Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 4 x + 9 x^{2} )( 1 - 5 x + 9 x^{2} )^{2}$
Frobenius angles:  $\pm0.186429498677$, $\pm0.186429498677$, $\pm0.267720472801$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 150 472500 423842400 299413800000 210063674403750 150727851509760000 109441730431489050150 79745813047623895200000 58141815205384172820002400 42389302413263648180920312500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 70 794 6946 60236 533680 4783964 43035586 387367706 3486631750

Decomposition

1.9.af 2 $\times$ 1.9.ae

Base change

This is a primitive isogeny class.