Properties

Label 3.3.aj_bk_add
Base Field $\F_{3}$
Dimension $3$
Ordinary No
$p$-rank $0$
Contains a Jacobian No

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )^{3}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 1 343 21952 753571 19902511 481890304 11681631109 293151929707 7626759805504 203370086883943

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 1 28 109 325 892 2431 6805 19684 58321

Decomposition

1.3.ad 3

Base change

This is a primitive isogeny class.