Properties

Label 2.64.ay_kj
Base Field $\F_{2^{6}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $1 - 24 x + 269 x^{2} - 1536 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.171549935071$, $\pm0.278210002934$
Angle rank:  $2$ (numerical)
Number field:  4.0.1462032.4
Galois group:  $D_{4}$
Jacobians:  24

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 the Jacobians of 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2806 16628356 68965410622 281679827727168 1153008584221334566 4722384091134702583204 19342809812444033679831598 79228159031062958723185796352 324518553051970019256411470899798 1329227996151929482239382905763301956

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 41 4059 263081 16789423 1073822921 68719732971 4398045760457 281474964335839 18014398475816873 1152921504925180539

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.1462032.4.
All geometric endomorphisms are defined over $\F_{2^{6}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.y_kj$2$(not in LMFDB)