Properties

Label 2.64.az_ku
Base Field $\F_{2^{6}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $1 - 25 x + 280 x^{2} - 1600 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.136006851804$, $\pm0.273761000528$
Angle rank:  $2$ (numerical)
Number field:  4.0.29189.1
Galois group:  $D_{4}$
Jacobians:  6

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2752 16517504 68870481472 281625326195456 1152987408580898752 4722381057964796230784 19342813538567409218189632 79228163789827253090325440000 324518556796747096480989254402752 1329227998519869554003002657855557504

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 40 4032 262720 16786176 1073803200 68719688832 4398046607680 281474981242368 18014398683693760 1152921506979041152

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.29189.1.
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_ku$2$(not in LMFDB)