$p$-adic field search results

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Results (18 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
3.1.15.22a1.1	$15$	$x^{15} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.4	$15$	$x^{15} + 3 x^{11} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 3 x^{11} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.7	$15$	$x^{15} + 6 x^{11} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 6 x^{11} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.10	$15$	$x^{15} + 3 x^{10} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.13	$15$	$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.16	$15$	$x^{15} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.19	$15$	$x^{15} + 6 x^{10} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.22	$15$	$x^{15} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a1.25	$15$	$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$3$	$t + 1$	$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[4, 1]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 1$	undefined
3.1.15.22a2.1	$15$	$x^{15} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.2	$15$	$x^{15} + 3 x^{11} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 3 x^{11} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.3	$15$	$x^{15} + 6 x^{11} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 6 x^{11} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.4	$15$	$x^{15} + 3 x^{10} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 3 x^{10} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.5	$15$	$x^{15} + 3 x^{11} + 3 x^{10} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 3 x^{11} + 3 x^{10} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.6	$15$	$x^{15} + 6 x^{11} + 3 x^{10} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 6 x^{11} + 3 x^{10} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.7	$15$	$x^{15} + 6 x^{10} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 6 x^{10} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.8	$15$	$x^{15} + 3 x^{11} + 6 x^{10} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 3 x^{11} + 6 x^{10} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined
3.1.15.22a2.9	$15$	$x^{15} + 6 x^{11} + 6 x^{10} + 6 x^{8} + 3$	$3$	$1$	$15$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[\frac{9}{5}]$	$[\frac{4}{5}]$	$[\frac{9}{5}, \frac{9}{5}, \frac{9}{5}, \frac{9}{5}]_{5}^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5},\frac{4}{5}]_{5}^{4}$	$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$	$[\frac{4}{5},\frac{4}{5},\frac{4}{5}]^{4}$	$1$	$t + 1$	$x^{15} + 6 x^{11} + 6 x^{10} + 6 x^{8} + 3$	$[8, 0]$	$[4, 2]$	$z^{12} + 2 z^9 + z^6 + z^3 + 2,2 z^2 + 2$	undefined

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