Properties

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

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.312832958189$
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
$A(\F_{q^r})$ 70 26460 4873120 817084800 137610200350 23276009352960 3936680039061070 665433838241625600 112458489573068467360 19005135175967126514300

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 157 2220 28609 370623 4822234 62737419 815751841 10604790060 137859735157

Decomposition

1.13.ah $\times$ 1.13.ae

Base change

This is a primitive isogeny class.