$p$-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
7.15.0.1	$15$	$x^{15} + 5 x^{6} + 6 x^{5} + 6 x^{4} + 4 x^{3} + x^{2} + 2 x + 4$	$7$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$15$	$1$	$[\ ]$	$[\ ]^{15}$	$t^{15} + 5 t^{6} + 6 t^{5} + 6 t^{4} + 4 t^{3} + t^{2} + 2 t + 4$	$x - 7$	$[0]$	$[]$
7.15.10.1	$15$	$x^{15} + 35 x^{12} + 3 x^{11} + 12 x^{10} + 490 x^{9} - 315 x^{8} - 2517 x^{7} + 3454 x^{6} - 834 x^{5} + 26565 x^{4} + 12846 x^{3} + 13662 x^{2} - 19944 x + 16290$	$7$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + t + 4$	$x^{3} + 7$	$[0]$	$[1]$
7.15.10.2	$15$	$x^{15} + 2401 x^{3} - 67228$	$7$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + t + 4$	$x^{3} + 7 t$	$[0]$	$[1]$
7.15.10.3	$15$	$x^{15} + 98 x^{9} + 2401 x^{3} + 268912$	$7$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]$	$[\ ]_{3}^{5}$	$t^{5} + t + 4$	$x^{3} + 7 t^{2}$	$[0]$	$[1]$
7.15.12.1	$15$	$x^{15} + 30 x^{14} + 360 x^{13} + 2180 x^{12} + 6960 x^{11} + 12117 x^{10} + 17860 x^{9} + 33840 x^{8} + 45000 x^{7} + 90640 x^{6} - 100029 x^{5} - 595410 x^{4} - 585880 x^{3} + 441960 x^{2} + 576240 x + 404231$	$7$	$5$	$3$	$12$	$F_5\times C_3$ (as 15T8)	$12$	$5$	$[\ ]$	$[\ ]_{5}^{12}$	$t^{3} + 6 t^{2} + 4$	$x^{5} + 7$	$[0]$	$[4]$
7.15.14.1	$15$	$x^{15} + 7$	$7$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 4$	$x^{15} + 7$	$[0]$	$[4]$
7.15.14.2	$15$	$x^{15} + 14$	$7$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 4$	$x^{15} + 14$	$[0]$	$[4]$
7.15.14.3	$15$	$x^{15} + 21$	$7$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 4$	$x^{15} + 21$	$[0]$	$[4]$