Properties

Label 2.256.acd_bwh
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:  $1 - 55 x + 1255 x^{2} - 14080 x^{3} + 65536 x^{4}$
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.

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
$A(\F_{q^r})$ 52657 4261373039 281449143572212 18446956110518746811 1208926920528802526722627 79228163972268622836212105264 5192296845876735754094326090652557 340282366823172952703069258309002281875 22300745198229718170004399621556937287048572 1461501637331306636050618941721672455157029824679

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

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.69351401.1.
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.cd_bwh$2$(not in LMFDB)