Properties

Label 2.17.an_cw
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:  $( 1 - 8 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.292637436158$
Angle rank:  $2$ (numerical)
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 130 77740 24261640 6990380800 2015239733650 582427647143680 168363781664704210 48661076024196480000 14063166150216570691720 4064241387720474658254700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 269 4940 83697 1419325 24129506 410304445 6975740833 118588565420 2015998851389

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ai $\times$ 1.17.af 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.ad_ag$2$(not in LMFDB)
2.17.d_ag$2$(not in LMFDB)
2.17.n_cw$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ad_ag$2$(not in LMFDB)
2.17.d_ag$2$(not in LMFDB)
2.17.n_cw$2$(not in LMFDB)
2.17.ah_bs$4$(not in LMFDB)
2.17.ad_y$4$(not in LMFDB)
2.17.d_y$4$(not in LMFDB)
2.17.h_bs$4$(not in LMFDB)