Properties

Label 2.17.aj_bq
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:  $( 1 - 8 x + 17 x^{2} )( 1 - x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.461304015105$
Angle rank:  $2$ (numerical)
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 170 83980 23876840 6906515200 2012918167850 582775213895680 168392714234005130 48660977581413350400 14063060265109115260520 4064237805908290336693900

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 293 4860 82689 1417689 24143906 410374953 6975726721 118587672540 2015997074693

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ai $\times$ 1.17.ab 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ah_ba$2$(not in LMFDB)
2.17.h_ba$2$(not in LMFDB)
2.17.j_bq$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ah_ba$2$(not in LMFDB)
2.17.h_ba$2$(not in LMFDB)
2.17.j_bq$2$(not in LMFDB)
2.17.ad_bk$4$(not in LMFDB)
2.17.ab_bg$4$(not in LMFDB)
2.17.b_bg$4$(not in LMFDB)
2.17.d_bk$4$(not in LMFDB)