Consider the elliptic curve E : y2 = x3 x. In this exercise, you'll find the group E(F11) and determine its group structure. (a) First, find all the squares modulo 11. (This will be helpful in part (b).) (b) Find all points in the set E(F11). (c) In part (b), you found that E(F11) contains 12 points, including the point at infinity. This means it is an abelian group of order 12. By a theorem about finite abelian groups, this means the isomorphism class of E(F11) is one of the following: Z12, Z6 Z2, Z4Z3, or Z2 Z2 Z3. Determine the isomorphism class of E(F11) by computing the orders of points in E and ruling out all but one the invalid possibilities. Consider the elliptic curve E : y2 = x3 x. In this exercise, you'll find the group E(F11) and determine its group structure. (a) First, find all the squares modulo 11. (This will be helpful in part (b).) (b) Find all points in the set E(F11). (c) In part (b), you found that E(F11) contains 12 points, including the point at infinity. This means it is an abelian group of order 12. By a theorem about finite abelian groups, this means the isomorphism class of E(F11) is one of the following: Z12, Z6 Z2, Z4Z3, or Z2 Z2 Z3. Determine the isomorphism class of E(F11) by computing the orders of points in E and ruling out all but one the invalid possibilities