$p$-adic field search results

Results (3 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
2.12.12.28	$12$	$x^{12} + 6 x^{11} + 21 x^{10} + 50 x^{9} + 90 x^{8} + 130 x^{7} + 159 x^{6} + 132 x^{5} + 10 x^{4} - 100 x^{3} - 53 x^{2} + 22 x + 19$	$2$	$6$	$2$	$12$	$S_4$ (as 12T9)	$2$	$3$	$[4/3]$	$[4/3, 4/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{6} + 2 x + 2$	$[1, 0]$	$[1, 1]$
2.12.20.34	$12$	$x^{12} + 4 x^{11} + 12 x^{10} + 24 x^{9} + 44 x^{8} + 32 x^{7} + 48 x^{6} + 16 x^{5} + 68 x^{4} + 32 x^{3} + 24 x^{2} + 28$	$2$	$6$	$2$	$20$	$S_4$ (as 12T9)	$2$	$3$	$[8/3]$	$[8/3, 8/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$	$[5, 0]$	$[1, 1]$
2.12.20.37	$12$	$x^{12} + 10 x^{11} + 51 x^{10} + 176 x^{9} + 450 x^{8} + 870 x^{7} + 1299 x^{6} + 1516 x^{5} + 1250 x^{4} + 542 x^{3} + 67 x^{2} - 56 x + 7$	$2$	$6$	$2$	$20$	$S_4$ (as 12T9)	$2$	$3$	$[8/3]$	$[8/3, 8/3]_{3}^{2}$	$t^{2} + t + 1$	$x^{6} + 2 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 6$	$[5, 0]$	$[1, 1]$