Properties

Label 3.2.9.42a
Base 3.1.1.0a1.1
Degree \(18\)
e \(9\)
f \(2\)
c \(42\)

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Defining polynomial over unramified subextension

$x^{9} + 9 b_{16} x^{7} + 3 a_{6} x^{6} + 9 b_{14} x^{5} + 9 a_{13} x^{4} + 9 c_{9} + 3$

Invariants

Residue field characteristic: $3$
Degree: $18$
Base field: $\Q_{3}$
Ramification index $e$: $9$
Residue field degree $f$: $2$
Discriminant exponent $c$: $42$
Artin slopes: $[2,\frac{17}{6}]$
Swan slopes: $[1,\frac{11}{6}]$
Means: $\langle\frac{2}{3},\frac{13}{9}\rangle$
Rams: $(1,\frac{7}{2})$
Field count: $2610$ (complete)
Ambiguity: $6$
Mass: $5184$
Absolute Mass: $2592$

Diagrams

Varying

Indices of inseparability: $[13,6,0]$
Associated inertia: $[1,1]$ (show 1314), $[2,1]$ (show 1296)
Jump Set: undefined

Fields


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Label Packet size Polynomial Galois group Galois degree $\#\Aut(K/\Q_p)$ Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
3.2.9.42a1.1 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^2:D_6$ (as 18T51) $108$ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.2 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.3 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^2:D_6$ (as 18T51) $108$ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.4 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.5 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^2:D_6$ (as 18T51) $108$ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.6 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.7 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.8 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^2:S_3^2$ (as 18T133) $324$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.9 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^2:D_6$ (as 18T51) $108$ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.10 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^2:S_3^2$ (as 18T133) $324$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.11 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.12 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.13 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.14 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.15 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.16 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^2:S_3^2$ (as 18T133) $324$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.17 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.18 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.19 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.20 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.21 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.22 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.23 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.24 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.25 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.26 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.27 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.28 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.29 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.30 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.31 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.32 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.33 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.34 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.35 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.36 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.37 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.38 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.39 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.40 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.41 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.42 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.43 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.44 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a1.45 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 ) + 9 x + 3$ $C_3^4:S_3^2$ (as 18T409) $2916$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (2 t + 2)$ undefined
3.2.9.42a2.1 $( x^{2} + 2 x + 2 )^{9} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (t + 1)$ undefined
3.2.9.42a2.2 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (t + 1)$ undefined
3.2.9.42a2.3 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^3:D_6$ (as 18T129) $324$ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (t + 1)$ undefined
3.2.9.42a2.4 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{4} + 3$ $C_3^3:S_3^2$ (as 18T256) $972$ $1$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (t + 1)$ undefined
3.2.9.42a2.5 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{4} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[13, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z + (t + 1)$ undefined
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