$p$-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
2.1.16.50h1.233	$16$	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.234	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.235	$16$	$x^{16} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.236	$16$	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.245	$16$	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.246	$16$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.247	$16$	$x^{16} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.248	$16$	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 26$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 13, 29, 45]$
2.1.16.50h1.633	$16$	$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.50h1.634	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.50h1.635	$16$	$x^{16} + 4 x^{14} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 4 x^{14} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.50h1.636	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 4 x^{10} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.50h1.669	$16$	$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.50h1.670	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.50h1.671	$16$	$x^{16} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.50h1.672	$16$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$2$	$1$	$16$	$50$	$C_2^3.\SD_{16}$ (as 16T374)	$2$	$1$	$[2, 2, 3, 4]$	$[1,1,2,3]$	$[2, 2, \frac{5}{2}, 3, 3, 4]^{2}$	$[1,1,\frac{3}{2},2,2,3]^{2}$	$[\frac{5}{2},3]^{2}$	$[\frac{3}{2},2]^{2}$	$2$	$t + 1$	$x^{16} + 8 x^{15} + 4 x^{14} + 2 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{3} + 30$	$[35, 22, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$

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