Properties

Label 2.1.2.2a1.2-1.8.44d
Base 2.1.2.2a1.2
Degree \(8\)
e \(8\)
f \(1\)
c \(44\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{8} + \left(b_{47} \pi^{6} + b_{39} \pi^{5}\right) x^{7} + \left(b_{38} \pi^{5} + b_{30} \pi^{4}\right) x^{6} + \left(b_{45} \pi^{6} + a_{37} \pi^{5}\right) x^{5} + \left(b_{20} \pi^{3} + a_{12} \pi^{2}\right) x^{4} + b_{43} \pi^{6} x^{3} + \left(b_{34} \pi^{5} + a_{26} \pi^{4}\right) x^{2} + b_{41} \pi^{6} x + c_{48} \pi^{7} + c_{40} \pi^{6} + c_{24} \pi^{4} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $8$
Base field: $\Q_{2}(\sqrt{-5})$
Ramification index $e$: $8$
Residue field degree $f$: $1$
Discriminant exponent $c$: $44$
Absolute Artin slopes: $[2,3,4,\frac{9}{2}]$
Swan slopes: $[3,5,6]$
Means: $\langle\frac{3}{2},\frac{13}{4},\frac{37}{8}\rangle$
Rams: $(3,7,11)$
Field count: $512$ (complete)
Ambiguity: $8$
Mass: $512$
Absolute Mass: $256$

Diagrams

Varying

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

Galois group: $C_2^5.(C_2\times D_4)$ (show 32), $C_2^3\wr C_2:C_4$ (show 32), $(D_4\times C_2^3).C_2^3$ (show 32), $C_2^4.(C_4\times D_4)$ (show 32), $C_2^6.Q_8$ (show 32), $(C_2^2\times C_4^2):Q_8$ (show 32), $(D_4\times C_2^3).C_2^3$ (show 32), $(D_4\times C_2^3).C_2^3$ (show 32), $C_2^6.\SD_{16}$ (show 64), $(D_4\times C_2^3).Q_{16}$ (show 64), $(C_2^2\times D_4^2).D_4$ (show 64), $(C_2^2\times D_4^2).D_4$ (show 64) (incomplete)
Hidden Artin slopes: $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ (show 256), not computed (show 96), $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ (show 32), $[\frac{17}{4},3,4,\frac{7}{2}]_{4}$ (show 128) (incomplete)
Indices of inseparability: $[45,34,20,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
Sort order Select

Showing 1-50 of 512

Next   displayed columns for results
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
2.1.16.60l1.513 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.514 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.515 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.516 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.517 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.518 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.519 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.520 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.521 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.522 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.523 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.524 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.525 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.526 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.527 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.528 $x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.529 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.530 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.531 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.532 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.533 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.534 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.535 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.536 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.537 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.538 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.539 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.540 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.541 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.542 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.543 $x^{16} + 8 x^{14} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.544 $x^{16} + 8 x^{14} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.545 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.546 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.547 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.548 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.549 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.550 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.551 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.552 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.553 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.554 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.555 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.556 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.557 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.558 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.559 $x^{16} + 8 x^{15} + 8 x^{13} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.560 $x^{16} + 8 x^{15} + 8 x^{13} + 18 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ $[2, 2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ $[1,1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ $[2,3,\frac{7}{2},4,\frac{17}{4}]^{4}$ $[1,2,\frac{5}{2},3,\frac{13}{4}]^{4}$ $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.561 $x^{16} + 8 x^{13} + 18 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.60l1.562 $x^{16} + 8 x^{13} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 30$ $(C_2^2\times D_4^2).D_4$ (as 16T1374) $2048$ $2$ not computed not computed not computed not computed $[45, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
Next   displayed columns for results