# Properties

 Label 3.16.ar_ff_azn 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: $( 1 - 7 x + 16 x^{2} )( 1 - 10 x + 49 x^{2} - 160 x^{3} + 256 x^{4} )$ Frobenius angles: $\pm0.0660425289118$, $\pm0.160861246510$, $\pm0.412497962872$ 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 it is unknown whether it contains a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1360 15536640 68444775760 279959936471040 1151407619028994000 4723739663040646940160 19346928220938637171199440 79231299381048171516249538560 324518148975527722013913000354640 1329226029373747921257879483034176000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 238 4080 65182 1047200 16782094 268492560 4295137342 68719391040 1099510001198

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah $\times$ 2.16.ak_bx 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.ad_af_x $2$ (not in LMFDB) 3.16.d_af_ax $2$ (not in LMFDB) 3.16.r_ff_zn $2$ (not in LMFDB)