Properties

Label 2.4.ab_ae
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 + 3 x + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.769946543837$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8 144 2744 64800 930248 16447536 265676888 4232347200 68712424424 1096109357904

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 8 40 256 904 4016 16216 64576 262120 1045328

Decomposition

1.4.ae $\times$ 1.4.d

Base change

This is a primitive isogeny class.