Construction of Elliptic Curves with Large Rank
Thomas J. Kretschmer · Mathematics of Computation · 1986
We describe an algorithm for finding elliptic curves over Q with large rank and nontrivial torsion group. In particular, an example of a curve of rank exactly 10 with a point of order 2 is given. This method seems to suggest that the rank may be large independently of the torsion group.