Properties

Label 2.256.acd_bwt
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:  $1 - 55 x + 1267 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.147664473873$, $\pm0.191492242764$
Angle rank:  $2$ (numerical)
Number field:  4.0.1681025.1
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
$A(\F_{q^r})$ 52669 4262976191 281482389468964 18447319787591103275 1208929674480074430953179 79228179788963311964981227856 5192296915593928104579550370728609 340282367038503239561400754449021816275 22300745198443721102700163780087343194797724 1461501637328533738955490532527569201406814864191

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65046 16777657 4295101338 1099515133752 281475038082711 72057594829782022 18446744080082750898 4722366482851242991177 1208925819612669435564406

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.1681025.1.
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_bwt$2$(not in LMFDB)