# Properties

 Label 2.2.ae_i Base Field $\F_{2}$ Dimension $2$ $p$-rank $0$ Principally polarizable Does not contain a Jacobian

## Invariants

 Base field: $\F_{2}$ Dimension: $2$ Weil polynomial: $( 1 - 2 x + 2 x^{2} )^{2}$ Frobenius angles: $\pm0.25$, $\pm0.25$ Angle rank: $0$ (numerical)

## Newton polygon

This isogeny class is supersingular.

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

## 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 $A(\F_{q^r})$ 1 25 169 625 1681 4225 12769 50625 231361 1050625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 5 17 33 49 65 97 193 449 1025

1.2.ac 2

## Base change

This is a primitive isogeny class.