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Properties

Label 2.1.8.24c1.56-1.2.16a
Base 2.1.8.24c1.56
Degree \(2\)
e \(2\)
f \(1\)
c \(16\)

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Defining polynomial

$x^{2} + \left(b_{29} \pi^{15} + b_{27} \pi^{14} + b_{25} \pi^{13} + b_{23} \pi^{12} + b_{21} \pi^{11} + b_{19} \pi^{10} + b_{17} \pi^{9} + a_{15} \pi^{8}\right) x + c_{30} \pi^{16} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.1.8.24c1.56
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $16$
Absolute Artin slopes: $[2,3,4,5]$
Swan slopes: $[15]$
Means: $\langle\frac{15}{2}\rangle$
Rams: $(15)$
Field count: $38$ (complete)
Ambiguity: $2$
Mass: $128$
Absolute Mass: $16$

Diagrams

Varying

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

Galois group: $C_8.C_4$ (show 4), $C_2^3.Q_8$ (show 2), $C_2^4.Q_8$ (show 4), $C_2^4.Q_8$ (show 4), $C_2^6:Q_8$ (show 16), $C_2^6.Q_8$ (show 8)
Hidden Artin slopes: $[\frac{7}{2}]$ (show 4), $[\frac{7}{2}]^{2}$ (show 2), $[2,\frac{7}{2}]^{2}$ (show 2), $[3,\frac{7}{2}]^{2}$ (show 2), $[2,3]^{2}$ (show 4), $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ (show 24)
Indices of inseparability: $[49,34,20,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing all 38

  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
2.1.16.64g1.4377 $x^{16} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4378 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4379 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4380 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4381 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4382 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4383 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4384 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4385 $x^{16} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T369) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, 5]^{2}$ $[1,1,2,\frac{5}{2},3,4]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4386 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T369) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4, 5]^{2}$ $[1,1,2,\frac{5}{2},3,4]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4387 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_8.C_4$ (as 16T49) $32$ $8$ $[2, 3, \frac{7}{2}, 4, 5]$ $[1,2,\frac{5}{2},3,4]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4388 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 46$ $C_8.C_4$ (as 16T49) $32$ $8$ $[2, 3, \frac{7}{2}, 4, 5]$ $[1,2,\frac{5}{2},3,4]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4389 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^3.Q_8$ (as 16T103) $64$ $4$ $[2, 3, \frac{7}{2}, 4, 5]^{2}$ $[1,2,\frac{5}{2},3,4]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4390 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_8.C_4$ (as 16T49) $32$ $8$ $[2, 3, \frac{7}{2}, 4, 5]$ $[1,2,\frac{5}{2},3,4]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4391 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^3.Q_8$ (as 16T103) $64$ $4$ $[2, 3, \frac{7}{2}, 4, 5]^{2}$ $[1,2,\frac{5}{2},3,4]^{2}$ $[\frac{7}{2}]^{2}$ $[\frac{5}{2}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4392 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_8.C_4$ (as 16T49) $32$ $8$ $[2, 3, \frac{7}{2}, 4, 5]$ $[1,2,\frac{5}{2},3,4]$ $[\frac{7}{2}]$ $[\frac{5}{2}]$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4393 $x^{16} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T403) $128$ $4$ $[2, 2, 3, 3, 4, 5]^{2}$ $[1,1,2,2,3,4]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4394 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T403) $128$ $4$ $[2, 2, 3, 3, 4, 5]^{2}$ $[1,1,2,2,3,4]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4395 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T403) $128$ $4$ $[2, 2, 3, 3, 4, 5]^{2}$ $[1,1,2,2,3,4]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4396 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T403) $128$ $4$ $[2, 2, 3, 3, 4, 5]^{2}$ $[1,1,2,2,3,4]^{2}$ $[2,3]^{2}$ $[1,2]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4397 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T369) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 5]^{2}$ $[1,2,2,\frac{5}{2},3,4]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4398 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 8 x^{2} + 16 x + 14$ $C_2^4.Q_8$ (as 16T369) $128$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 5]^{2}$ $[1,2,2,\frac{5}{2},3,4]^{2}$ $[3,\frac{7}{2}]^{2}$ $[2,\frac{5}{2}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4399 $x^{16} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4400 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4401 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4402 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4403 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4404 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4405 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4406 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 2 x^{8} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6.Q_8$ (as 16T968) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4407 $x^{16} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4408 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4409 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4410 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4411 $x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4412 $x^{16} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4413 $x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.64g1.4414 $x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ $C_2^6:Q_8$ (as 16T958) $512$ $2$ $[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, 5]^{2}$ $[1,2,2,\frac{5}{2},3,3,\frac{13}{4},4]^{2}$ $[3,\frac{7}{2},4,\frac{17}{4}]^{2}$ $[2,\frac{5}{2},3,\frac{13}{4}]^{2}$ $[49, 34, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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