Properties

Label 2.256.ace_bxr
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:  $1 - 56 x + 1291 x^{2} - 14336 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.106180922549$, $\pm0.202099312409$
Angle rank:  $2$ (numerical)
Number field:  4.0.988625.1
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
$A(\F_{q^r})$ 52436 4258851920 281445873145196 18447076191623078720 1208928347728738094846916 79228173872570398643673853520 5192296895548774941062835925137116 340282367005153905981012646949345342720 22300745198626576216742662354720283121341876 1461501637330858735667487427103734971468540450000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 201 64983 16775481 4295044623 1099513927081 281475017063463 72057594551599641 18446744078274879903 4722366482889964067721 1208925819614592627768823

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.988625.1.
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.ce_bxr$2$(not in LMFDB)