Properties

Label 2.64.ay_kh
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:  $1 - 24 x + 267 x^{2} - 1536 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.150875654972$, $\pm0.291070697150$
Angle rank:  $2$ (numerical)
Number field:  4.0.214225.2
Galois group:  $D_{4}$
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2804 16610896 68927476556 281638472559424 1152981782755796324 4722375738924561791056 19342812955601542238096444 79228165186853019245302043904 324518557521454710847554140312276 1329227998095914516379911094892359376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 41 4055 262937 16786959 1073797961 68719611431 4398046475129 281474986205599 18014398723923113 1152921506611318775

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.214225.2.
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_kh$2$(not in LMFDB)