Properties

Label 5.3.ak_bx_agd_ox_abct
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:  $(1-3x+3x^{2})^{2}(1-4x+10x^{2}-21x^{3}+30x^{4}-36x^{5}+27x^{6})$
Frobenius angles:  $\pm0.0145064862012$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.383559653096$, $\pm0.564732805964$
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
$A(\F_{q^r})$ 7 44247 11398576 2968663971 907636535197 217880406261504 50713356559716571 12492634994784032907 2962941353177669635072 699162416223096543672927

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 21 68 264 773 2220 6740 19740 57488

Decomposition

1.3.ad 2 $\times$ 3.3.ae_k_av

Base change

This is a primitive isogeny class.