# Properties

 Label 2.4.ag_r Base Field $\F_{2^2}$ Dimension $2$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^2}$ Dimension: $2$ Weil polynomial: $( 1 - 3 x + 4 x^{2} )^{2}$ Frobenius angles: $\pm0.230053456163$, $\pm0.230053456163$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4 256 5476 82944 1170724 17172736 265624804 4236447744 68197233316 1096996485376

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 15 83 319 1139 4191 16211 64639 260147 1046175

## Decomposition

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^2}$.
 Subfield Primitive Model $\F_{2}$ 2.2.a_ad