Properties

Label 2.2.ad_g
Base Field $\F_{2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )$
Frobenius angles:  $\pm0.25$, $\pm0.384973271919$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 2 40 182 400 902 3640 16046 64800 249158 992200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 8 18 24 30 56 126 256 486 968

Decomposition

1.2.ac $\times$ 1.2.ab

Base change

This is a primitive isogeny class.