Properties

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

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $( 1 - 8 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.381477984739$
Angle rank:  $2$ (numerical)
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 150 81900 24242400 6945120000 2011609803750 582452363001600 168388692037314150 48662783705128320000 14063149824404621522400 4064231032629148100947500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 285 4936 83153 1416767 24130530 410365151 6975985633 118588427752 2015993714925

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ai $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.af_k$2$(not in LMFDB)
2.17.f_k$2$(not in LMFDB)
2.17.l_cg$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.af_k$2$(not in LMFDB)
2.17.f_k$2$(not in LMFDB)
2.17.l_cg$2$(not in LMFDB)
2.17.af_bo$4$(not in LMFDB)
2.17.ab_bc$4$(not in LMFDB)
2.17.b_bc$4$(not in LMFDB)
2.17.f_bo$4$(not in LMFDB)