# Properties

 Label 2.16.ap_dk 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: $( 1 - 4 x )^{2}( 1 - 7 x + 16 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.160861246510$ 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 $A(\F_{q^r})$ 90 54000 16233210 4276044000 1099117082250 281474121474000 72056913100240410 18446530487208984000 4722336341568877842090 1208922742163319108750000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 208 3962 65248 1048202 16777168 268432922 4294917568 68719038122 1099508828848

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai $\times$ 1.16.ah 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.ah : $$\Q(\sqrt{-15})$$.
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 2.16.ab_ay $2$ 2.256.abx_boq 2.16.b_ay $2$ 2.256.abx_boq 2.16.p_dk $2$ 2.256.abx_boq 2.16.ad_e $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.16.ab_ay $2$ 2.256.abx_boq 2.16.b_ay $2$ 2.256.abx_boq 2.16.p_dk $2$ 2.256.abx_boq 2.16.ad_e $3$ (not in LMFDB) 2.16.ah_bg $4$ (not in LMFDB) 2.16.h_bg $4$ (not in LMFDB) 2.16.al_ci $6$ (not in LMFDB) 2.16.d_e $6$ (not in LMFDB) 2.16.l_ci $6$ (not in LMFDB)