# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $1 - 22 x + 226 x^{2} - 1375 x^{3} + 5198 x^{4} - 11638 x^{5} + 12167 x^{6}$ Frobenius angles: $\pm0.0527001661086$, $\pm0.227767494529$, $\pm0.313634986415$ Angle rank: $3$ (numerical) Number field: 6.0.651528243.1 Galois group: $S_4\times C_2$

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 $A(\F_{q^r})$ 4557 139567239 1822286102553 21986705596018779 266638895595308819247 3243579938145113146735743 39469541552566786342430931693 480247114772583627424736085624627 5843209134077744319625892429755651392 71094356552824358812240542221662732488879

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 498 12311 280762 6436432 148009833 3404649250 78310390226 1801152072260 41426515736358

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is 6.0.651528243.1.
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.w_is_cax $2$ (not in LMFDB)