LMFDB - $p$-adic family 2.1.4.10a1.3-1.4.22c

Defining polynomial

$x^{4} + \left(b_{27} \pi^{7} + b_{23} \pi^{6} + a_{19} \pi^{5}\right) x^{3} + \left(b_{18} \pi^{5} + b_{14} \pi^{4} + a_{10} \pi^{3}\right) x^{2} + \left(b_{25} \pi^{7} + b_{21} \pi^{6}\right) x + c_{28} \pi^{8} + c_{20} \pi^{6} + \pi$

Invariants

Residue field characteristic:	$2$
Degree:	$4$
Base field:	2.1.4.10a1.3
Ramification index $e$:	$4$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$22$
Absolute Artin slopes:	$[3,\frac{7}{2},4,\frac{9}{2}]$
Swan slopes:	$[5,7]$
Means:	$\langle\frac{5}{2},\frac{19}{4}\rangle$
Rams:	$(5,9)$
Field count:	$96$ (complete)
Ambiguity:	$4$
Mass:	$64$
Absolute Mass:	$32$

Diagrams

Varying

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

Galois group:	$D_4:C_4$ (show 8), $C_4\wr C_2$ (show 4), $C_4^2:C_2^2$ (show 4), $C_4^2:D_4$ (show 4), $(C_2\times C_8):D_4$ (show 4), $\OD_{16}:D_4$ (show 8), $C_2^4.D_4$ (show 8), $(C_2\times C_4^2):C_4$ (show 16), $C_4^2:D_4$ (show 2), $C_4^2:D_4$ (show 2), $C_2\wr D_4$ (show 2), $C_4^2:D_4$ (show 2), $C_2^3:\SD_{16}$ (show 8), $C_2^3:D_8$ (show 8), $C_2^4.(C_4\times D_4)$ (show 8), $C_2^4.(C_4\times D_4)$ (show 8)
Hidden Artin slopes:	$[2,2,3]^{4}$ (show 16), $[2,2]^{2}$ (show 36), $[2,3]^{2}$ (show 28), $[2]$ (show 12), $[2]^{2}$ (show 4)
Indices of inseparability:	$[47,38,28,16,0]$
Associated inertia:	$[1,1,1,1]$
Jump Set:	$[1,3,7,15,31]$

Fields

Galois group	Galois Artin	Indices

Assoc. Inertia	Jump Set

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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
2.1.16.62l1.193	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{6} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.194	$x^{16} + 8 x^{15} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.195	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.196	$x^{16} + 8 x^{15} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.197	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{6} + 16 x^{3} + 10$	$C_4^2:D_4$ (as 16T365)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.198	$x^{16} + 8 x^{15} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 16 x^{3} + 10$	$C_4^2:D_4$ (as 16T365)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.199	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$C_4^2:D_4$ (as 16T341)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.200	$x^{16} + 8 x^{15} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$C_4^2:D_4$ (as 16T341)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.201	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{6} + 10$	$C_2\wr D_4$ (as 16T395)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.202	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 10$	$C_2\wr D_4$ (as 16T395)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.203	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 10$	$C_4^2:D_4$ (as 16T399)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.204	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 10$	$C_4^2:D_4$ (as 16T399)	$128$	$2$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.205	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{6} + 16 x^{3} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.206	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 16 x^{3} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.207	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.208	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$C_2^4.(C_4\times D_4)$ (as 16T933)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$	$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$	$[2,2,3]^{4}$	$[1,1,2]^{4}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.209	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 10$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.210	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 10$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.211	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 10$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.212	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 10$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.213	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{3} + 10$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.214	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 16 x^{3} + 10$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.215	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.216	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.217	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 26$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.218	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 26$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.219	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 26$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.220	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 26$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.221	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{3} + 26$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.222	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 16 x^{3} + 26$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.223	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 26$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.224	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 26$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.225	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 10$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.226	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 10$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.227	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 10$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.228	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 10$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.229	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{3} + 10$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.230	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 10$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.231	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.232	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 10$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.233	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 26$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.234	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 26$	$D_4:C_4$ (as 16T26)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]$	$[1,2,\frac{5}{2},3,\frac{7}{2}]$	$[2]$	$[1]$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.235	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 26$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.236	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 8 x^{6} + 16 x^{5} + 26$	$C_2^4.D_4$ (as 16T302)	$128$	$4$	$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,2]^{2}$	$[1,1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.237	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{3} + 26$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.238	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 26$	$\OD_{16}:D_4$ (as 16T299)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.239	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 26$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.240	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 26$	$(C_2\times C_4^2):C_4$ (as 16T314)	$128$	$4$	$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2,3]^{2}$	$[1,2]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.337	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{8} + 8 x^{6} + 8 x^{4} + 10$	$C_4^2:C_2^2$ (as 16T122)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2]^{2}$	$[1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.62l1.338	$x^{16} + 8 x^{15} + 4 x^{12} + 24 x^{8} + 8 x^{6} + 8 x^{4} + 10$	$C_4^2:C_2^2$ (as 16T122)	$64$	$4$	$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$	$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$	$[2]^{2}$	$[1]^{2}$	$[47, 38, 28, 16, 0]$	$[1, 1, 1, 1]$	$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15, 31]$

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Label	2.1.4.10a1.3-1.4.22c
Base	2.1.4.10a1.3
Degree	\(4\)
e	\(4\)
f	\(1\)
c	\(22\)