Properties

Label 3.9.am_cl_aii
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $(1-3x)^{4}(1+9x^{2})$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.5$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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 409600 333592480 262144000000 202526270768800 149682572152422400 109219023005014191520 79693524873773056000000 58137920802815301366574240 42389722467083977911101440000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 64 622 6076 58078 529984 4774222 43007356 387341758 3486666304

Decomposition

1.9.ag 2 $\times$ 1.9.a

Base change

This is a primitive isogeny class.