Properties

Label 3.13.ap_eg_atb
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.256122854178$, $\pm0.363422825076$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 693 4700619 11042583552 23457973758219 51092996893356033 112345575772777611264 247031404823063675979549 542813356177029969244688475 1192548565270092874353721795584 2620003212890448180857709012026739

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 165 2288 28757 370619 4822092 62740103 815749637 10604635184 137858890125

Decomposition

1.13.ah $\times$ 1.13.af $\times$ 1.13.ad

Base change

This is a primitive isogeny class.