Properties

Label 2.9.ai_be
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x )^{2}( 1 - 2 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.391826552031$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 32 6144 524576 41779200 3429976352 281307027456 22870322227232 1852970355916800 150078119690079776 12156855415820949504

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 78 722 6366 58082 529326 4781618 43045566 387377858 3486552078

Decomposition

1.9.ag $\times$ 1.9.ac

Base change

This is a primitive isogeny class.