# Properties

 Label 2.2.a_ad Base Field $\F_{2}$ Dimension $2$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2}$ Dimension: $2$ Weil polynomial: $1 - 3 x^{2} + 4 x^{4}$ Frobenius angles: $\pm0.115026728081$, $\pm0.884973271919$ Angle rank: $1$ (numerical) Number field: $$\Q(i, \sqrt{7})$$ Galois group: $C_2^2$

This isogeny class is simple.

## 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 $A(\F_{q^r})$ 2 4 74 256 1082 5476 16298 82944 261146 1170724

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 -1 9 15 33 83 129 319 513 1139

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.