Properties

Label 3.23.az_kp_acns
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 9 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0613235619868$, $\pm0.112386341891$, $\pm0.259095524151$
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 does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3810 128496060 1782882261000 21924411514513200 266681908802990270550 3244122685618237790136000 39471218661524051700437001690 480250580780479167837626170060800 5843216772734766184281269580383151000 71094383152247762252138928556357953486300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 455 12044 279967 6437469 148034600 3404793923 78310955407 1801154426852 41426531235775

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 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.ah_an_jc$2$(not in LMFDB)
3.23.h_an_ajc$2$(not in LMFDB)
3.23.z_kp_cns$2$(not in LMFDB)