^{10} + 13 x^{9} - 174 x^{7} - 45 x^{6} + 3 x^{5} + 513 x^{4} + 63 x^{2} - 216 x + 109$	$2$	$3$	$5$	$10$	$S_3 \times C_5$ (as 15T4)	$10$	$3$	$[\ ]$	$[\ ]_{3}^{10}$	$t^{5} + t^{2} + 1$	$x^{3} + 2$	$[0]$	$[2]$
2.15.12.1	$15$	$x^{15} + 5 x^{13} + 5 x^{12} + 10 x^{11} + 26 x^{10} + 20 x^{9} - 145 x^{7} + 70 x^{6} + 73 x^{5} + 315 x^{4} - 105 x^{3} + 200 x^{2} + 5 x + 1$	$2$	$5$	$3$	$12$	$F_5\times C_3$ (as 15T8)	$12$	$5$	$[\ ]$	$[\ ]_{5}^{12}$	$t^{3} + t + 1$	$x^{5} + 2$	$[0]$	$[4]$
2.15.14.1	$15$	$x^{15} + 2$	$2$	$15$	$1$	$14$	$C_{15} : C_4$ (as 15T6)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 1$	$x^{15} + 2$	$[0]$	$[4]$