# Properties

 Label 2.256.acd_bwl 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: $1 - 55 x + 1259 x^{2} - 14080 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0964771915839$, $\pm0.223068968241$ Angle rank: $2$ (numerical) Number field: 4.0.53173329.1 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 $A(\F_{q^r})$ 52661 4261907391 281460225416804 18447077610889969419 1208927848188066205388651 79228169421608608895157438096 5192296871357367435481149985048361 340282366916870212929525420748118133459 22300745198476039386327002695290212593095164 1461501637331554786568331080456912176260495911151

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 202 65030 16776337 4295044954 1099513472752 281475001250471 72057594215876422 18446744073489011314 4722366482858086653937 1208925819615168387579350

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.53173329.1.
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_bwl $2$ (not in LMFDB)