$p$-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
17.15.0.1	$15$	$x^{15} + 4 x^{6} + 4 x^{5} + 16 x^{4} + 6 x^{3} + 14 x^{2} + 14 x + 14$	$17$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$15$	$1$	$[\ ]$	$[\ ]^{15}$	$t^{15} + 4 t^{6} + 4 t^{5} + 16 t^{4} + 6 t^{3} + 14 t^{2} + 14 t + 14$	$x - 17$	$[0]$	$[]$
17.15.10.1	$15$	$x^{15} + 85 x^{12} + 3 x^{11} + 42 x^{10} + 2890 x^{9} - 765 x^{8} - 21417 x^{7} + 49214 x^{6} - 4614 x^{5} + 546465 x^{4} + 424746 x^{3} + 247392 x^{2} - 1027674 x + 1410480$	$17$	$3$	$5$	$10$	$S_3 \times C_5$ (as 15T4)	$10$	$3$	$[\ ]$	$[\ ]_{3}^{10}$	$t^{5} + t + 14$	$x^{3} + 17$	$[0]$	$[2]$
17.15.12.1	$15$	$x^{15} + 5 x^{13} + 70 x^{12} + 10 x^{11} + 331 x^{10} + 1970 x^{9} + 165 x^{8} - 15535 x^{7} + 28060 x^{6} + 10318 x^{5} + 504940 x^{4} + 183500 x^{3} + 248865 x^{2} - 505940 x + 539184$	$17$	$5$	$3$	$12$	$F_5\times C_3$ (as 15T8)	$12$	$5$	$[\ ]$	$[\ ]_{5}^{12}$	$t^{3} + t + 14$	$x^{5} + 17$	$[0]$	$[4]$
17.15.14.1	$15$	$x^{15} + 17$	$17$	$15$	$1$	$14$	$C_{15} : C_4$ (as 15T6)	$4$	$15$	$[\ ]$	$[\ ]_{15}^{4}$	$t + 14$	$x^{15} + 17$	$[0]$	$[4]$