Properties

Label 2.3.b_e
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:  $( 1 - x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$
Frobenius angles:  $\pm0.406785250661$, $\pm0.695913276015$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 18 180 648 7200 52398 492480 5164254 43574400 381068712 3487086900

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 17 26 89 215 674 2357 6641 19358 59057

Decomposition

1.3.ab $\times$ 1.3.c

Base change

This is a primitive isogeny class.