Properties

 Label 1.8.e Base Field $\F_{2^3}$ Dimension $1$ $p$-rank $0$ Principally polarizable Contains a Jacobian

Invariants

 Base field: $\F_{2^3}$ Dimension: $1$ Weil polynomial: $1 + 4 x + 8 x^{2}$ Frobenius angles: $\pm0.75$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

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

Point counts

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13 65 481 4225 32513 262145 2099201 16769025 134234113 1073741825

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 13 65 481 4225 32513 262145 2099201 16769025 134234113 1073741825

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 $\F_{2^3}$.

 Subfield Primitive Model $\F_{2}$ 1.2.ac