Properties

Label 3.2.3.8a1.2-1.3.11a
Base 3.2.3.8a1.2
Degree \(3\)
e \(3\)
f \(1\)
c \(11\)

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Defining polynomial

$x^{3} + b_{11} \pi^{4} x^{2} + \left(b_{13} \pi^{5} + b_{10} \pi^{4}\right) x + \pi$

Invariants

Residue field characteristic: $3$
Degree: $3$
Base field: 3.2.3.8a1.2
Ramification index $e$: $3$
Residue field degree $f$: $1$
Discriminant exponent $c$: $11$
Absolute Artin slopes: $[2,\frac{19}{6}]$
Swan slopes: $[\frac{9}{2}]$
Means: $\langle3\rangle$
Rams: $(\frac{9}{2})$
Field count: $243$ (complete)
Ambiguity: $1$
Mass: $729$
Absolute Mass: $243$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 3 }$ within this relative family, not the relative extension.

Indices of inseparability: $[15,6,0]$
Associated inertia: $[1,1]$
Jump Set: undefined

Fields


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Label Polynomial $/ \Q_p$ Galois group $/ \Q_p$ Galois degree $/ \Q_p$ $\#\Aut(K/\Q_p)$ Artin slope content $/ \Q_p$ Swan slope content $/ \Q_p$ Hidden Artin slopes $/ \Q_p$ Hidden Swan slopes $/ \Q_p$ Ind. of Insep. $/ \Q_p$ Assoc. Inertia $/ \Q_p$ Resid. Poly Jump Set
3.2.9.46a1.136 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.137 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.138 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.139 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.140 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.141 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.142 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.143 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.144 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.145 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.146 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.147 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.148 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.149 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.150 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.151 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.152 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.153 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.154 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.155 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.156 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.157 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.158 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.159 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.160 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.161 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.162 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.163 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.164 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.165 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.166 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.167 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.168 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.169 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.170 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.171 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.172 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.173 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.174 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.175 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.176 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.177 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.178 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.179 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.180 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.181 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 45\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.182 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.183 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 72\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $\He_3^2:S_3^2$ (as 18T650) $26244$ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.184 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.46a1.185 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + \left(45 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[15, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
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