Properties

Label 2.9.af_v
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:  $1 - 5 x + 21 x^{2} - 45 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.245455701794$, $\pm0.462927342931$
Angle rank:  $2$ (numerical)
Number field:  4.0.11661.1
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
$A(\F_{q^r})$ 53 8109 573725 43147989 3492709328 283090258125 22878778137653 1852122293214309 150069344388524525 12157769552734531584

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 99 785 6579 59150 532683 4783385 43025859 387355205 3486814254

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.