Properties

Label 2.4.ai_y
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:  $( 1 - 2 x )^{4}$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$
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
$A(\F_{q^r})$ 1 81 2401 50625 923521 15752961 260144641 4228250625 68184176641 1095222947841

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 1 33 193 897 3841 15873 64513 260097 1044481

Decomposition

1.4.ae 2

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^2}$.

SubfieldPrimitive Model
$\F_{2}$2.2.a_ae