Properties

Label 2.64.ax_jv
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:  $1 - 23 x + 255 x^{2} - 1472 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.169239670103$, $\pm0.304790147482$
Angle rank:  $2$ (numerical)
Number field:  4.0.4967865.1
Galois group:  $D_{4}$
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2857 16704879 68985316276 281653698196635 1152978529675528627 4722371530491762339696 19342811694724951602849877 79228164879524085074453319315 324518556651503723272347975428956 1329227996825784130300448171052360279

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 42 4078 263157 16787866 1073794932 68719550191 4398046188438 281474985113746 18014398675631133 1152921505509656278

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.4967865.1.
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.x_jv$2$(not in LMFDB)