Given the following elliptic curve y² x³ + 3x + 7 mod 13, answer the following:

1. [Points 3] Confirm that it is an elliptic curve
2. [Points 4] What are the lower and upper bounds on the number of integer points on this curve? (Hint: Use Hasse's theorem)
3. [Points 7] Find the double of the point (3,2) on this curve.
4. [Points 7] Find the addition of points (3,2) and (8,6) on this curve.