Properties

Label 2.256.acf_byv
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:  $1 - 57 x + 1321 x^{2} - 14592 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.104135360699$, $\pm0.185878890687$
Angle rank:  $2$ (numerical)
Number field:  4.0.618033.2
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
$A(\F_{q^r})$ 52209 4255398963 281423363274036 18446988037652966403 1208928218644825872878169 79228174955607329335718899968 5192296906647403767307910986695249 340282367064557474321704655225099615427 22300745198831596705695498751371675142090644 1461501637331137851905420932891069625929627121283

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 200 64930 16774139 4295024098 1099513809680 281475020911183 72057594705624056 18446744081495153794 4722366482933378844971 1208925819614823507309490

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.618033.2.
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_byv$2$(not in LMFDB)