Families of noncongruent numbers, by Franz Lemmermeyer
Let Ek denote the elliptic curve
defined by y2 = x(x2 - k2).
We consider the curves with k = pl, p = l = 1 mod 8
primes, and show that the density of rank-0 curves among
them is at least 1/2 by explicitly constructing nontrivial
elements in the 2-part of the Tate-Shafarevich group of
Franz Lemmermeyer <firstname.lastname@example.org>