Properties

Label 2.27.ao_dx
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:  $1 - 14 x + 101 x^{2} - 378 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.199652566054$, $\pm0.31937161955$
Angle rank:  $2$ (numerical)
Number field:  4.0.182848.5
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
$A(\F_{q^r})$ 439 536897 394648708 283555170889 205967278901999 150092305683567248 109418086016687170343 79766404396394534336457 58149742052062799892262948 42391157214746074368079015697

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 736 20048 533556 14354214 387414478 10460266866 282429399524 7625598147104 205891126944016

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.