Properties

Label 2.3.ab_ab
Base Field $\F_{3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $1-x-x^{2}-3x^{3}+9x^{4}$
Frobenius angles:  $\pm0.126866938441$, $\pm0.718153680921$
Angle rank:  $2$ (numerical)
Number field:  4.0.10933.1
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
$A(\F_{q^r})$ 5 65 455 8125 60400 538265 5191555 43363125 391801865 3530259200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 7 15 99 248 739 2369 6611 19905 59782

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.