Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 + x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.593214749339$
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
$A(\F_{q^r})$ 5 735 15680 621075 20196275 442552320 10837299905 294564072075 7679454345920 202567769810175

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 9 20 93 329 828 2267 6837 19820 58089

Decomposition

1.3.ad 2 $\times$ 1.3.b

Base change

This is a primitive isogeny class.