Properties

Label 2.64.az_kv
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:  $1 - 25 x + 281 x^{2} - 1600 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.147941739316$, $\pm0.266903916760$
Angle rank:  $2$ (numerical)
Number field:  4.0.136721.1
Galois group:  $D_{4}$
Jacobians:  27

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 27 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2753 16526259 68890246100 281648455008579 1153004588987170553 4722389004085515360000 19342814554516940983644353 79228161826906932524684849859 324518554637247201290550249398900 1329227997198787070375622325550257059

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 40 4034 262795 16787554 1073819200 68719804463 4398046838680 281474974268674 18014398563817435 1152921505833184754

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.136721.1.
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_kv$2$(not in LMFDB)