$p$-adic field search results

Results (4 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
89.1.20.19a1.1	$20$	$x^{20} + 89$	$89$	$1$	$20$	$19$	$C_4\times D_5$ (as 20T6)	$2$	$20$	$[\ ]$	$[\ ]$	$[\ ]_{20}^{2}$	$[\ ]_{20}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$4$	$t + 86$	$x^{20} + 89$	$[0]$	$[2]$	$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$	undefined
89.1.20.19a1.2	$20$	$x^{20} + 267$	$89$	$1$	$20$	$19$	$C_4\times D_5$ (as 20T6)	$2$	$20$	$[\ ]$	$[\ ]$	$[\ ]_{20}^{2}$	$[\ ]_{20}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$4$	$t + 86$	$x^{20} + 267$	$[0]$	$[2]$	$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$	undefined
89.1.20.19a1.3	$20$	$x^{20} + 801$	$89$	$1$	$20$	$19$	$C_4\times D_5$ (as 20T6)	$2$	$20$	$[\ ]$	$[\ ]$	$[\ ]_{20}^{2}$	$[\ ]_{20}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$4$	$t + 86$	$x^{20} + 801$	$[0]$	$[2]$	$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$	undefined
89.1.20.19a1.4	$20$	$x^{20} + 2403$	$89$	$1$	$20$	$19$	$C_4\times D_5$ (as 20T6)	$2$	$20$	$[\ ]$	$[\ ]$	$[\ ]_{20}^{2}$	$[\ ]_{20}^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$4$	$t + 86$	$x^{20} + 2403$	$[0]$	$[2]$	$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$	undefined

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