# Properties

 Label 2.256.acg_bzz 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: $1 - 58 x + 1351 x^{2} - 14848 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.100628845752$, $\pm0.169176663725$ Angle rank: $2$ (numerical) Number field: 4.0.1666112.1 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 $A(\F_{q^r})$ 51982 4251815708 281398136131378 18446871064572620768 1208927883204478915070782 79228174973278286216762677148 5192296914088865540202522940929058 340282367121007860494572325030644065152 22300745199105339882282243520522262839882798 1461501637332054401357041105688503752611534070108

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 199 64875 16772635 4294996863 1099513504599 281475020973963 72057594808895083 18446744084555335359 4722366482991346217383 1208925819615581659246315

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1666112.1.
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.cg_bzz $2$ (not in LMFDB)