Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{2}(1-7x+25x^{2}-63x^{3}+81x^{4})$
Frobenius angles:  $0.0$, $0.0$, $\pm0.0842035494981$, $\pm0.435433986784$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 148 419136 355995796 267618336000 202370077769728 149832701070421824 109445572704243096532 79756006542021879936000 58142390196365891358008404 42390350735061693695017353216

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 65 669 6209 58032 530513 4784133 43041089 387371541 3486717980

Decomposition

1.9.ag $\times$ 2.9.ah_z

Base change

This is a primitive isogeny class.