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Degree $n$
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Results (10 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
3.3.1.0a1.1
$3$
$x^{3} + 2 x + 1$
$3$
$3$
$1$
$0$
$C_3$ (as 3T1)
$3$
$1$
$[\ ]$
$[\ ]$
$[\ ]^{3}$
$[\ ]^{3}$
$[\ ]$
$[\ ]$
$3$
$t^{3} + 2 t + 1$
$x - 3$
$[0]$
$[\ ]$
undefined
3.1.3.3a1.1
$3$
$x^{3} + 3 x + 3$
$3$
$1$
$3$
$3$
$S_3$ (as 3T2)
$1$
$2$
$[\frac{3}{2}]$
$[\frac{1}{2}]$
$[\frac{3}{2}]_{2}$
$[\frac{1}{2}]_{2}$
$[\ ]_{2}$
$[\ ]_{2}$
$1$
$t + 1$
$x^{3} + 3 x + 3$
$[1, 0]$
$[1]$
$z + 2$
undefined
3.1.3.3a1.2
$3$
$x^{3} + 6 x + 3$
$3$
$1$
$3$
$3$
$S_3$ (as 3T2)
$1$
$2$
$[\frac{3}{2}]$
$[\frac{1}{2}]$
$[\frac{3}{2}]_{2}$
$[\frac{1}{2}]_{2}$
$[\ ]_{2}$
$[\ ]_{2}$
$1$
$t + 1$
$x^{3} + 6 x + 3$
$[1, 0]$
$[1]$
$z + 1$
undefined
3.1.3.4a1.1
$3$
$x^{3} + 3 x^{2} + 3$
$3$
$1$
$3$
$4$
$S_3$ (as 3T2)
$2$
$1$
$[2]$
$[1]$
$[2]^{2}$
$[1]^{2}$
$[\ ]^{2}$
$[\ ]^{2}$
$1$
$t + 1$
$x^{3} + 3 x^{2} + 3$
$[2, 0]$
$[2]$
$z^{2} + 1$
undefined
3.1.3.4a2.1
$3$
$x^{3} + 6 x^{2} + 3$
$3$
$1$
$3$
$4$
$C_3$ (as 3T1)
$1$
$1$
$[2]$
$[1]$
$[2]$
$[1]$
$[\ ]$
$[\ ]$
$3$
$t + 1$
$x^{3} + 6 x^{2} + 3$
$[2, 0]$
$[1]$
$z^{2} + 2$
undefined
3.1.3.4a2.2
$3$
$x^{3} + 6 x^{2} + 12$
$3$
$1$
$3$
$4$
$C_3$ (as 3T1)
$1$
$1$
$[2]$
$[1]$
$[2]$
$[1]$
$[\ ]$
$[\ ]$
$3$
$t + 1$
$x^{3} + 6 x^{2} + 12$
$[2, 0]$
$[1]$
$z^{2} + 2$
undefined
3.1.3.4a2.3
$3$
$x^{3} + 6 x^{2} + 21$
$3$
$1$
$3$
$4$
$C_3$ (as 3T1)
$1$
$1$
$[2]$
$[1]$
$[2]$
$[1]$
$[\ ]$
$[\ ]$
$3$
$t + 1$
$x^{3} + 6 x^{2} + 21$
$[2, 0]$
$[1]$
$z^{2} + 2$
undefined
3.1.3.5a1.1
$3$
$x^{3} + 3$
$3$
$1$
$3$
$5$
$S_3$ (as 3T2)
$1$
$2$
$[\frac{5}{2}]$
$[\frac{3}{2}]$
$[\frac{5}{2}]_{2}$
$[\frac{3}{2}]_{2}$
$[\ ]_{2}$
$[\ ]_{2}$
$1$
$t + 1$
$x^{3} + 3$
$[3, 0]$
$[1]$
$z + 2$
undefined
3.1.3.5a1.2
$3$
$x^{3} + 9 x + 3$
$3$
$1$
$3$
$5$
$S_3$ (as 3T2)
$1$
$2$
$[\frac{5}{2}]$
$[\frac{3}{2}]$
$[\frac{5}{2}]_{2}$
$[\frac{3}{2}]_{2}$
$[\ ]_{2}$
$[\ ]_{2}$
$1$
$t + 1$
$x^{3} + 9 x + 3$
$[3, 0]$
$[1]$
$z + 2$
undefined
3.1.3.5a1.3
$3$
$x^{3} + 18 x + 3$
$3$
$1$
$3$
$5$
$S_3$ (as 3T2)
$1$
$2$
$[\frac{5}{2}]$
$[\frac{3}{2}]$
$[\frac{5}{2}]_{2}$
$[\frac{3}{2}]_{2}$
$[\ ]_{2}$
$[\ ]_{2}$
$1$
$t + 1$
$x^{3} + 18 x + 3$
$[3, 0]$
$[1]$
$z + 2$
undefined
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