Properties

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

Learn more about

Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $1 - 9 x + 51 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.223072927732$, $\pm0.393933150683$
Angle rank:  $2$ (numerical)
Number field:  4.0.290173.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 179 90037 25084523 7010010709 2015786994224 582638993341213 168386664616004363 48661319226685136517 14062991191427179169723 4064221499894161540617472

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 311 5103 83931 1419714 24138263 410360211 6975775699 118587090069 2015988986366

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.290173.1.
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.j_bz$2$(not in LMFDB)