Properties

Label 2.27.ao_dt
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $1 - 14 x + 97 x^{2} - 378 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.136634956619$, $\pm0.355731932508$
Angle rank:  $2$ (numerical)
Number field:  4.0.940608.1
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
$A(\F_{q^r})$ 435 530265 391296420 282729344025 205866829758675 150093595042154640 109421042455718983515 79766996198001599728425 58149802567442403911339460 42391159625598429277301892825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 728 19880 532004 14347214 387417806 10460549498 282431494916 7625606082920 205891138653368

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.