Properties

Label 3.9.ar_et_ass
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:  $( 1 - 3 x )^{4}( 1 - 5 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.186429498677$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 80 307200 338162240 273408000000 204155398264400 149654483848396800 109276452979038199760 79718479101345792000000 58134788964313019891117120 42386979579626804725870080000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 39 632 6351 58553 529884 4776737 43020831 387320888 3486440679

Decomposition

1.9.ag 2 $\times$ 1.9.af

Base change

This is a primitive isogeny class.