Properties

 Label 2.4.ab_ad Base Field $\F_{2^2}$ Dimension $2$ $p$-rank $2$ Principally polarizable Contains a Jacobian

Invariants

 Base field: $\F_{2^2}$ Dimension: $2$ Weil polynomial: $1-x-3x^{2}-4x^{3}+16x^{4}$ Frobenius angles: $\pm0.0862360434115$, $\pm0.752902710078$ Angle rank: $1$ (numerical) Number field: $\Q(\sqrt{-3}, \sqrt{5})$ Galois group: $V_4$

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 contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9 171 2916 69939 988749 16842816 272594709 4280336739 69130081476 1101267647451

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 10 43 274 964 4111 16636 65314 263707 1050250

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.