# Properties

 Label 2.256.ach_caz 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: $1 - 59 x + 1377 x^{2} - 15104 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0363747766709$, $\pm0.176437257411$ Angle rank: $2$ (numerical) Number field: 4.0.1665657.4 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 $A(\F_{q^r})$ 51751 4247566827 281358201468400 18446577982334005875 1208926029731150837928031 79228164488965816687424107200 5192296860188277101655497675123791 340282366867703868977100332234272387875 22300745198018608063440365321057209694047600 1461501637327836655848217480211972777528731851387

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 198 64810 16770255 4294928626 1099511818878 281474983726207 72057594060874158 18446744070823698466 4722366482761221803535 1208925819612092821932730

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1665657.4.
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.ch_caz $2$ (not in LMFDB)