# Properties

 Label 2.256.acf_byr 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: $1 - 57 x + 1317 x^{2} - 14592 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0716566769452$, $\pm0.201368865130$ Angle rank: $2$ (numerical) Number field: 4.0.15360865.2 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 $A(\F_{q^r})$ 52205 4254864115 281411877547820 18446855403405581875 1208927131907351124367625 79228167947404481179410208960 5192296869570599837079810195062645 340282366902963055886432777798539831875 22300745198276544950996059160172166648920380 1461501637329919292145447938803799830291365362875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 200 64922 16773455 4294993218 1099512821300 281474996013047 72057594191080040 18446744072735102818 4722366482815842064055 1208925819613815538300802

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.15360865.2.
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_byr $2$ (not in LMFDB)