Properties

Label 2.2.a_e
Base Field $\F_{2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $( 1 + 2 x^{2} )^{2}$
Frobenius angles:  $\pm0.5$, $\pm0.5$
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 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 81 81 1089 6561 16641 50625 263169 1185921

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 13 9 1 33 97 129 193 513 1153

Decomposition

1.2.a 2

Base change

This is a primitive isogeny class.