Properties

Label 2.64.ax_jn
Base Field $\F_{2^{6}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $1 - 23 x + 247 x^{2} - 1472 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.104834709086$, $\pm0.336541401594$
Angle rank:  $2$ (numerical)
Number field:  4.0.14609609.1
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
$A(\F_{q^r})$ 2849 16635311 68840010932 281504412908411 1152888636118903299 4722344725625371899824 19342817404734605202838109 79228176137569045668147057299 324518563234009544487047210606972 1329227999248216358799324426426690951

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 42 4062 262605 16778970 1073711212 68719160127 4398047486742 281475025110354 18014399041033605 1152921507610781302

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.14609609.1.
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_jn$2$(not in LMFDB)