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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 156 72072 17795700 4342338000 1098937569756 281253172800600 72044401777344516 18446667793926372000 4722409916727814104300 1208929030305993442758312

Point counts of the (virtual) curve

$r$ 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:
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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)