# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 8 x + 23 x^{2} )( 1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.0869454733845$, $\pm0.186011988595$, $\pm0.334554373298$ 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 $A(\F_{q^r})$ 4544 139010048 1817511950912 21974468178477056 266689032350853700544 3244152252081269342019584 39472180178332293828683799616 480254677475099551401650832801792 5843221972145488345017783228569415104 71094359362063254822390494808856716320768

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 496 12278 280604 6437642 148035952 3404876862 78311623420 1801156029554 41426517373296

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.ai $\times$ 2.23.ao_dm 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.ag_b_cy $2$ (not in LMFDB) 3.23.g_b_acy $2$ (not in LMFDB) 3.23.w_ir_cam $2$ (not in LMFDB)