Properties

Label 3.9.am_cp_ajg
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:  $( 1 - 3 x )^{2}( 1 - 6 x + 22 x^{2} - 54 x^{3} + 81 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.1623814046$, $\pm0.459361842123$
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
$A(\F_{q^r})$ 176 461824 369093296 272660889600 204594348562736 150389774076365824 109487872955533446704 79743783410341930598400 58139152588206855049302704 42389594227025987064446946304

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 72 694 6332 58678 532488 4785982 43034492 387349966 3486655752

Decomposition

1.9.ag $\times$ 2.9.ag_w

Base change

This is a primitive isogeny class.