# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4} )$ Frobenius angles: $\pm0.144663500024$, $\pm0.186011988595$, $\pm0.268275520367$ 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 does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4336 137503232 1827473007472 22073623188350976 267076867910104960256 3244957169135969968669184 39472469355019846936115252336 480250837384476815234872348876800 5843209279678578949287087454703881264 71094344483179411944713742576450050588672

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 489 12343 281865 6446996 148072677 3404901809 78310997249 1801152117139 41426508703404

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.ai $\times$ 2.23.ap_dx 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.ah_e_eo $2$ (not in LMFDB) 3.23.h_e_aeo $2$ (not in LMFDB) 3.23.x_jk_cfq $2$ (not in LMFDB)