# Properties

 Label 2.256.acd_bwj 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: $1 - 55 x + 1257 x^{2} - 14080 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0854412706717$, $\pm0.227850675283$ Angle rank: $2$ (numerical) Number field: 4.0.794025.3 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 $A(\F_{q^r})$ 52659 4261640211 281454684479424 18447016895039614275 1208927385567873129763179 79228166719099687418808251136 5192296858898357228009800717155219 340282366872789923180196189995456734275 22300745198375247831153247039384697791971264 1461501637331583968822110182836950589233583414691

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 202 65026 16776007 4295030818 1099513052002 281474991649231 72057594042972922 18446744071099414018 4722366482836743211927 1208925819615192526573906

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.794025.3.
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.cd_bwj $2$ (not in LMFDB)