# Properties

 Label 3.16.au_gy_abjr Base Field $\F_{2^{4}}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 7 x + 16 x^{2} )( 1 - 13 x + 73 x^{2} - 208 x^{3} + 256 x^{4} )$ Frobenius angles: $\pm0.0987587980325$, $\pm0.160861246510$, $\pm0.265114785720$ Angle rank: $3$ (numerical)

This isogeny class is not 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 does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1090 14414160 69055969000 283892560379040 1155895247097177250 4724672241671715456000 19344203806287267287679010 79229328343334966979423600960 324520417014837036820015674721000 1329230839907278291474161111114234000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 217 4116 66097 1051277 16785406 268454757 4295030497 68719871316 1099513980377

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah $\times$ 2.16.an_cv and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ag_ac_dr $2$ (not in LMFDB) 3.16.g_ac_adr $2$ (not in LMFDB) 3.16.u_gy_bjr $2$ (not in LMFDB)