Properties

Label 3.3.ah_y_abz
Base Field $\F_{3}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.406785250661$
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
$A(\F_{q^r})$ 3 735 28224 621075 15642933 442552320 11691927831 294564072075 7574065265088 202567769810175

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 9 36 93 267 828 2433 6837 19548 58089

Decomposition

1.3.ad 2 $\times$ 1.3.ab

Base change

This is a primitive isogeny class.