# Properties

 Label 2.16.an_cu 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: $( 1 - 4 x )^{2}( 1 - 5 x + 16 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.285098958592$ 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 $A(\F_{q^r})$ 108 59400 16717428 4291650000 1097863340508 281253172800600 72040004267638788 18445823385372900000 4722337859020785820908 1208925571535592304185000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 232 4084 65488 1047004 16763992 268369924 4294752928 68719060204 1099511402152

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai $\times$ 1.16.af 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 $\infty$. 1.16.af : $$\Q(\sqrt{-39})$$.
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 2.16.ad_ai $2$ 2.256.az_lc 2.16.d_ai $2$ 2.256.az_lc 2.16.n_cu $2$ 2.256.az_lc 2.16.ab_m $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.16.ad_ai $2$ 2.256.az_lc 2.16.d_ai $2$ 2.256.az_lc 2.16.n_cu $2$ 2.256.az_lc 2.16.ab_m $3$ (not in LMFDB) 2.16.af_bg $4$ (not in LMFDB) 2.16.f_bg $4$ (not in LMFDB) 2.16.aj_ca $6$ (not in LMFDB) 2.16.b_m $6$ (not in LMFDB) 2.16.j_ca $6$ (not in LMFDB)