Properties

Label 3.2.9.38b
Base 3.1.1.0a1.1
Degree \(18\)
e \(9\)
f \(2\)
c \(38\)

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Defining polynomial over unramified subextension

$x^{9} + 9 c_{15} x^{6} + 9 b_{14} x^{5} + 9 b_{13} x^{4} + 3 a_{3} x^{3} + 9 a_{11} x^{2} + 3$

Invariants

Residue field characteristic: $3$
Degree: $18$
Base field: $\Q_{3}$
Ramification index $e$: $9$
Residue field degree $f$: $2$
Discriminant exponent $c$: $38$
Artin slopes: $[\frac{3}{2},\frac{8}{3}]$
Swan slopes: $[\frac{1}{2},\frac{5}{3}]$
Means: $\langle\frac{1}{3},\frac{11}{9}\rangle$
Rams: $(\frac{1}{2},4)$
Field count: $5220$ (complete)
Ambiguity: $6$
Mass: $5184$
Absolute Mass: $2592$

Diagrams

Varying

Indices of inseparability: $[11,3,0]$
Associated inertia: $[1,1]$ (show 3924), $[1,2]$ (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
3.2.9.38b1.1 $( x^{2} + 2 x + 2 )^{9} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $6$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.2 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.3 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.4 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.5 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.6 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $6$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.7 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.8 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.9 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.10 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.11 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $6$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.12 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.13 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.14 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.15 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.16 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.17 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.18 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.19 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.20 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.21 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.22 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.23 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 18 x ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.24 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + 18 x ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.25 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.26 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.27 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.28 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.29 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.30 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.31 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.32 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.33 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.34 $( x^{2} + 2 x + 2 )^{9} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.35 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.36 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.37 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.38 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.39 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.40 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.41 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.42 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{5} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.43 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^2:D_6$ (as 18T57) $108$ $6$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.44 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.45 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.46 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.47 $( x^{2} + 2 x + 2 )^{9} + 18 x ( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.48 $( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ not computed $ $not computed$ $ $6$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.49 $( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^3:D_6$ (as 18T126) $324$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
3.2.9.38b1.50 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{5} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 3$ $C_3^5:D_6$ (as 18T406) $2916$ $3$ not computed not computed not computed not computed $[11, 3, 0]$ $[1, 1]$ $z^3 + (t + 1),(t + 1) z^2 + (t + 1)$ undefined
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