Properties

Label 2.4.a_ai
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 + 2 x )^{2}$
Frobenius angles:  $0.0$, $0.0$, $1.0$, $1.0$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 9 81 3969 50625 1046529 15752961 268402689 4228250625 68718952449 1095222947841

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 1 65 193 1025 3841 16385 64513 262145 1044481

Decomposition

1.4.ae $\times$ 1.4.e

Base change

This is a primitive isogeny class.