Properties

Label 2.9.ah_bb
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $1-7x+27x^{2}-63x^{3}+81x^{4}$
Frobenius angles:  $\pm0.154979380638$, $\pm0.40871325752$
Angle rank:  $2$ (numerical)
Number field:  4.0.4901.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

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

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
$A(\F_{q^r})$ 39 6981 558207 43009941 3480111024 283070677149 22915957788399 1853806262083269 150091476390429327 12157204863902981376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 87 765 6555 58938 532647 4791153 43064979 387412335 3486652302

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.