Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )$
Frobenius angles:  $\pm0.384973271919$, $\pm0.615026728081$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 8 64 56 256 968 3136 16472 82944 263144 937024

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 11 9 15 33 47 129 319 513 911

Decomposition

1.2.ab $\times$ 1.2.b

Base change

This is a primitive isogeny class.