Properties

Label 3.4.ag_v_aby
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 4 x^{2} )( 1 - 4 x + 9 x^{2} - 16 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.117169895439$, $\pm0.333333333333$, $\pm0.478661301576$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 18 5796 319302 15672384 1038842838 69811550676 4453330049046 282840203632896 18114346718963622 1157753840091358356

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 23 77 239 989 4163 16589 65855 263597 1052963

Decomposition

1.4.ac $\times$ 2.4.ae_j

Base change

This is a primitive isogeny class.