Properties

Label 2.9.ah_bd
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:  $1 - 7 x + 29 x^{2} - 63 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.220419591014$, $\pm0.370053256546$
Angle rank:  $2$ (numerical)
Number field:  4.0.11125.1
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
$A(\F_{q^r})$ 41 7421 590441 44117845 3488356096 282243197261 22879848052081 1853164829201445 150087147610208801 12157092956562108416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 91 807 6723 59078 531091 4783607 43050083 387401163 3486620206

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.