Properties

Label 2.13.ak_bz
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.256122854178$, $\pm0.256122854178$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 81 29241 5143824 835152201 138435340761 23293210300416 3935794779943569 665324522896775625 112452896477996048016 19005002916235392383721

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 172 2338 29236 372844 4825798 62723308 815617828 10604262634 137858775772

Decomposition

1.13.af 2

Base change

This is a primitive isogeny class.