Properties

Label 2.256.ach_cbd
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:  $1 - 59 x + 1381 x^{2} - 15104 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0938889128788$, $\pm0.152829054823$
Angle rank:  $2$ (numerical)
Number field:  4.0.472625.1
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
$A(\F_{q^r})$ 51755 4248102155 281370091077680 18446722437716197955 1208927299912111402734375 79228173506360040919010914880 5192296914634401684025985192958155 340282367154627726345593598757978187555 22300745199351726161686108619761770918660080 1461501637333276565596680014260373870334113671875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 198 64818 16770963 4294962258 1099512974098 281475015762423 72057594816465918 18446744086377871938 4722366483043520541483 1208925819616592609810698

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.472625.1.
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.ch_cbd$2$(not in LMFDB)