The conductor of these objects is an integer defined using primes when they do not have a good reduction. These objects are isomorphic over C if and only if they have the same j-invariant. (-5[1])The order of the zero of these objects’ Hasse-Weil L-functions at 1 is equal to their rank, according to the Birch-Swinnerton-Dyer conjecture. The SIKE system is based on isogenies of supersingular types of (-5[1])these (15[1])objects. (-5[1])A (*) line drawn between two points on these objects must have a third intersection (10[1])point, assuming a point at infinity is added. (10[1])These objects are used by Lenstra’s factorization (10[1])algorithm. A correspondence between modular forms (10[1])and these objects is given by the Taniyama-Shimura conjecture. (-5[1])These objects can be represented by real solutions to y squared (10[1])equals x cubed (10[1])plus a x plus b. For 10 points, name these objects used by Andrew Wiles in his proof of Fermat’s last theorem. ■END■ (10[1]0[1])