Properties

Label 2.13.ai_bp
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:  $( 1 - 5 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$
Frobenius angles:  $\pm0.256122854178$, $\pm0.363422825076$
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
$A(\F_{q^r})$ 99 31977 5189184 826829289 137766360699 23277766127616 3936722393153187 665415199774578825 112455591899559644736 19004941444519141523577

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 188 2358 28948 371046 4822598 62738094 815728996 10604516814 137858329868

Decomposition

1.13.af $\times$ 1.13.ad

Base change

This is a primitive isogeny class.