# 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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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)