Properties

Label 3.9.am_cr_ajr
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:  $( 1 - 5 x + 9 x^{2} )( 1 - 7 x + 25 x^{2} - 63 x^{3} + 81 x^{4} )$
Frobenius angles:  $\pm0.0842035494981$, $\pm0.186429498677$, $\pm0.435433986784$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 185 491175 389699540 279117561375 205690848972800 150628817342260800 109603353472979254745 79780980334317986811375 58145166278065401279216020 42390479255647993064939520000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 76 733 6484 58993 533329 4791022 43054564 387390037 3486728551

Decomposition

1.9.af $\times$ 2.9.ah_z

Base change

This is a primitive isogeny class.