Properties

Label 2.27.an_dh
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:  $1 - 13 x + 85 x^{2} - 351 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.102890325329$, $\pm0.402107243364$
Angle rank:  $2$ (numerical)
Number field:  4.0.26725.1
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
$A(\F_{q^r})$ 451 531729 388703821 281959405101 205787444281936 150095998478366721 109422141705521090281 79766931279383751149109 58149762609533932624003519 42391158263816840284149345024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 731 19749 530555 14341680 387424007 10460654583 282431265059 7625600842953 205891132039286

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.