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Properties

Label 2.1.16.42k
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(42\)

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Defining polynomial

$x^{16} + 4 b_{31} x^{15} + 4 b_{29} x^{13} + 2 a_{12} x^{12} + 4 a_{27} x^{11} + \left(2 b_{8} + 4 c_{24}\right) x^{8} + 4 b_{22} x^{6} + 8 c_{36} x^{4} + 8 b_{35} x^{3} + 4 a_{18} x^{2} + 8 b_{33} x + 4 c_{16} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $42$
Artin slopes: $[2,2,\frac{5}{2},\frac{13}{4}]$
Swan slopes: $[1,1,\frac{3}{2},\frac{9}{4}]$
Means: $\langle\frac{1}{2},\frac{3}{4},\frac{9}{8},\frac{27}{16}\rangle$
Rams: $(1,1,3,9)$
Field count: $160$ (complete)
Ambiguity: $8$
Mass: $64$
Absolute Mass: $64$

Diagrams

Varying

Indices of inseparability: $[27,18,12,8,0]$ (show 80), $[27,18,12,12,0]$ (show 80)
Associated inertia: $[2,1,1]$ (show 80), $[3,1,1]$ (show 80)
Jump Set: $[1,2,7,15,31]$ (show 80), $[1,3,6,12,32]$ (show 40), $[1,3,9,25,41]$ (show 40)

Galois groups and Hidden Artin slopes

Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing all 40

  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
2.1.16.42k1.41 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.42 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 8 x + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.43 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.44 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{4} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.45 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{3} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.46 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.47 16 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.48 16 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 8 x + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.49 8 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$ $C_4^2.Q_{16}$ (as 16T697) $256$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.50 8 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 8 x^{3} + 4 x^{2} + 6$ $C_4^2.Q_{16}$ (as 16T697) $256$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.51 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.52 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 8 x + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.53 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.54 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.55 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.56 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{3} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.57 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$ $C_8^2:C_2^2$ (as 16T568) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.58 16 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1264) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.59 8 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 6$ $C_4^2.Q_{16}$ (as 16T697) $256$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.60 8 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{3} + 4 x^{2} + 6$ $C_4^2.Q_{16}$ (as 16T697) $256$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.61 8 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 6$ $C_2^3.\SD_{16}$ (as 16T374) $128$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$ $[3,3]^{2}$ $[2,2]^{2}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.62 8 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 6$ $C_2^3.\SD_{16}$ (as 16T374) $128$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$ $[3,3]^{2}$ $[2,2]^{2}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.63 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.64 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.65 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.66 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.67 16 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.68 16 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.69 8 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 6$ $C_2^3.\SD_{16}$ (as 16T374) $128$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$ $[3,3]^{2}$ $[2,2]^{2}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.70 16 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.71 16 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.72 16 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.73 8 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 6$ $C_2^3.\SD_{16}$ (as 16T374) $128$ $2$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$ $[3,3]^{2}$ $[2,2]^{2}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.74 16 $x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.75 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.76 16 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.77 16 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.78 16 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 6$ $C_2^6.\SD_{16}$ (as 16T1250) $1024$ $2$ $[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[2,2,3,3]_{4}$ $[1,1,2,2]_{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.79 16 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
2.1.16.42k1.80 16 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 6$ $C_2^4.\SD_{16}$ (as 16T673) $256$ $4$ $[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$ $[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$ $[3,3]^{4}$ $[2,2]^{4}$ $[27, 18, 12, 12, 0]$ $[2, 1, 1]$ $z^{12} + 1,z^2 + 1,z + 1$ $[1, 3, 6, 12, 32]$
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