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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 52432 4258317312 281434589337328 18446949261723340800 1208927345324213933319952 79228167730545048624652723200 5192296865352619289961792337272112 340282366887917491720515405383244595200 22300745198307350342139981857039489223596368 1461501637330658778050424238776000921258364019712

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon 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)