# Properties

 Label 2.256.ace_bxr Base Field $\F_{2^{8}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{8}}$ Dimension: $2$ L-polynomial: $1 - 56 x + 1291 x^{2} - 14336 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.106180922549$, $\pm0.202099312409$ Angle rank: $2$ (numerical) Number field: 4.0.988625.1 Galois group: $D_{4}$

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 52436 4258851920 281445873145196 18447076191623078720 1208928347728738094846916 79228173872570398643673853520 5192296895548774941062835925137116 340282367005153905981012646949345342720 22300745198626576216742662354720283121341876 1461501637330858735667487427103734971468540450000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 201 64983 16775481 4295044623 1099513927081 281475017063463 72057594551599641 18446744078274879903 4722366482889964067721 1208925819614592627768823

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.988625.1.
All geometric endomorphisms are defined over $\F_{2^{8}}$.

## 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 2.256.ce_bxr $2$ (not in LMFDB)