# Properties

 Label 2.256.acf_byn 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: $1 - 57 x + 1313 x^{2} - 14592 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0304074499543$, $\pm0.212246711417$ Angle rank: $2$ (numerical) Number field: 4.0.91225.2 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 $A(\F_{q^r})$ 52201 4254329299 281400391948036 18446722494498460899 1208926035142562228890201 79228160746997182833895417600 5192296829914948102988565228519961 340282366714225239976130758851790038339 22300745197483652787713429872517925298829956 1461501637326903863994702391455093457225671630259

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 200 64914 16772771 4294962274 1099511823800 281474970432063 72057593640747320 18446744062503605314 4722366482647940617571 1208925819611321234595954

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.91225.2.
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_byn $2$ (not in LMFDB)