Properties

Label 2.9.ag_z
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:  $1 - 6 x + 25 x^{2} - 54 x^{3} + 81 x^{4}$
Frobenius angles:  $\pm0.236852280319$, $\pm0.414859841358$
Angle rank:  $2$ (numerical)
Number field:  4.0.35392.1
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
$A(\F_{q^r})$ 47 7849 586748 43585497 3482812847 282594265744 22886808861551 1852790231601513 150070452685995836 12157132460245471609

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 96 802 6644 58984 531750 4785064 43041380 387358066 3486631536

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.