$p$-adic field search results

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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
5.3.5.27a1.1	$15$	$( x^{3} + 3 x + 3 )^{5} + 5$	$5$	$3$	$5$	$27$	$F_5\times C_3$ (as 15T8)	$3$	$4$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$[\frac{9}{4}]_{4}^{3}$	$[\frac{5}{4}]_{4}^{3}$	$[\ ]_{4}$	$[\ ]_{4}$	$3$	$t^{3} + 3 t + 3$	$x^{5} + 5$	$[5, 0]$	$[1]$	$z + (4 t + 3)$	undefined
5.3.5.27a1.10	$15$	$( x^{3} + 3 x + 3 )^{5} + 25 ( x^{3} + 3 x + 3 ) + 5$	$5$	$3$	$5$	$27$	$F_5\times C_3$ (as 15T8)	$3$	$4$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$[\frac{9}{4}]_{4}^{3}$	$[\frac{5}{4}]_{4}^{3}$	$[\ ]_{4}$	$[\ ]_{4}$	$3$	$t^{3} + 3 t + 3$	$x^{5} + 25 x + 5$	$[5, 0]$	$[1]$	$z + (4 t + 3)$	undefined
5.3.5.27a1.19	$15$	$( x^{3} + 3 x + 3 )^{5} + 50 ( x^{3} + 3 x + 3 ) + 5$	$5$	$3$	$5$	$27$	$F_5\times C_3$ (as 15T8)	$3$	$4$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$[\frac{9}{4}]_{4}^{3}$	$[\frac{5}{4}]_{4}^{3}$	$[\ ]_{4}$	$[\ ]_{4}$	$3$	$t^{3} + 3 t + 3$	$x^{5} + 50 x + 5$	$[5, 0]$	$[1]$	$z + (4 t + 3)$	undefined
5.3.5.27a1.28	$15$	$( x^{3} + 3 x + 3 )^{5} + 75 ( x^{3} + 3 x + 3 ) + 5$	$5$	$3$	$5$	$27$	$F_5\times C_3$ (as 15T8)	$3$	$4$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$[\frac{9}{4}]_{4}^{3}$	$[\frac{5}{4}]_{4}^{3}$	$[\ ]_{4}$	$[\ ]_{4}$	$3$	$t^{3} + 3 t + 3$	$x^{5} + 75 x + 5$	$[5, 0]$	$[1]$	$z + (4 t + 3)$	undefined
5.3.5.27a1.37	$15$	$( x^{3} + 3 x + 3 )^{5} + 100 ( x^{3} + 3 x + 3 ) + 5$	$5$	$3$	$5$	$27$	$F_5\times C_3$ (as 15T8)	$3$	$4$	$[\frac{9}{4}]$	$[\frac{5}{4}]$	$[\frac{9}{4}]_{4}^{3}$	$[\frac{5}{4}]_{4}^{3}$	$[\ ]_{4}$	$[\ ]_{4}$	$3$	$t^{3} + 3 t + 3$	$x^{5} + 100 x + 5$	$[5, 0]$	$[1]$	$z + (4 t + 3)$	undefined

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