ON QUOTIENT CURVES OF THE FERMAT CURVE OF DEGREE TWELVE ATTAINING THE SERRE BOUND

Abstract

We find explicitly new algebraic curves of genera three, four and ten attaining the Serre bound over prime fields, where we also obtain the conditions on the order of the finite field on which such an algebraic curve attains the Serre bound. Moreover, we show that if a standard conjecture of primes is true, then there are infinitely many primes satisfy the conditions.