Properties

Label 3.13.as_fq_abac
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.187167041811$, $\pm0.256122854178$
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
$A(\F_{q^r})$ 504 4021920 10695089664 23612933635200 51398916541701624 112526703776073646080 247057847714898179985816 542777263568205236101440000 1192520607056636317090407802368 2619996007938946139356712420637600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 138 2216 28946 372836 4829868 62746820 815695394 10604386568 137858511018

Decomposition

1.13.ah $\times$ 1.13.ag $\times$ 1.13.af

Base change

This is a primitive isogeny class.