Properties

Label 2.4.ae_i
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.5$
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 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
$A(\F_{q^r})$ 5 225 3185 50625 985025 16769025 264273665 4228250625 68451564545 1099509530625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 17 49 193 961 4097 16129 64513 261121 1048577

Decomposition

1.4.ae $\times$ 1.4.a

Base change

This is a primitive isogeny class.