Properties

Label 1.9.ae
Base Field $\F_{3^2}$
Dimension $1$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $1$
Weil polynomial:  $1 - 4 x + 9 x^{2}$
Frobenius angles:  $\pm0.267720472801$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-5}) \)
Galois group:  $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

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
$A(\F_{q^r})$ 6 84 774 6720 59286 530964 4778934 43034880 387409446 3486846804

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 84 774 6720 59286 530964 4778934 43034880 387409446 3486846804

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.