Modular Parametrizations of Neumann-Setzer Elliptic Curves

William Stein, Mark Watkins

Suppose $p$ is a prime of the form $u^2+64$ for some integer $u$, which we take to be 3 mod 4. Then there are two Neumann--Setzer elliptic curves $E_0$ and $E_1$ of prime conductor…