Properties

Label 2.9.ah_ba
Base Field $\F_{3^2}$
Dimension $2$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1 - 7 x + 26 x^{2} - 63 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.122441590128$, $\pm0.422937410221$
Angle rank:  $2$ (numerical)
Number field:  4.0.49708.1
Galois group:  $D_{4}$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 38 6764 542336 42423808 3469878838 283042989056 22916426899222 1853786180671488 150096592887827072 12157669652650588844

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 85 744 6465 58763 532594 4791251 43064513 387425544 3486785605

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.