Properties

Label 2.64.aba_ld
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:  $1 - 26 x + 289 x^{2} - 1664 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.0466571603306$, $\pm0.280701937272$
Angle rank:  $2$ (numerical)
Number field:  4.0.1088.2
Galois group:  $D_{4}$
Jacobians:  21

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 21 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2696 16380896 68712350792 281487809821568 1152890210522185416 4722323806521178206944 19342785219848857670346248 79228152082414704039889874432 324518552853931502099526217320968 1329227997560012002030049950440159456

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 3999 262119 16777983 1073712679 68718855711 4398040168743 281474939649279 18014398464823527 1152921506146497439

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.1088.2.
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.ba_ld$2$(not in LMFDB)