Properties

Label 2.3.ab_e
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:  $( 1 - 2 x + 3 x^{2} )( 1 + x + 3 x^{2} )$
Frobenius angles:  $\pm0.304086723985$, $\pm0.593214749339$
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
$A(\F_{q^r})$ 10 180 760 7200 66550 492480 4424710 43574400 393902680 3487086900

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 17 30 89 273 674 2019 6641 20010 59057

Decomposition

1.3.ac $\times$ 1.3.b

Base change

This is a primitive isogeny class.