# Properties

 Label 2.256.acc_bvd 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: $( 1 - 31 x + 256 x^{2} )( 1 - 23 x + 256 x^{2} )$ Frobenius angles: $\pm0.0797861753495$, $\pm0.244714587078$ Angle rank: $2$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 52884 4264565760 281466823649076 18447002862035005440 1208926859782367266984404 79228162822639307396459904000 5192296841607094209720966733670004 340282366830574067043862655008663388160 22300745198419151124950987386614135583933716 1461501637332603708350389678031738843754839424000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 203 65071 16776731 4295027551 1099512573803 281474977806223 72057593803008443 18446744068810887871 4722366482846040096011 1208925819616036035341551

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abf $\times$ 1.256.ax 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 $\F_{2^{8}}$.

## 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.ai_aht $2$ (not in LMFDB) 2.256.i_aht $2$ (not in LMFDB) 2.256.cc_bvd $2$ (not in LMFDB)