Properties

Label 2.3.ad_g
Base Field $\F_{3}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.5$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 4 112 784 5824 66124 614656 4964572 42515200 387459856 3501133552

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 13 28 73 271 838 2269 6481 19684 59293

Decomposition

1.3.ad $\times$ 1.3.a

Base change

This is a primitive isogeny class.