Properties

Label 2.13.ak_bv
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.363422825076$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 77 27489 4868864 811722681 137321294957 23277766127616 3937639431868373 665478087042808809 112458102440893104896 19004999110047710270049

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 164 2218 28420 369844 4822598 62752708 815806084 10604753554 137858748164

Decomposition

1.13.ah $\times$ 1.13.ad

Base change

This is a primitive isogeny class.