Properties

Label 2.17.an_cy
Base Field $\F_{17}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$
Frobenius angles:  $\pm0.177280642489$, $\pm0.240632536990$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 132 79200 24659712 7053552000 2021889165252 582896408371200 168380808657984516 48660354784857024000 14062989450255637909248 4064225418633377836476000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 273 5018 84449 1424005 24148926 410345941 6975637441 118587075386 2015990930193

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ah $\times$ 1.17.ag and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{17}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ab_ai$2$(not in LMFDB)
2.17.b_ai$2$(not in LMFDB)
2.17.n_cy$2$(not in LMFDB)