Properties

Label 3.13.aq_eq_auw
Base Field $\F_{13}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.187167041811$, $\pm0.363422825076$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 616 4398240 10789402624 23377613212800 51150534515943016 112452094830577582080 247116075883767141604168 542851238517134881136140800 1192549190986974855482957436928 2619987533557127401286211408631200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 154 2236 28658 371038 4826668 62761606 815806562 10604640748 137858065114

Decomposition

1.13.ah $\times$ 1.13.ag $\times$ 1.13.ad

Base change

This is a primitive isogeny class.