# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 93 x^{2} - 322 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.112386341891$, $\pm0.159380640241$, $\pm0.302130010970$ 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 $A(\F_{q^r})$ 4305 136240335 1814329989360 22002220775841075 266837831376550576275 3244513159378067756256000 39472643340755411955757410045 480255369579683167363482050829675 5843227061888887236240622663388489040 71094384856645752858025824689556577523175

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 485 12256 280957 6441231 148052420 3404916817 78311736277 1801157598448 41426532228925

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj $\times$ 2.23.ao_dp 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.af_ak_hl $2$ (not in LMFDB) 3.23.f_ak_ahl $2$ (not in LMFDB) 3.23.x_ji_cez $2$ (not in LMFDB)