Properties

Label 2.256.acd_bwh
Base field $\F_{2^{8}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{2^{8}}$
Dimension:  $2$
L-polynomial:  $1 - 55 x + 1255 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0739610199852$, $\pm0.232151876775$
Angle rank:  $2$ (numerical)
Number field:  4.0.69351401.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $52657$ $4261373039$ $281449143572212$ $18446956110518746811$ $1208926920528802526722627$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $202$ $65022$ $16775677$ $4295016666$ $1099512629052$ $281474981890527$ $72057593862261622$ $18446744068409672658$ $4722366482805926107477$ $1208925819614963122282102$

Jacobians and polarizations

This isogeny class contains a Jacobian, and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{8}}$.

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.69351401.1.

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.cd_bwh$2$(not in LMFDB)