LMFDB - p-adic field search results

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Degree $n$	Residue characteristic $p$	Discriminant exponent $c$	Galois group

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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
2.4.4.44a1.495	$16$	$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.496	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.497	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.498	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.499	$16$	$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.500	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.501	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.502	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.503	$16$	$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.504	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.505	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.506	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.507	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.508	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.509	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.510	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.607	$16$	$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.608	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.609	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.610	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.611	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.612	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.613	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.614	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.615	$16$	$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.616	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.617	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.618	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.619	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.620	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.621	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.622	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.671	$16$	$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.672	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.673	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.674	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.675	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.676	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.677	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.678	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.679	$16$	$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.680	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.681	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.682	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.683	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.684	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.685	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.686	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3).C_4$ (as 16T888)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1499	$16$	$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 t x^{2} + 8 t^{2} x + 16 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1500	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$	$2$	$4$	$4$	$44$	$(C_2\times C_4^3):C_4$ (as 16T898)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 3, 3, 3, 4]^{4}$	$[1,1,1,2,2,2,3]^{4}$	$[2,2,2,3,3]$	$[1,1,1,2,2]$	$4$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 16 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$

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