Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - x + 3 x^{2} )( 1 + x + 3 x^{2} )$
Frobenius angles:  $\pm0.406785250661$, $\pm0.593214749339$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 15 225 720 5625 58575 518400 4780455 44555625 387441360 3431030625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 20 28 68 244 710 2188 6788 19684 58100

Decomposition

1.3.ab $\times$ 1.3.b

Base change

This is a primitive isogeny class.