Properties

Label 4.3.ah_z_acl_et
Base Field $\F_{3}$
Dimension $4$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 10 x^{2} - 21 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$
Frobenius angles:  $\pm0.0145064862012$, $\pm0.166666666667$, $\pm0.383559653096$, $\pm0.564732805964$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 7 6321 407092 32622681 3349212307 277908681456 22350531758359 1880571277251849 150525368480881408 11889101913430315161

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 11 21 59 237 719 2139 6659 19740 57731

Decomposition

1.3.ad $\times$ 3.3.ae_k_av

Base change

This is a primitive isogeny class.