Properties

Label 3.9.ao_dl_amy
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:  $( 1 - 3 x )^{2}( 1 - 8 x + 32 x^{2} - 72 x^{3} + 81 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.141826552031$, $\pm0.358173447969$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 136 422144 379534792 278446182400 203895946508936 149682801616414976 109421208202385063624 79786472428670445158400 58152155528179998307022728 42389722512576532224166095104

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 64 716 6468 58476 529984 4783068 43057532 387436604 3486666304

Decomposition

1.9.ag $\times$ 2.9.ai_bg

Base change

This is a primitive isogeny class.