$p$-adic field search results

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Results (12 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
3.2.6.22a1.43	$12$	$( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 9 t x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.44	$12$	$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 9 x^{3} + \left(18 t + 9\right) x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.45	$12$	$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 18 x^{3} + 9 t x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.49	$12$	$( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + \left(18 t + 18\right) x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.50	$12$	$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 9 x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.51	$12$	$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 18 x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.55	$12$	$( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + \left(9 t + 18\right) x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.56	$12$	$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 9 x^{3} + 18 t x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.57	$12$	$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3\times S_3^2$ (as 12T70)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 18 x^{3} + \left(9 t + 18\right) x^{2} + 9 x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.58	$12$	$( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3:S_3^2$ (as 12T71)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + \left(18 t + 18\right) x^{2} + \left(9 t + 9\right) x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.63	$12$	$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3:S_3^2$ (as 12T71)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + \left(9 t + 18\right) x^{2} + \left(9 t + 9\right) x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$
3.2.6.22a1.68	$12$	$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$	$3$	$2$	$6$	$22$	$C_3:S_3^2$ (as 12T71)	$2$	$2$	$[\frac{5}{2}]$	$[\frac{3}{2}]$	$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$	$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$	$[\frac{3}{2},2]$	$[\frac{1}{2},1]$	$3$	$t^{2} + 2 t + 2$	$x^{6} + 9 t x^{2} + \left(9 t + 9\right) x + 3$	$[6, 0]$	$[1, 1]$	$z^3 + 2,2 z^2 + 2$	$[1, 7]$

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