Consider the elliptic curve E : y2 =x3 + 7x + b (mod 11).

a. [3 Points] Determine b so that the point P = (4,5) is on the curve E.

b. [3 Points] Using the b found in part a, list all points on E.

c. [3 Points] Using the b found in part a, find the sum (4,5) + (5,4) on E.

d. [5 Points] Using the b found in part a, find the point (4, 5) + (4, 5) + (4,5)