Properties

Label 3.13.aq_en_aub
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 41 x^{2} - 117 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.109149799241$, $\pm0.400911184348$
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
$A(\F_{q^r})$ 595 4210815 10399333840 23003113884975 50983602291823600 112461589614792922560 247169665734669259945615 542879775564162421878399375 1192562007348115729035492404560 2620005718030021365669969970483200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 148 2155 28196 369823 4827073 62775214 815849444 10604754715 137859021943

Decomposition

1.13.ah $\times$ 2.13.aj_bp

Base change

This is a primitive isogeny class.