Properties

Label 2.64.aba_lh
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:  $( 1 - 15 x + 64 x^{2} )( 1 - 11 x + 64 x^{2} )$
Frobenius angles:  $\pm0.113134082257$, $\pm0.258708130235$
Angle rank:  $2$ (numerical)
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2700 16416000 68794587900 281591199360000 1152978430634923500 4722379786386660384000 19342812470159589278795100 79228162322671151715125760000 324518556003408069492621952212300 1329227998721923169188366866266400000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 4007 262431 16784143 1073794839 68719670327 4398046364751 281474976029983 18014398639654599 1152921507154294727

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The isogeny class factors as 1.64.ap $\times$ 1.64.al 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.ae_abl$2$(not in LMFDB)
2.64.e_abl$2$(not in LMFDB)
2.64.ba_lh$2$(not in LMFDB)