# Properties

 Label 3.16.ar_fj_abat Base Field $\F_{2^{4}}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $1 - 17 x + 139 x^{2} - 695 x^{3} + 2224 x^{4} - 4352 x^{5} + 4096 x^{6}$ Frobenius angles: $\pm0.0495644041837$, $\pm0.241489249045$, $\pm0.365060689978$ Angle rank: $3$ (numerical) Number field: 6.0.54300016.1 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 $A(\F_{q^r})$ 1396 16087504 70241589700 282148694053504 1151188072907707396 4719459706559299682800 19340800569079425688935924 79227370267614197669527131136 324517563472724761126433827873300 1329226135964393386511270924994503824

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 246 4188 65694 1047000 16766886 268407524 4294924350 68719267056 1099510089366

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The endomorphism algebra of this simple isogeny class is 6.0.54300016.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

## 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 3.16.r_fj_bat $2$ (not in LMFDB)