Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x )^{2}( 1 - 4 x + 9 x^{2} )^{2}$
Frobenius angles:  $0.0$, $0.0$, $\pm0.267720472801$, $\pm0.267720472801$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 144 451584 404975376 289013760000 205842492172944 149414556962571264 109134579795894076176 79698265784545443840000 58140513921676054150333584 42391239803178853461541438464

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 68 764 6716 59036 529028 4770524 43009916 387359036 3486791108

Decomposition

1.9.ag $\times$ 1.9.ae 2

Base change

This is a primitive isogeny class.