# Properties

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

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 4 x )^{2}( 1 - 13 x + 73 x^{2} - 208 x^{3} + 256 x^{4} )$ Frobenius angles: $0$, $0$, $\pm0.0987587980325$, $\pm0.265114785720$ Angle rank: $2$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1, 1]$

## 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 $A(\F_{q^r})$ 981 13513275 67012992900 280719491159475 1151799949582824861 4720074334860797640000 19339664290701495772047381 79225409994745543438690210275 324517536542506584635842405716900 1329229152997726620844881738443806875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 202 3995 65362 1047556 16769071 268391756 4294818082 68719261355 1099512585002

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai $\times$ 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: 1.16.ai : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 2.16.an_cv : 4.0.5225.1.
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.af_ap_gm $2$ (not in LMFDB) 3.16.f_ap_agm $2$ (not in LMFDB) 3.16.v_hl_bmm $2$ (not in LMFDB) 3.16.aj_bl_aeu $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.af_ap_gm $2$ (not in LMFDB) 3.16.f_ap_agm $2$ (not in LMFDB) 3.16.v_hl_bmm $2$ (not in LMFDB) 3.16.aj_bl_aeu $3$ (not in LMFDB) 3.16.an_dl_aqa $4$ (not in LMFDB) 3.16.n_dl_qa $4$ (not in LMFDB) 3.16.ar_fl_abbg $6$ (not in LMFDB) 3.16.j_bl_eu $6$ (not in LMFDB) 3.16.r_fl_bbg $6$ (not in LMFDB)