# Properties

 Label 2.256.acg_bzx 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: $( 1 - 31 x + 256 x^{2} )( 1 - 27 x + 256 x^{2} )$ Frobenius angles: $\pm0.0797861753495$, $\pm0.180343027596$ 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 $A(\F_{q^r})$ 51980 4251548160 281392292285180 18446801860866263040 1208927296503727709019500 79228171015869159229184064000 5192296891873673192653689090467420 340282367015983191966168674620574146560 22300745198696535948327624892870249642332620 1461501637330875658776560408980422547339665984000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 199 64871 16772287 4294980751 1099512970999 281475006914423 72057594500597359 18446744078861936671 4722366482904778617127 1208925819614606626236551

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abf $\times$ 1.256.abb 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.ae_amn $2$ (not in LMFDB) 2.256.e_amn $2$ (not in LMFDB) 2.256.cg_bzx $2$ (not in LMFDB)