Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.445913276015$, $\pm0.5$
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
$A(\F_{q^r})$ 8 7616 490784 26930176 3258722968 327058457600 24316960184056 1811776064716800 147899391592223264 12208097778913566656

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 13 24 45 227 838 2321 6413 19392 59293

Decomposition

1.3.ad $\times$ 1.3.a $\times$ 2.3.ae_i

Base change

This is a primitive isogeny class.