Properties

Label 2.4.ah_u
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:  $0.0$, $0.0$, $\pm0.230053456163$
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
$A(\F_{q^r})$ 2 144 3626 64800 1039802 16447536 262870442 4232347200 68190704666 1096109357904

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 8 58 256 1018 4016 16042 64576 260122 1045328

Decomposition

1.4.ae $\times$ 1.4.ad

Base change

This is a primitive isogeny class.