Properties

Label 3.9.an_cx_akk
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{4}(1-x+9x^{2})$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.446699620962$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 144 405504 345473856 263577600000 201288133872144 149492695217209344 109311070808310723216 79712256748496486400000 58132025383198596524944704 42388138175288714679311806464

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 63 648 6111 57717 529308 4778253 43017471 387302472 3486535983

Decomposition

1.9.ag 2 $\times$ 1.9.ab

Base change

This is a primitive isogeny class.