Properties

Label 3.13.as_fo_azo
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:  $( 1 - 4 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.312832958189$
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
$A(\F_{q^r})$ 490 3889620 10369999360 23181512860800 51035082173203450 112337097044228259840 247028747081462727683890 542828560531927606535692800 1192579293990000853492740835840 2620029920524230708253944980630100

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 134 2150 28418 370196 4821728 62739428 815772482 10604908430 137860295414

Decomposition

1.13.ah 2 $\times$ 1.13.ae

Base change

This is a primitive isogeny class.