Properties

Label 2.3.ac_e
Base Field $\F_{3}$
Dimension $2$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $1 - 2 x + 4 x^{2} - 6 x^{3} + 9 x^{4}$
Frobenius angles:  $\pm0.210767374595$, $\pm0.567777800232$
Angle rank:  $2$ (numerical)
Number field:  4.0.7488.1
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
$A(\F_{q^r})$ 6 132 702 6864 74526 571428 4598502 42611712 387350262 3444740772

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 14 26 86 302 782 2102 6494 19682 58334

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.