The Brumer-McGuinness Tables

• 1989-1990 using Macintosh II computer.

• Table of 310716 curves of prime conductor < (some curves were undoubtedly missed...)

• They systematically enumerated equations of elliptic curves and threw out those curves whose conductor is bigger than or composite.

• Computed points on these curves and were surprised to find that 40% of their "even" curves have infinitely many rational points. ("Conventional wisdom: asymptotically 0% of all even curves have rank > 0.")

Notes: