Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 2 x + 4 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.210767374595$, $\pm0.304086723985$, $\pm0.567777800232$
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
$A(\F_{q^r})$ 12 1584 26676 658944 18035292 390856752 9666051204 278169255936 7698199106988 205072307638704

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 16 36 100 300 736 2016 6460 19872 58816

Decomposition

1.3.ac $\times$ 2.3.ac_e

Base change

This is a primitive isogeny class.