Champion primes for elliptic curves
Let \(E_{a,b}\) be the elliptic curve \(y^2=x^3+ax+b\) over the finite field \(\mathbb F_p\) with \(p\) prime. If \(E_{a,b}\) is nonsingular over \(\mathbb F_p\) and \(\#E_{a,b}(\mathbb F_p)=p+1+\lfloor 2\sqrt p\rfloor\), then \(p\) is called a champion prime for \(E_{a,b}\). In the paper under review, the authors study champion primes for elliptic curves. One of their results is that the set of elliptic curves with trace of Frobenius at p a minimum has density one.
scientific article; zbMATH DE number 6360725