Properties

Label 3.9.an_da_alc
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x )^{2}( 1 - 7 x + 27 x^{2} - 63 x^{3} + 81 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.154979380638$, $\pm0.40871325752$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 156 446784 377347932 275263622400 203809222009536 150022929758135616 109506104223812307804 79775957159986564838400 58142604826943975535823548 42388116549795431088838754304

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 69 711 6393 58452 531189 4786779 43051857 387372969 3486534204

Decomposition

1.9.ag $\times$ 2.9.ah_bb

Base change

This is a primitive isogeny class.