Properties

Label 3.9.an_db_ali
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{2}(1-5x+9x^{2})(1-2x+9x^{2})$
Frobenius angles:  $0.0$, $0.0$, $\pm0.186429498677$, $\pm0.391826552031$
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
$A(\F_{q^r})$ 160 460800 388186240 278876160000 204169342352800 149880384228556800 109445583963585327520 79764953883927183360000 58140206538251422992085120 42387026651061413776139520000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 71 732 6479 58557 530684 4784133 43045919 387356988 3486444551

Decomposition

1.9.ag $\times$ 1.9.af $\times$ 1.9.ac

Base change

This is a primitive isogeny class.