# Properties

 Label 2.256.ach_cbd 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: $1 - 59 x + 1381 x^{2} - 15104 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0938889128788$, $\pm0.152829054823$ Angle rank: $2$ (numerical) Number field: 4.0.472625.1 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 $A(\F_{q^r})$ 51755 4248102155 281370091077680 18446722437716197955 1208927299912111402734375 79228173506360040919010914880 5192296914634401684025985192958155 340282367154627726345593598757978187555 22300745199351726161686108619761770918660080 1461501637333276565596680014260373870334113671875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 198 64818 16770963 4294962258 1099512974098 281475015762423 72057594816465918 18446744086377871938 4722366483043520541483 1208925819616592609810698

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.472625.1.
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.ch_cbd $2$ (not in LMFDB)