Properties

Label 2.17.ak_bz
Base Field $\F_{17}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $1 - 10 x + 51 x^{2} - 170 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.101757099716$, $\pm0.415175272105$
Angle rank:  $2$ (numerical)
Number field:  4.0.27200.2
Galois group:  $D_{4}$
Jacobians:  6

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 161 83881 24237584 6938720201 2012801907361 582696338646016 168404020269239489 48662783951221586825 14063108020149657479696 4064232036283697612305321

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 292 4934 83076 1417608 24140638 410402504 6975985668 118588075238 2015994212772

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.27200.2.
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.k_bz$2$(not in LMFDB)