Properties

Label 2.17.ak_cd
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:  $( 1 - 7 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$
Frobenius angles:  $\pm0.177280642489$, $\pm0.381477984739$
Angle rank:  $2$ (numerical)
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 165 86625 24837120 7001465625 2015920649325 582708639744000 168398390059478205 48662637733954715625 14063077296683264424960 4064222296481060552540625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 300 5054 83828 1419808 24141150 410388784 6975964708 118587816158 2015989381500

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ah $\times$ 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.ae_n$2$(not in LMFDB)
2.17.e_n$2$(not in LMFDB)
2.17.k_cd$2$(not in LMFDB)