# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $1 - 23 x + 241 x^{2} - 1473 x^{3} + 5543 x^{4} - 12167 x^{5} + 12167 x^{6}$ Frobenius angles: $\pm0.0674379021370$, $\pm0.168826572348$, $\pm0.311698514191$ Angle rank: $3$ (numerical) Number field: 6.0.173393831.1 Galois group: $A_4\times C_2$

This isogeny class is simple and geometrically 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 $A(\F_{q^r})$ 4289 135596735 1807498648799 21962411298569975 266679478378081493999 3244036783688524877654015 39471465782985360090139173376 480252672097995461155376821454375 5843220513641392795144039931057467793 71094368595923794346330351102325782734175

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 483 12211 280451 6437411 148030683 3404815240 78311296419 1801155579973 41426522753843

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is 6.0.173393831.1.
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.x_jh_cer $2$ (not in LMFDB)