The Smallest Conductor for an Elliptic Curve of Rank Four is Composite

William Stein, Andrei Jorza, Jennifer Balakrishnan

August 20, 2003




Using various computational techniques, we determined all elliptic curves of prime conductor p up to 234431 and conclusively settled a question of primality regarding the smallest conductor for an elliptic curve of rank 4, namely, that the conductor is composite.