Properties

Label 2.3.ac_d
Base Field $\F_{3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 + x + 3 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.593214749339$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 5 105 560 6825 74525 564480 4776245 44342025 390136880 3444620025

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 12 20 84 302 774 2186 6756 19820 58332

Decomposition

1.3.ad $\times$ 1.3.b

Base change

This is a primitive isogeny class.