Properties

Label 3.3.ae_l_ax
Base Field $\F_{3}$
Dimension $3$
$p$-rank $3$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 3 x^{2} )( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0975263560046$, $\pm0.406785250661$, $\pm0.527857038681$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9 1215 19764 370575 13301424 416229840 10850949279 287364977775 7751691822564 207007401427200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 16 27 52 225 781 2268 6676 20007 59371

Decomposition

1.3.ab $\times$ 2.3.ad_f

Base change

This is a primitive isogeny class.