Properties

Label 3.13.aq_eu_avu
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.187167041811$, $\pm0.256122854178$, $\pm0.256122854178$
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
$A(\F_{q^r})$ 648 4678560 11398713984 24052383388800 51565503209383368 112526703776073646080 247000310295547016257704 542725971452014256712000000 1192493984943955799137953449088 2619988058269821139027985850544800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 162 2356 29474 374038 4829868 62732206 815618306 10604149828 137858092722

Decomposition

1.13.ag $\times$ 1.13.af 2

Base change

This is a primitive isogeny class.