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Properties

Label 3.1.12.22a
Base 3.1.1.0a1.1
Degree \(12\)
e \(12\)
f \(1\)
c \(22\)

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Defining polynomial

$x^{12} + 3 a_{11} x^{11} + 9 b_{16} x^{4} + 9 b_{14} x^{2} + 9 b_{13} x + 3 d_{0}$

Invariants

Residue field characteristic: $3$
Degree: $12$
Base field: $\Q_{3}$
Ramification index $e$: $12$
Residue field degree $f$: $1$
Discriminant exponent $c$: $22$
Artin slopes: $[\frac{19}{8}]$
Swan slopes: $[\frac{11}{8}]$
Means: $\langle\frac{11}{12}\rangle$
Rams: $(\frac{11}{2})$
Field count: $54$ (complete)
Ambiguity: $2$
Mass: $54$
Absolute Mass: $54$

Diagrams

Varying

Indices of inseparability: $[11,0]$
Associated inertia: $[2,1]$
Jump Set: undefined (show 27), $[2,14]$ (show 27)

Galois groups and Hidden Artin slopes

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Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
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Showing 1-50 of 54

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
3.1.12.22a1.1 12 $x^{12} + 3 x^{11} + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.2 12 $x^{12} + 3 x^{11} + 9 x^{4} + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.3 12 $x^{12} + 3 x^{11} + 18 x^{4} + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.4 12 $x^{12} + 3 x^{11} + 9 x^{2} + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.5 12 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.6 12 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.7 6 $x^{12} + 3 x^{11} + 18 x^{2} + 3$ $F_9:C_2$ (as 12T84) $144$ $1$ $[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{19}{8}]^{2}_{2}$ $[\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.8 6 $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 3$ $F_9:C_2$ (as 12T84) $144$ $1$ $[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{19}{8}]^{2}_{2}$ $[\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.9 6 $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 3$ $F_9:C_2$ (as 12T84) $144$ $1$ $[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{19}{8}]^{2}_{2}$ $[\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.10 36 $x^{12} + 3 x^{11} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.11 36 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.12 36 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.13 36 $x^{12} + 3 x^{11} + 9 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.14 36 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.15 36 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.16 36 $x^{12} + 3 x^{11} + 18 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.17 36 $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.18 36 $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.19 36 $x^{12} + 6 x^{11} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.20 36 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.21 36 $x^{12} + 6 x^{11} + 18 x^{4} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.22 36 $x^{12} + 6 x^{11} + 9 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.23 36 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.24 36 $x^{12} + 6 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.25 36 $x^{12} + 6 x^{11} + 18 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.26 36 $x^{12} + 6 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.27 36 $x^{12} + 6 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 3$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.28 12 $x^{12} + 3 x^{11} + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.29 12 $x^{12} + 3 x^{11} + 9 x^{4} + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.30 12 $x^{12} + 3 x^{11} + 18 x^{4} + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.31 6 $x^{12} + 3 x^{11} + 9 x^{2} + 6$ $F_9:C_2$ (as 12T84) $144$ $1$ $[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{19}{8}]^{2}_{2}$ $[\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.32 6 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 6$ $F_9:C_2$ (as 12T84) $144$ $1$ $[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{19}{8}]^{2}_{2}$ $[\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.33 6 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 6$ $F_9:C_2$ (as 12T84) $144$ $1$ $[\frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{19}{8}]^{2}_{2}$ $[\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.34 12 $x^{12} + 3 x^{11} + 18 x^{2} + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.35 12 $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.36 12 $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.37 36 $x^{12} + 3 x^{11} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.38 36 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.39 36 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.40 36 $x^{12} + 3 x^{11} + 9 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.41 36 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.42 36 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.43 36 $x^{12} + 3 x^{11} + 18 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.44 36 $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.45 36 $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.46 36 $x^{12} + 6 x^{11} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.47 36 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.48 36 $x^{12} + 6 x^{11} + 18 x^{4} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.49 36 $x^{12} + 6 x^{11} + 9 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.50 36 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 6$ $C_3^4:\SD_{16}$ (as 12T212) $1296$ $1$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
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