Properties

Label 2.3.ag_p
Base Field $\F_{3}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$
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 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
$A(\F_{q^r})$ 1 49 784 8281 73441 614656 5148361 44129449 387459856 3458263249

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 4 28 100 298 838 2350 6724 19684 58564

Decomposition

1.3.ad 2

Base change

This is a primitive isogeny class.