Properties

Label 2.17.aj_ca
Base Field $\F_{17}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $( 1 - 6 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$
Frobenius angles:  $\pm0.240632536990$, $\pm0.381477984739$
Angle rank:  $2$ (numerical)
Jacobians:  9

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 contains the Jacobians of 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 180 90720 25220160 7019913600 2015468442900 582517904209920 168377202796652820 48661208597686003200 14063030583913576802880 4064224963422141102261600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 313 5130 84049 1419489 24133246 410337153 6975759841 118587422250 2015990704393

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ag $\times$ 1.17.ad 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.ad_q$2$(not in LMFDB)
2.17.d_q$2$(not in LMFDB)
2.17.j_ca$2$(not in LMFDB)