# Properties

 Label 2.2.b_ab Base Field $\F_{2}$ Dimension $2$ $p$-rank $2$ Not principally polarizable Does not contain a Jacobian

## Invariants

 Base field: $\F_{2}$ Dimension: $2$ Weil polynomial: $1 + x - x^{2} + 2 x^{3} + 4 x^{4}$ Frobenius angles: $\pm0.281693394748$, $\pm0.948360061415$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3}, \sqrt{-7})$$ 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 not principally polarizable, and therefore does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 7 7 196 259 1477 3136 14749 58275 268324 1109227

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 2 19 18 44 47 116 226 523 1082

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.