# Properties

 Label 3.23.ax_jh_aceq Base Field $\F_{23}$ Dimension $3$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 92 x^{2} - 322 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.112386341891$, $\pm0.135789939707$, $\pm0.314924263207$ Angle rank: $3$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1, 1]$

## 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 $A(\F_{q^r})$ 4290 135624060 1808039324520 21969744191881200 266739205154465707950 3244372546491988002336960 39472897837403617193938415370 480257541194117605634752487193600 5843233974769971834562226813683119960 71094398476475424486958657923029006922300

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 483 12214 280543 6438851 148046004 3404938769 78312090383 1801159729318 41426540165163

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj $\times$ 2.23.ao_do 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_al_hc $2$ (not in LMFDB) 3.23.f_al_ahc $2$ (not in LMFDB) 3.23.x_jh_ceq $2$ (not in LMFDB)