# Properties

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

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $1 - 22 x + 225 x^{2} - 1366 x^{3} + 5175 x^{4} - 11638 x^{5} + 12167 x^{6}$ Frobenius angles: $\pm0.0404981459123$, $\pm0.210373719318$, $\pm0.328791241931$ Angle rank: $3$ (numerical) Number field: 6.0.1108246464.1 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 $A(\F_{q^r})$ 4542 138957948 1816458854922 21960510012207216 266581691987972792142 3243596627864919477833244 39470059593764327916287932458 480248461449294341158084920880896 5843207861674666241771931654862245654 71094335019665046439306034548883099739708

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 496 12272 280428 6435052 148010596 3404693938 78310609820 1801151680046 41426503189036

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is 6.0.1108246464.1.
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_cao $2$ (not in LMFDB)