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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 51528 4244258304 281339127473400 18446539219339106304 1208926423577776982271528 79228170066487847342857920000 5192296904146649303155641600755928 340282367136475290119893635897809854464 22300745199399677488006315674185281944078600 1461501637333948938371793613032427942867584413184

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon 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)