# Properties

 Label 2.256.acd_bwh 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: $1 - 55 x + 1255 x^{2} - 14080 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0739610199852$, $\pm0.232151876775$ Angle rank: $2$ (numerical) Number field: 4.0.69351401.1 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 $A(\F_{q^r})$ 52657 4261373039 281449143572212 18446956110518746811 1208926920528802526722627 79228163972268622836212105264 5192296845876735754094326090652557 340282366823172952703069258309002281875 22300745198229718170004399621556937287048572 1461501637331306636050618941721672455157029824679

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 202 65022 16775677 4295016666 1099512629052 281474981890527 72057593862261622 18446744068409672658 4722366482805926107477 1208925819614963122282102

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.69351401.1.
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_bwh $2$ (not in LMFDB)