Properties

Label 2.9.ae_k
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1 - 4 x + 10 x^{2} - 36 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.135555600465$, $\pm0.578465250809$
Angle rank:  $2$ (numerical)
Number field:  4.0.7488.1
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
$A(\F_{q^r})$ 52 6864 495508 42611712 3529300372 283147145424 22876764228916 1853786054934528 150118550166346996 12157524888063167184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 86 678 6494 59766 532790 4782966 43064510 387482214 3486744086

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.