$p$-adic field search results

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Results (16 matches)

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Label	$n$	Polynomial	$p$	$f$	$e$	$c$	Galois group	$u$	$t$	Visible Artin slopes	Visible Swan slopes	Artin slope content	Swan slope content	Hidden Artin slopes	Hidden Swan slopes	$\#\Aut(K/\Q_p)$	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia	Resid. Poly	Jump Set
2.1.16.50h2.23	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.24	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.27	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 18$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.28	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 2$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.103	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 10$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 10$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.104	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 26$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.107	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 26$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.108	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 10$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{3} + 10$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.161	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 2$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 2$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.162	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 18$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 18$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.165	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 18$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 18$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.166	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 2$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 2$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.241	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 10$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 10$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.242	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$D_4\times A_4$ (as 16T179)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 26$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.245	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 26$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$
2.1.16.50h2.246	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 10$	$2$	$1$	$16$	$50$	$D_4.A_4$ (as 16T180)	$3$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, 2, 3, 4]^{3}$	$[1,1,1,2,3]^{3}$	$[2]^{3}$	$[1]^{3}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 10$	$[35, 22, 12, 8, 0]$	$[3, 1, 1]$	$z^{12} + z^4 + 1,z^2 + 1,z + 1$	$[1, 2, 7, 15, 31]$

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