Properties

Label 3.16.ar_fi_abaj
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:  $1 - 17 x + 138 x^{2} - 685 x^{3} + 2208 x^{4} - 4352 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.102554998327$, $\pm0.191626633307$, $\pm0.385414273973$
Angle rank:  $3$ (numerical)
Number field:  6.0.760751703.1
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
$A(\F_{q^r})$ 1389 15969333 69915830319 282217734025173 1153050302391052719 4723958363298965952867 19346810277976122888019776 79232291052667199818908578037 324519594466146738549178747137381 1329225801078059516121697687080158643

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 244 4167 65708 1048695 16782871 268490922 4295191100 68719697136 1099509812359

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.760751703.1.
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_baj$2$(not in LMFDB)