Properties

Label 5.3.ak_by_agj_po_abea
Base Field $\F_{3}$
Dimension $5$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
Weil polynomial:  $(1-3x+3x^{2})(1-2x+3x^{2})(1-5x+13x^{2}-25x^{3}+39x^{4}-45x^{5}+27x^{6})$
Frobenius angles:  $\pm0.0714477711956$, $\pm0.166666666667$, $\pm0.27207177608$, $\pm0.304086723985$, $\pm0.560185743604$
Angle rank:  $4$ (numerical)

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 10 65100 17401720 4231500000 1047034665050 205272777326400 45933031888370560 12044887313550000000 3037517520176589850120 726468123674976294727500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 10 33 98 294 727 2003 6498 20229 59750

Decomposition

1.3.ad $\times$ 1.3.ac $\times$ 3.3.af_n_az

Base change

This is a primitive isogeny class.