Properties

Label 3.3.ae_m_ay
Base Field $\F_{3}$
Dimension $3$
$p$-rank $1$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 + 3 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.406785250661$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 12 1680 28224 436800 14084412 442552320 11274543012 283788960000 7574065265088 205078897808400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 18 36 66 240 828 2352 6594 19548 58818

Decomposition

1.3.ad $\times$ 1.3.ab $\times$ 1.3.a

Base change

This is a primitive isogeny class.