Properties

Label 3.13.aq_es_avk
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.256122854178$, $\pm0.312832958189$
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
$A(\F_{q^r})$ 630 4524660 11052236160 23612933635200 51200489634024150 112337097044228259840 246971216439371889206910 542777263568205236101440000 1192552670567179325263778029440 2620021970752207141908792554997300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 158 2290 28946 371398 4821728 62724814 815695394 10604671690 137859877118

Decomposition

1.13.ah $\times$ 1.13.af $\times$ 1.13.ae

Base change

This is a primitive isogeny class.