Properties

Label 2.64.ay_kd
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:  $( 1 - 15 x + 64 x^{2} )( 1 - 9 x + 64 x^{2} )$
Frobenius angles:  $\pm0.113134082257$, $\pm0.309839631512$
Angle rank:  $2$ (numerical)
Jacobians:  105

This isogeny class is not 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 105 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2800 16576000 68851627600 281554963200000 1152925088621614000 4722353120372542144000 19342811847298974717936400 79228170911081655733939200000 324518562293698929071779850585200 1329228000411530789994216990366400000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 41 4047 262649 16781983 1073745161 68719282287 4398046223129 281475006542143 18014398988835881 1152921508619795727

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The isogeny class factors as 1.64.ap $\times$ 1.64.aj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ag_ah$2$(not in LMFDB)
2.64.g_ah$2$(not in LMFDB)
2.64.y_kd$2$(not in LMFDB)