# Properties

 Label 3.16.at_gj_abgh Base Field $\F_{2^{4}}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 7 x + 16 x^{2} )( 1 - 12 x + 65 x^{2} - 192 x^{3} + 256 x^{4} )$ Frobenius angles: $\pm0.0826163580681$, $\pm0.160861246510$, $\pm0.320878822416$ Angle rank: $3$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1180 14896320 69208190620 282707366123520 1153429935459389500 4722384534384662176320 19343877084616967315681980 79231339525536857449738321920 324522997082592600242039991153820 1329231323102387391224167479407448000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 226 4126 65822 1049038 16777282 268450222 4295139518 68720417662 1099514380066

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah $\times$ 2.16.am_cn and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{4}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.af_ad_ct $2$ (not in LMFDB) 3.16.f_ad_act $2$ (not in LMFDB) 3.16.t_gj_bgh $2$ (not in LMFDB)