# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $1 - 22 x + 226 x^{2} - 1374 x^{3} + 5198 x^{4} - 11638 x^{5} + 12167 x^{6}$ Frobenius angles: $\pm0.0726497276025$, $\pm0.215791854394$, $\pm0.318152272543$ Angle rank: $3$ (numerical) Number field: 6.0.1108002176.1 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 $A(\F_{q^r})$ 4558 139593308 1822812807016 21993683946249056 266692352831520365038 3243853199287119272656832 39470552648261328279518346578 480249876007481667892450720029056 5843214445873942394508029117026639384 71094362384835330131654903250949767568988

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 498 12314 280850 6437722 148022304 3404736470 78310840482 1801153709606 41426519134658

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is 6.0.1108002176.1.
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_caw $2$ (not in LMFDB)