3 | | Basically, I am convinced that you never want to compute the group order or even the point order separately, ever. You should just always list all the multiples of P until you repeat back to where you started. In any other context, this would be a **slow** way to compute the ~~group~~ order, but in this context, it's a **free** computation, since you need the entire list of points anyway in order to apply Velu's formulas. |

| 3 | Basically, I am convinced that you never want to compute the group order or even the point order separately, ever. You should just always list all the multiples of P until you repeat back to where you started. In any other context, this would be a **slow** way to compute the point order, but in this context, it's a **free** computation, since you need the entire list of points anyway in order to apply Velu's formulas. |