Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.304086723985$
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
$A(\F_{q^r})$ 2 84 1064 8736 65582 536256 4769438 43365504 391199816 3500898324

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 9 38 105 269 738 2183 6609 19874 59289

Decomposition

1.3.ad $\times$ 1.3.ac

Base change

This is a primitive isogeny class.