Properties

Label 5.3.am_ct_akk_bcb_acec
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:  $(1-2x+3x^{2})(1-x+3x^{2})(1-3x+3x^{2})^{3}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.406785250661$
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
$A(\F_{q^r})$ 6 61740 30030336 5425711200 1025894832006 237321336913920 55763924890428978 12773919445824700800 2962972938074416823808 709169165824859455646700

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 8 46 116 292 836 2428 6884 19738 58328

Decomposition

1.3.ad 3 $\times$ 1.3.ac $\times$ 1.3.ab

Base change

This is a primitive isogeny class.