Properties

Label 2.1.4.9a1.5-1.4.18c
Base 2.1.4.9a1.5
Degree \(4\)
e \(4\)
f \(1\)
c \(18\)

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Defining polynomial

$x^{4} + \left(b_{23} \pi^{6} + b_{19} \pi^{5} + a_{15} \pi^{4}\right) x^{3} + \left(b_{10} \pi^{3} + a_{6} \pi^{2}\right) x^{2} + \left(b_{21} \pi^{6} + b_{17} \pi^{5}\right) x + c_{24} \pi^{7} + c_{12} \pi^{4} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.9a1.5
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $18$
Absolute Artin slopes: $[2,3,\frac{7}{2},4]$
Swan slopes: $[3,6]$
Means: $\langle\frac{3}{2},\frac{15}{4}\rangle$
Rams: $(3,9)$
Field count: $52$ (incomplete)
Ambiguity: $4$
Mass: $32$
Absolute Mass: $16$ ($14$ currently in the LMFDB)

Diagrams

Varying

The following invariants arise for fields within the LMFDB; since not all fields in this family are stored, it may be incomplete.

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $C_4:C_4$ (show 2), $C_4 \times D_4$ (show 2), $C_2^2:Q_8$ (show 2), $C_4:D_4$ (show 1), $C_2^2\wr C_2$ (show 1), $C_4:D_4$ (show 1), $C_2^2\wr C_2$ (show 1), $C_2^2.D_4$ (show 1), $C_2^3.D_4$ (show 1), $C_2\wr C_2^2$ (show 1), $C_2\wr C_2^2$ (show 1), $C_2^2:\SD_{16}$ (show 4), $C_2^3.D_4$ (show 1), $C_4^2:D_4$ (show 8), $C_2^4.D_4$ (show 2), $C_2^4.D_4$ (show 2), $C_4^2:D_4$ (show 2), $C_4^2.D_4$ (show 4), $C_4^2:D_4$ (show 2), $C_4^2:D_4$ (show 2), $C_4^2.D_4$ (show 4), $C_4^2:D_4$ (show 2), $C_4^2:D_4$ (show 1), $C_4^2:D_4$ (show 4) (incomplete)
Hidden Artin slopes: $[\ ]$ (show 2), $[\ ]^{2}$ (show 9), $[2]^{2}$ (show 8), $[2,\frac{7}{2}]^{2}$ (show 21), $[2]^{4}$ (show 12) (incomplete)
Indices of inseparability: $[39,30,20,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 52

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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
2.1.16.54o1.217 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.218 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.219 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T340) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.220 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T340) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.221 $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.222 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^4.D_4$ (as 16T326) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.223 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^4.D_4$ (as 16T326) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.224 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^2\wr C_2$ (as 16T46) $32$ $4$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.225 $x^{16} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4:D_4$ (as 16T34) $32$ $4$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.226 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_4 \times D_4$ (as 16T19) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.227 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4 \times D_4$ (as 16T19) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.228 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^2:Q_8$ (as 16T31) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.229 $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.230 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_2^2:Q_8$ (as 16T31) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.291 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 14$ $C_4^2:D_4$ (as 16T400) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.292 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_4^2:D_4$ (as 16T402) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.293 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_4^2:D_4$ (as 16T400) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.294 $x^{16} + 4 x^{14} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_4:D_4$ (as 16T43) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.295 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_2^2\wr C_2$ (as 16T39) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.296 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_2^2.D_4$ (as 16T54) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.297 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 14$ $C_4:C_4$ (as 16T8) $16$ $16$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.298 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_4:C_4$ (as 16T8) $16$ $16$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.299 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_2^3.D_4$ (as 16T177) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.300 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 30$ $C_2\wr C_2^2$ (as 16T150) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.391 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.392 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.393 $x^{16} + 4 x^{14} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.394 $x^{16} + 4 x^{14} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.395 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_2^2:\SD_{16}$ (as 16T155) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.396 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_2^2:\SD_{16}$ (as 16T155) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.397 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_2^3.D_4$ (as 16T146) $64$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.398 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_2^4.D_4$ (as 16T218) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.399 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T366) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.400 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$ $C_4^2:D_4$ (as 16T410) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.401 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T410) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.402 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T366) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.403 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 14$ $C_4^2:D_4$ (as 16T410) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.404 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T410) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.405 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_2^4.D_4$ (as 16T218) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.406 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_2\wr C_2^2$ (as 16T147) $64$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.407 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 14$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.408 $x^{16} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.409 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.410 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 14$ $C_4^2:D_4$ (as 16T211) $128$ $8$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.411 $x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_2^2:\SD_{16}$ (as 16T155) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.412 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_2^2:\SD_{16}$ (as 16T155) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.413 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 14$ $C_4^2.D_4$ (as 16T380) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.414 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2.D_4$ (as 16T380) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.415 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2:D_4$ (as 16T352) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.416 $x^{16} + 8 x^{15} + 4 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ $C_4^2.D_4$ (as 16T380) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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