Properties

Label 4.3.ah_ba_aco_ey
Base Field $\F_{3}$
Dimension $4$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 45 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.0714477711956$, $\pm0.27207177608$, $\pm0.304086723985$, $\pm0.560185743604$
Angle rank:  $4$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 10 9300 621490 46500000 3863596550 261827522100 20243733754240 1813169850000000 154314037806166930 12353429416140532500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 13 33 89 267 673 1922 6417 20229 59993

Decomposition

1.3.ac $\times$ 3.3.af_n_az

Base change

This is a primitive isogeny class.