Properties

Label 3.9.an_de_aly
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-4x+9x^{2})(1-9x+37x^{2}-81x^{3}+81x^{4})$
Frobenius angles:  $\pm0.114191348093$, $\pm0.267720472801$, $\pm0.309392441858$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 174 509124 426676014 293621993280 206850076714464 149815730489696964 109320697113771753966 79766025227552010251520 58158572040630690203813886 42394586255218617219591880704

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 77 801 6817 59322 530453 4778673 43046497 387479349 3487066352

Decomposition

1.9.ae $\times$ 2.9.aj_bl

Base change

This is a primitive isogeny class.