Properties

Label 2.169.abx_bkb
Base Field $\F_{13^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 937 x^{2} - 8281 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0546290859232$, $\pm0.144071978349$
Angle rank:  $2$ (numerical)
Number field:  4.0.63725.1
Galois group:  $D_{4}$
Jacobians:  3

This isogeny class is simple and geometrically 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
$A(\F_{q^r})$ 21169 800802101 23275156499641 665391630093649349 19004962180730770132624 542800859353697857490675141 15502933118188460997199657976089 442779264526745585934223215518376389 12646218554090026251167863159276894578721 361188648086261033867669145852153977938968576

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 28035 4822057 815700099 137858480286 23298088941651 3937376465835409 665416610310150339 112455406964048221873 19004963774971806607150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.63725.1.
All geometric endomorphisms are defined over $\F_{13^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.bx_bkb$2$(not in LMFDB)