Properties

Label 2.9.af_y
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 9 x^{2} )( 1 - 2 x + 9 x^{2} )$
Frobenius angles:  $\pm0.333333333333$, $\pm0.391826552031$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 56 8736 608384 43365504 3444208376 281307027456 22880789191736 1853817880072704 150108621822959744 12157473068982617376

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 105 830 6609 58325 529326 4783805 43065249 387456590 3486729225

Decomposition

1.9.ad $\times$ 1.9.ac

Base change

This is a primitive isogeny class.