Properties

Label 3.16.ar_fi_abal
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:  $1 - 17 x + 138 x^{2} - 687 x^{3} + 2208 x^{4} - 4352 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0523737408415$, $\pm0.219476755816$, $\pm0.380403485950$
Angle rank:  $3$ (numerical)
Number field:  6.0.1426375023.1
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
$A(\F_{q^r})$ 1387 15949113 69790623547 281625434126637 1151390286952763317 4720894880421092876163 19342739410852730686360408 79228208757929714130588656757 324516451134900590276140233052897 1329224039535501339770396357868416463

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 244 4161 65572 1047185 16771987 268434432 4294969804 68719031508 1099508355239

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.1426375023.1.
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_fi_bal$2$(not in LMFDB)