Properties

Label 2.64.az_kx
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:  $1 - 25 x + 283 x^{2} - 1600 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.175919588531$, $\pm0.248073742622$
Angle rank:  $2$ (numerical)
Number field:  4.0.223025.1
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2755 16543775 68929780420 281694513099275 1153038144866480125 4722403273088293936400 19342814415985591763607295 79228155790818457613912712275 324518548807264550235411841993180 1329227993834627426070464732084859375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 40 4038 262945 16790298 1073850450 68720012103 4398046807180 281474952824178 18014398240188385 1152921502915241398

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.223025.1.
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.z_kx$2$(not in LMFDB)