# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $1 - 22 x + 225 x^{2} - 1365 x^{3} + 5175 x^{4} - 11638 x^{5} + 12167 x^{6}$ Frobenius angles: $\pm0.0651622826372$, $\pm0.199262186058$, $\pm0.331801443904$ Angle rank: $3$ (numerical) Number field: 6.0.1812258679.1 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 $A(\F_{q^r})$ 4543 138983999 1816985370508 21967488578046319 266635359771532381168 3243874500256400201904944 39471121664207816317658420189 480251594036143765878840599355631 5843215144968184778878353052784930236 71094348788475867567602845815142109598464

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 496 12275 280516 6436347 148023277 3404785554 78311120628 1801153925099 41426511212091

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is 6.0.1812258679.1.
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_ir_can $2$ (not in LMFDB)