# Properties

 Label 2.16.aj_ca Base Field $\F_{2^{4}}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 5 x + 16 x^{2} )( 1 - 4 x + 16 x^{2} )$ Frobenius angles: $\pm0.285098958592$, $\pm0.333333333333$ Angle rank: $1$ (numerical) Jacobians: 0

This isogeny class is not simple.

## Newton polygon

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

## 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 $A(\F_{q^r})$ 156 72072 17795700 4342338000 1098937569756 281253172800600 72044401777344516 18446667793926372000 4722409916727814104300 1208929030305993442758312

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 8 280 4340 66256 1048028 16763992 268386308 4294949536 68720108780 1099514547880

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.af $\times$ 1.16.ae and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{2^{4}}$
 The base change of $A$ to $\F_{2^{12}}$ is 1.4096.el $\times$ 1.4096.ey. The endomorphism algebra for each factor is: 1.4096.el : $$\Q(\sqrt{-39})$$. 1.4096.ey : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$.
All geometric endomorphisms are defined over $\F_{2^{12}}$.

## 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 2.16.ab_m $2$ 2.256.x_ya 2.16.b_m $2$ 2.256.x_ya 2.16.j_ca $2$ 2.256.x_ya 2.16.d_ai $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.16.ab_m $2$ 2.256.x_ya 2.16.b_m $2$ 2.256.x_ya 2.16.j_ca $2$ 2.256.x_ya 2.16.d_ai $3$ (not in LMFDB) 2.16.an_cu $6$ (not in LMFDB) 2.16.ad_ai $6$ (not in LMFDB) 2.16.n_cu $6$ (not in LMFDB) 2.16.af_bg $12$ (not in LMFDB) 2.16.f_bg $12$ (not in LMFDB)