# Properties

 Label 2.256.acf_byp 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: $1 - 57 x + 1315 x^{2} - 14592 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0539555453686$, $\pm0.207165299693$ Angle rank: $2$ (numerical) Number field: 4.0.14994657.1 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 $A(\F_{q^r})$ 52203 4254596703 281406134732148 18446788983284614827 1208926584778371253287933 79228164371239899555327022032 5192296850065819969568020106794647 340282366812005424322566106116926126163 22300745197910167305565079368070464598302092 1461501637328641042063862296378461562517503940223

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 200 64918 16773113 4294977754 1099512323690 281474983307959 72057593920396844 18446744067804279730 4722366482738258579849 1208925819612758194615318

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.14994657.1.
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.cf_byp $2$ (not in LMFDB)