Properties

Label 4.3.ah_z_acn_fa
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:  $( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.0975263560046$, $\pm0.445913276015$, $\pm0.527857038681$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 6 5508 343674 22847184 3077562336 307605413700 23403352250802 1834606210793472 151367919900582942 12322899257743899648

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 11 15 31 212 791 2237 6495 19851 59846

Decomposition

2.3.ae_i $\times$ 2.3.ad_f

Base change

This is a primitive isogeny class.