# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 85 x^{2} - 299 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.112386341891$, $\pm0.166921904620$, $\pm0.337099187115$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4545 139036095 1818038596140 21981448813532175 266742709730253471600 3244429883396733155158320 39473235136455346558249073235 480257711767160190726785430108975 5843228343266986326257979405330678780 71094366742695305772458221652309737593600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 496 12281 280692 6438937 148048621 3404967862 78312118196 1801157993429 41426521673971

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj $\times$ 2.23.an_dh 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.ae_aj_gl $2$ (not in LMFDB) 3.23.e_aj_agl $2$ (not in LMFDB) 3.23.w_ir_cal $2$ (not in LMFDB)