# Properties

 Label 2.256.ace_bxn 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: $( 1 - 31 x + 256 x^{2} )( 1 - 25 x + 256 x^{2} )$ Frobenius angles: $\pm0.0797861753495$, $\pm0.214582404850$ 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 $A(\F_{q^r})$ 52432 4258317312 281434589337328 18446949261723340800 1208927345324213933319952 79228167730545048624652723200 5192296865352619289961792337272112 340282366887917491720515405383244595200 22300745198307350342139981857039489223596368 1461501637330658778050424238776000921258364019712

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 201 64975 16774809 4295015071 1099513015401 281474995242607 72057594132543801 18446744071919481151 4722366482822365359369 1208925819614427226704655

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abf $\times$ 1.256.az 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.ag_akd $2$ (not in LMFDB) 2.256.g_akd $2$ (not in LMFDB) 2.256.ce_bxn $2$ (not in LMFDB)