Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals

Stephan Baier, Vijay M. Patankar

Let $E$ be an elliptic curve over $\mathbb{Q}$. Let $p$ be a prime of good reduction for $E$. Then, for a prime $p\ne \ell$, the Frobenius automorphism associated to $p$ (unique…