Properties

Label 2.13.aj_bn
Base Field $\F_{13}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
L-polynomial:  $1 - 9 x + 39 x^{2} - 117 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.0228181011636$, $\pm0.419357734967$
Angle rank:  $2$ (numerical)
Number field:  4.0.10933.1
Galois group:  $D_{4}$
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 83 27805 4765943 801479125 137005100048 23279891985805 3937478512982279 665397985659625125 112452004640700347987 19004802581974649094400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 167 2171 28059 368990 4823039 62750147 815707891 10604178533 137857322582

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The endomorphism algebra of this simple isogeny class is 4.0.10933.1.
All geometric endomorphisms are defined over $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.13.j_bn$2$2.169.ad_ajn