Properties

Label 3.3.ae_h_aj
Base Field $\F_{3}$
Dimension $3$
$p$-rank $2$

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - x + x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.201748855633$, $\pm0.672988571819$
Angle rank:  $2$ (numerical)

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 7 735 15484 812175 19152112 409706640 11277867097 286068339375 7430044424908 204475608556800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 8 21 116 315 773 2352 6644 19173 58643

Decomposition

1.3.ad $\times$ 2.3.ab_b

Base change

This is a primitive isogeny class.