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Properties

Label 2.9.2.18a
Base 2.1.1.0a1.1
Degree \(18\)
e \(2\)
f \(9\)
c \(18\)

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Defining polynomial over unramified subextension

$x^{2} + 2 a_{1} x + 4 c_{2} + 2$

Invariants

Residue field characteristic: $2$
Degree: $18$
Base field: $\Q_{2}$
Ramification index $e$: $2$
Residue field degree $f$: $9$
Discriminant exponent $c$: $18$
Artin slopes: $[2]$
Swan slopes: $[1]$
Means: $\langle\frac{1}{2}\rangle$
Rams: $(1)$
Field count: $118$ (complete)
Ambiguity: $18$
Mass: $511$
Absolute Mass: $511/9$

Diagrams

Varying

Indices of inseparability: $[1,0]$
Associated inertia: $[1]$
Jump Set: $[1,2]$ (show 1), $[1,3]$ (show 116), $[1,4]$ (show 1)

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Fields

Galois group Galois Artin Indices
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Showing 1-50 of 118

Next   displayed columns for results
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
2.9.2.18a1.1 2 $( x^{9} + x^{4} + 1 )^{2} + 2 ( x^{9} + x^{4} + 1 ) + 2$ $C_{18}$ (as 18T1) $18$ $18$ $[2]^{9}$ $[1]^{9}$ $[\ ]$ $[\ ]$ $[1, 0]$ $[1]$ $z + t^8$ $[1, 2]$
2.9.2.18a1.2 2 $( x^{9} + x^{4} + 1 )^{2} + 2 ( x^{9} + x^{4} + 1 ) + 6$ $C_{18}$ (as 18T1) $18$ $18$ $[2]^{9}$ $[1]^{9}$ $[\ ]$ $[\ ]$ $[1, 0]$ $[1]$ $z + t^8$ $[1, 4]$
2.9.2.18a2.1 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x ( x^{9} + x^{4} + 1 ) + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^4 + 1)$ $[1, 3]$
2.9.2.18a2.2 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^4 + 1)$ $[1, 3]$
2.9.2.18a3.1 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x^{3} ( x^{9} + x^{4} + 1 ) + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^6 + t^2)$ $[1, 3]$
2.9.2.18a3.2 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x^{3} ( x^{9} + x^{4} + 1 ) + 4 x^{6} + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^6 + t^2)$ $[1, 3]$
2.9.2.18a4.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{4} + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2]$ $[1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^3)$ $[1, 3]$
2.9.2.18a4.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{4} + 2\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2]$ $[1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^3)$ $[1, 3]$
2.9.2.18a5.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{4} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^4 + t^3 + 1)$ $[1, 3]$
2.9.2.18a5.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{4} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^4 + t^3 + 1)$ $[1, 3]$
2.9.2.18a6.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_9$ (as 18T177) $576$ $2$ $[2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1]^{9}$ $[2,2,2,2,2]$ $[1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^4 + t^3 + t^2 + 1)$ $[1, 3]$
2.9.2.18a6.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x^{3} + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1]^{18}$ $[2,2,2,2,2]^{2}$ $[1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^4 + t^3 + t^2 + 1)$ $[1, 3]$
2.9.2.18a7.1 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x^{5} ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_9$ (as 18T177) $576$ $2$ $[2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1]^{9}$ $[2,2,2,2,2]$ $[1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^4)$ $[1, 3]$
2.9.2.18a7.2 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x^{5} ( x^{9} + x^{4} + 1 ) + 4 x + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1]^{18}$ $[2,2,2,2,2]^{2}$ $[1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^4)$ $[1, 3]$
2.9.2.18a8.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{5} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^6 + t^4 + t^2)$ $[1, 3]$
2.9.2.18a8.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{5} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^6 + t^4 + t^2)$ $[1, 3]$
2.9.2.18a9.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^4 + t + 1)$ $[1, 3]$
2.9.2.18a9.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^4 + t + 1)$ $[1, 3]$
2.9.2.18a10.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^6 + t^5 + t^4 + t^2 + 1)$ $[1, 3]$
2.9.2.18a10.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^6 + t^5 + t^4 + t^2 + 1)$ $[1, 3]$
2.9.2.18a11.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2]$ $[1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^6 + t^4 + t^2 + t + 1)$ $[1, 3]$
2.9.2.18a11.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2]$ $[1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^6 + t^4 + t^2 + t + 1)$ $[1, 3]$
2.9.2.18a12.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^6 + t^2 + t)$ $[1, 3]$
2.9.2.18a12.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^6 + t^2 + t)$ $[1, 3]$
2.9.2.18a13.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{4} + 2 x^{2} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^3 + t)$ $[1, 3]$
2.9.2.18a13.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{4} + 2 x^{2} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^3 + t)$ $[1, 3]$
2.9.2.18a14.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^5 + t^3 + t^2)$ $[1, 3]$
2.9.2.18a14.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^5 + t^3 + t^2)$ $[1, 3]$
2.9.2.18a15.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^5 + t^4)$ $[1, 3]$
2.9.2.18a15.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^5 + t^4)$ $[1, 3]$
2.9.2.18a16.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^6 + t^2 + t + 1)$ $[1, 3]$
2.9.2.18a16.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^6 + t^2 + t + 1)$ $[1, 3]$
2.9.2.18a17.1 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x^{7} ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_9$ (as 18T177) $576$ $2$ $[2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1]^{9}$ $[2,2,2,2,2]$ $[1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^6 + t^5 + t)$ $[1, 3]$
2.9.2.18a17.2 1 $( x^{9} + x^{4} + 1 )^{2} + 2 x^{7} ( x^{9} + x^{4} + 1 ) + 4 x + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1]^{18}$ $[2,2,2,2,2]^{2}$ $[1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^6 + t^5 + t)$ $[1, 3]$
2.9.2.18a18.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{3} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2]$ $[1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^4 + t^2 + 1)$ $[1, 3]$
2.9.2.18a18.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{3} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2]$ $[1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^4 + t^2 + 1)$ $[1, 3]$
2.9.2.18a19.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1]^{18}$ $[2,2,2,2,2]^{2}$ $[1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^7 + t^6 + t^4 + t^3 + 1)$ $[1, 3]$
2.9.2.18a19.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x^{3} + 2$ $C_2^6:C_9$ (as 18T177) $576$ $2$ $[2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1]^{9}$ $[2,2,2,2,2]$ $[1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^7 + t^6 + t^4 + t^3 + 1)$ $[1, 3]$
2.9.2.18a20.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x^{3} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^5 + t^4 + t^3 + t^2 + t + 1)$ $[1, 3]$
2.9.2.18a20.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x^{3} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^5 + t^4 + t^3 + t^2 + t + 1)$ $[1, 3]$
2.9.2.18a21.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{5} + 2 x^{4}\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2^6:C_{18}$ (as 18T264) $1152$ $2$ $[2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1]^{18}$ $[2,2,2,2,2]^{2}$ $[1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t)$ $[1, 3]$
2.9.2.18a21.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{5} + 2 x^{4}\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ $C_2^6:C_9$ (as 18T177) $576$ $2$ $[2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1]^{9}$ $[2,2,2,2,2]$ $[1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t)$ $[1, 3]$
2.9.2.18a22.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^4 + t^3)$ $[1, 3]$
2.9.2.18a22.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^8 + t^7 + t^6 + t^4 + t^3)$ $[1, 3]$
2.9.2.18a23.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^6 + t^5)$ $[1, 3]$
2.9.2.18a23.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^6 + t^5)$ $[1, 3]$
2.9.2.18a24.1 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^2 + t)$ $[1, 3]$
2.9.2.18a24.2 2 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 6$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^2 + t)$ $[1, 3]$
2.9.2.18a25.1 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ $C_2\wr C_9$ (as 18T460) $4608$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{18}$ $[1,1,1,1,1,1,1,1]^{18}$ $[2,2,2,2,2,2,2]^{2}$ $[1,1,1,1,1,1,1]^{2}$ $[1, 0]$ $[1]$ $z + (t^7 + t^3 + t^2 + t)$ $[1, 3]$
2.9.2.18a25.2 1 $( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ $C_2^8:C_9$ (as 18T368) $2304$ $2$ $[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ $[1,1,1,1,1,1,1,1]^{9}$ $[2,2,2,2,2,2,2]$ $[1,1,1,1,1,1,1]$ $[1, 0]$ $[1]$ $z + (t^7 + t^3 + t^2 + t)$ $[1, 3]$
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