Properties

Label 2.256.acf_byp
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:  $1 - 57 x + 1315 x^{2} - 14592 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0539555453686$, $\pm0.207165299693$
Angle rank:  $2$ (numerical)
Number field:  4.0.14994657.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically 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
$A(\F_{q^r})$ 52203 4254596703 281406134732148 18446788983284614827 1208926584778371253287933 79228164371239899555327022032 5192296850065819969568020106794647 340282366812005424322566106116926126163 22300745197910167305565079368070464598302092 1461501637328641042063862296378461562517503940223

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 200 64918 16773113 4294977754 1099512323690 281474983307959 72057593920396844 18446744067804279730 4722366482738258579849 1208925819612758194615318

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.14994657.1.
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.cf_byp$2$(not in LMFDB)