Properties

Label 2.3.b_g
Base Field $\F_{3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 + 3 x^{2} )( 1 + x + 3 x^{2} )$
Frobenius angles:  $\pm0.5$, $\pm0.593214749339$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20 240 560 4800 67100 564480 4605740 42720000 390136880 3487321200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 21 20 57 275 774 2105 6513 19820 59061

Decomposition

1.3.a $\times$ 1.3.b

Base change

This is a primitive isogeny class.