Properties

Label 5.3.am_cq_ajj_xx_abut
Base Field $\F_{3}$
Dimension $5$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})^{3}(1-3x+5x^{2}-9x^{3}+9x^{4})$
Frobenius angles:  $\pm0.0975263560046$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.527857038681$
Angle rank:  $2$ (numerical)

Newton polygon

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3 27783 12051648 3723394311 1242872006928 278579339071488 55815405838726341 12620464084636766631 3024365235163963572672 718721523070745713682688

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 2 19 86 337 953 2428 6806 20143 59117

Decomposition

1.3.ad 3 $\times$ 2.3.ad_f

Base change

This is a primitive isogeny class.