Properties

Label 3.2.1.0a1.1-1.9.20a
Base 3.2.1.0a1.1
Degree \(9\)
e \(9\)
f \(1\)
c \(20\)

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Defining polynomial

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

Invariants

Residue field characteristic: $3$
Degree: $9$
Base field: $\Q_{3}(\sqrt{2})$
Ramification index $e$: $9$
Residue field degree $f$: $1$
Discriminant exponent $c$: $20$
Absolute Artin slopes: $[\frac{3}{2},\frac{17}{6}]$
Swan slopes: $[\frac{1}{2},\frac{11}{6}]$
Means: $\langle\frac{1}{3},\frac{4}{3}\rangle$
Rams: $(\frac{1}{2},\frac{9}{2})$
Field count: $2943$ (complete)
Ambiguity: $1$
Mass: $5832$
Absolute Mass: $2916$

Diagrams

Varying

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

Indices of inseparability: $[12,3,0]$
Associated inertia: $[1,1]$
Jump Set: undefined

Fields


Showing 1-50 of at least 1000

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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
3.2.9.40a1.1 $( x^{2} + 2 x + 2 )^{9} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.2 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5:D_6$ (as 18T411) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.3 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^3:D_6$ (as 18T136) $324$ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.4 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.5 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^3:D_6$ (as 18T136) $324$ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.6 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.7 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.8 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.9 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.10 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.11 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.12 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.13 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.14 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.15 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.16 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^3:D_6$ (as 18T136) $324$ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.17 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.18 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.19 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5:D_6$ (as 18T411) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.20 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.21 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.22 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.23 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.24 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.25 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.26 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.27 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.28 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.29 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.30 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.31 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^3:D_6$ (as 18T136) $324$ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.32 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.33 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^3:D_6$ (as 18T136) $324$ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.34 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.35 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^3:D_6$ (as 18T136) $324$ $2$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.36 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.37 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.38 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.39 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.40 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.41 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.42 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.43 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.44 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.45 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{7} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5.D_6$ (as 18T407) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.46 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.47 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.48 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.49 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ $C_3^5:D_6$ (as 18T411) $2916$ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
3.2.9.40a1.50 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{7} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 3$ not computed $ $not computed$ $ $1$ not computed not computed not computed not computed $[12, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z + 2$ undefined
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