Properties

 Label 1.4.d Base Field $\F_{2^2}$ Dimension $1$ $p$-rank $1$ Principally polarizable Contains a Jacobian

Invariants

 Base field: $\F_{2^2}$ Dimension: $1$ Weil polynomial: $1 + 3 x + 4 x^{2}$ Frobenius angles: $\pm0.769946543837$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-7})$$ Galois group: $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8 16 56 288 968 4144 16472 65088 263144 1047376

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 8 16 56 288 968 4144 16472 65088 263144 1047376

Decomposition

This is a simple isogeny class.

Base change

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 $\F_{2}$ 1.2.ab $\F_{2}$ 1.2.b