# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $1 - 23 x + 239 x^{2} - 1455 x^{3} + 5497 x^{4} - 12167 x^{5} + 12167 x^{6}$ Frobenius angles: $\pm0.00834882690376$, $\pm0.146501337941$, $\pm0.332481005938$ Angle rank: $3$ (numerical) Number field: 6.0.8140239.1 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 $A(\F_{q^r})$ 4259 134367191 1794937674977 21896570024354599 266464474854732220789 3243586226293778010426431 39470904213038541922027933888 480252002295730338688144711687911 5843215984668431085449503414474646483 71094341432463566832133585915640919471911

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 479 12127 279611 6432221 148010123 3404766800 78311187203 1801154183935 41426506925759

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is 6.0.8140239.1.
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_jf_cdz $2$ (not in LMFDB)