Properties

Label 2.9.ag_s
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x )^{2}( 1 + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.5$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 40 6400 493480 40960000 3458204200 282428473600 22855881310120 1851890728960000 150079384876830760 12157665452083360000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 82 676 6238 58564 531442 4778596 43020478 387381124 3486784402

Decomposition

1.9.ag $\times$ 1.9.a

Base change

This is a primitive isogeny class.