Properties

Label 3.23.ay_jz_acjo
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

Learn more about

Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 8 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0613235619868$, $\pm0.186011988595$, $\pm0.259095524151$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4064 132909056 1804761744800 21995043121823744 266846417175622796384 3244343213603839689574400 39470946344042972177091717664 480247447854664225297119452332032 5843203541679642058554235714410418400 71094342719706279721894470404325059741696

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 472 12192 280868 6441440 148044664 3404770432 78310444540 1801150348416 41426507675832

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ai $\times$ 2.23.aq_ee and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{23}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ai_d_ey$2$(not in LMFDB)
3.23.i_d_aey$2$(not in LMFDB)
3.23.y_jz_cjo$2$(not in LMFDB)