Properties

Label 4.3.ak_bv_afi_kw
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:  $( 1 - 3 x + 3 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.445913276015$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 2 3332 490784 38291344 3619319362 327058457600 25217176717378 1880566937174016 147899391592223264 12058613378200922372

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 4 24 72 254 838 2402 6656 19392 58564

Decomposition

1.3.ad 2 $\times$ 2.3.ae_i

Base change

This is a primitive isogeny class.