# Properties

 Label 3.16.ar_fi_abaj 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: $1 - 17 x + 138 x^{2} - 685 x^{3} + 2208 x^{4} - 4352 x^{5} + 4096 x^{6}$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1389 15969333 69915830319 282217734025173 1153050302391052719 4723958363298965952867 19346810277976122888019776 79232291052667199818908578037 324519594466146738549178747137381 1329225801078059516121697687080158643

 $r$ 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.
 Twist Extension Degree Common base change 3.16.r_fi_baj $2$ (not in LMFDB)