# Properties

 Label 2.256.aci_cch 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: $( 1 - 31 x + 256 x^{2} )( 1 - 29 x + 256 x^{2} )$ Frobenius angles: $\pm0.0797861753495$, $\pm0.138932406859$ Angle rank: $2$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 51528 4244258304 281339127473400 18446539219339106304 1208926423577776982271528 79228170066487847342857920000 5192296904146649303155641600755928 340282367136475290119893635897809854464 22300745199399677488006315674185281944078600 1461501637333948938371793613032427942867584413184

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 197 64759 16769117 4294919599 1099512177077 281475003541543 72057594670919117 18446744085393826399 4722366483053674629797 1208925819617148783534679

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abf $\times$ 1.256.abd and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_aox $2$ (not in LMFDB) 2.256.c_aox $2$ (not in LMFDB) 2.256.ci_cch $2$ (not in LMFDB)