Properties

Label 3.3.ag_t_abn
Base Field $\F_{3}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.227267020856$, $\pm0.464830336654$
Angle rank:  $2$ (numerical)

Newton polygon

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

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 1015 29540 593775 16802000 455743120 11052196895 275721202575 7429279071620 204702932896000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 12 37 92 283 849 2308 6404 19171 58707

Decomposition

1.3.ad $\times$ 2.3.ad_h

Base change

This is a primitive isogeny class.