# Properties

 Label 3.23.ax_jj_acfk 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: $( 1 - 7 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.0613235619868$, $\pm0.239612957690$, $\pm0.259095524151$ 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 $A(\F_{q^r})$ 4318 136802876 1819545179800 22019736747021104 266812073826110743018 3243948787556459503774400 39469443190034239532520905702 480244003529391045774537458429952 5843200394530446652676150204822883400 71094355630649454237829073958243677685596

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 487 12292 281183 6440611 148026664 3404640765 78309882895 1801149378316 41426515199007

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.ah $\times$ 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.aj_t_u $2$ (not in LMFDB) 3.23.j_t_au $2$ (not in LMFDB) 3.23.x_jj_cfk $2$ (not in LMFDB)