Properties

Label 2.256.acc_bvd
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:  $( 1 - 31 x + 256 x^{2} )( 1 - 23 x + 256 x^{2} )$
Frobenius angles:  $\pm0.0797861753495$, $\pm0.244714587078$
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
$A(\F_{q^r})$ 52884 4264565760 281466823649076 18447002862035005440 1208926859782367266984404 79228162822639307396459904000 5192296841607094209720966733670004 340282366830574067043862655008663388160 22300745198419151124950987386614135583933716 1461501637332603708350389678031738843754839424000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 203 65071 16776731 4295027551 1099512573803 281474977806223 72057593803008443 18446744068810887871 4722366482846040096011 1208925819616036035341551

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The isogeny class factors as 1.256.abf $\times$ 1.256.ax 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.ai_aht$2$(not in LMFDB)
2.256.i_aht$2$(not in LMFDB)
2.256.cc_bvd$2$(not in LMFDB)