Properties

Label 3.9.an_dc_alo
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:  $( 1 - 3 x )^{2}( 1 - 7 x + 29 x^{2} - 63 x^{3} + 81 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.220419591014$, $\pm0.370053256546$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 164 474944 399138116 282354208000 204292086406144 149584378657173824 109333550382282058276 79748353993923303552000 58140927939196599206072324 42387726366240839097262014464

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 73 753 6561 58592 529633 4779233 43036961 387361797 3486502108

Decomposition

1.9.ag $\times$ 2.9.ah_bd

Base change

This is a primitive isogeny class.