Properties

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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1396 16087504 70241589700 282148694053504 1151188072907707396 4719459706559299682800 19340800569079425688935924 79227370267614197669527131136 324517563472724761126433827873300 1329226135964393386511270924994503824

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon base change
3.16.r_fj_bat$2$(not in LMFDB)