Properties

Label 2.256.acf_byn
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:  $1 - 57 x + 1313 x^{2} - 14592 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0304074499543$, $\pm0.212246711417$
Angle rank:  $2$ (numerical)
Number field:  4.0.91225.2
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
$A(\F_{q^r})$ 52201 4254329299 281400391948036 18446722494498460899 1208926035142562228890201 79228160746997182833895417600 5192296829914948102988565228519961 340282366714225239976130758851790038339 22300745197483652787713429872517925298829956 1461501637326903863994702391455093457225671630259

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 200 64914 16772771 4294962274 1099511823800 281474970432063 72057593640747320 18446744062503605314 4722366482647940617571 1208925819611321234595954

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.91225.2.
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_byn$2$(not in LMFDB)