Properties

Label 2.9.ai_bf
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:  $1 - 8 x + 31 x^{2} - 72 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.0954872438962$, $\pm0.376614839446$
Angle rank:  $2$ (numerical)
Number field:  4.0.13968.2
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
$A(\F_{q^r})$ 33 6369 542916 42653193 3458101713 282075265296 22896052702017 1854001264401033 150113610854233092 12157767541858520769

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 80 746 6500 58562 530774 4786994 43069508 387469466 3486813680

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.