Properties

Label 3.3.ae_j_ap
Base Field $\F_{3}$
Dimension $3$
Ordinary No
$p$-rank $1$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.268536328535$, $\pm0.622727850897$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 9 1071 18900 737919 19160784 386845200 10239885819 286632090927 7563732995700 204701246781696

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 12 27 108 315 729 2142 6660 19521 58707

Decomposition

1.3.ad $\times$ 2.3.ab_d

Base change

This is a primitive isogeny class.