# Properties

 Label 2.256.acd_bwt 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: $1 - 55 x + 1267 x^{2} - 14080 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.147664473873$, $\pm0.191492242764$ Angle rank: $2$ (numerical) Number field: 4.0.1681025.1 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 $A(\F_{q^r})$ 52669 4262976191 281482389468964 18447319787591103275 1208929674480074430953179 79228179788963311964981227856 5192296915593928104579550370728609 340282367038503239561400754449021816275 22300745198443721102700163780087343194797724 1461501637328533738955490532527569201406814864191

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 202 65046 16777657 4295101338 1099515133752 281475038082711 72057594829782022 18446744080082750898 4722366482851242991177 1208925819612669435564406

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1681025.1.
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_bwt $2$ (not in LMFDB)