# Properties

 Label 3.16.av_hn_abnb 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: $( 1 - 7 x + 16 x^{2} )^{3}$ Frobenius angles: $\pm0.160861246510$, $\pm0.160861246510$, $\pm0.160861246510$ Angle rank: $1$ (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 $A(\F_{q^r})$ 1000 13824000 68417929000 284371070976000 1158452071890625000 4729246818274054656000 19349349617882459638009000 79232664195372087170924544000 324519767412018097477971305521000 1329225450601162408904302776000000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 206 4076 66206 1053596 16801646 268526156 4295211326 68719733756 1099509522446

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ah 3 and its endomorphism algebra is $\mathrm{M}_{3}($$$\Q(\sqrt{-15})$$$)$
All geometric endomorphisms are defined over $\F_{2^{4}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.ah_ab_ep $2$ (not in LMFDB) 3.16.h_ab_aep $2$ (not in LMFDB) 3.16.v_hn_bnb $2$ (not in LMFDB) 3.16.a_a_ah $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.ah_ab_ep $2$ (not in LMFDB) 3.16.h_ab_aep $2$ (not in LMFDB) 3.16.v_hn_bnb $2$ (not in LMFDB) 3.16.a_a_ah $3$ (not in LMFDB) 3.16.ah_bh_aep $4$ (not in LMFDB) 3.16.h_bh_ep $4$ (not in LMFDB) 3.16.ao_du_arn $6$ (not in LMFDB) 3.16.a_a_h $6$ (not in LMFDB) 3.16.o_du_rn $6$ (not in LMFDB)