Properties

Label 2.4.a_ab
Base Field $\F_{2^2}$
Dimension $2$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 4 x^{2} )( 1 + 3 x + 4 x^{2} )$
Frobenius angles:  $\pm0.230053456163$, $\pm0.769946543837$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 16 256 4144 82944 1047376 17172736 268460656 4236447744 68719003024 1096996485376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 15 65 319 1025 4191 16385 64639 262145 1046175

Decomposition

1.4.ad $\times$ 1.4.d

Base change

This is a primitive isogeny class.