Properties

Label 3.13.aq_ep_aup
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 43 x^{2} - 117 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.161492811255$, $\pm0.37797305228$
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
$A(\F_{q^r})$ 609 4335471 10658834928 23255678882079 51107185572367344 112477288427059953600 247157259456221726495541 542875527099808293462869007 1192557015791458154074080282096 2619990439286919822544018391652096

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 152 2209 28508 370723 4827749 62772064 815843060 10604710327 137858218007

Decomposition

1.13.ah $\times$ 2.13.aj_br

Base change

This is a primitive isogeny class.