Question

1. (Complex Multiplication) Let E : y x3 y23 to this congruence mod p. So for example, #E(Z3) = 3 because we have the solutions (0, 0), (1,0) and (2,0) and no more. - x. Then we can reduce E mod p to get mod p for various primes p. We write #E(Z») for the number of solutions This particular equation has some miraculous explore here patterns we (a) Make a chart that lists p, #E(Zp), and #E(Z) - p for the primes less than 30. What patterns do you notice? |(b) Make another table which lists the primes p less than 30 which can be written as a2b2, and find the corresponding = d your chart? a and b. How do these values relate to

Answer 1

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