Properties

Label 3.13.ap_ed_asg
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 2 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.187167041811$, $\pm0.410543812489$
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
$A(\F_{q^r})$ 672 4515840 10695089664 23218281676800 51125806828172832 112526703776073646080 247165037795274499902624 542838651836084540787916800 1192520607056636317090407802368 2619979964361922025454129187891200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 159 2216 28463 370859 4829868 62774039 815787647 10604386568 137857666839

Decomposition

1.13.ah $\times$ 1.13.ag $\times$ 1.13.ac

Base change

This is a primitive isogeny class.