Quadratic forms and elliptic curves. III (Q1357038)

[For parts I and II of this paper see the two preceding reviews.] In this part III the authors show, subject to the ``parity conjecture'' (an elliptic curve \(E\) over \(\mathbb{Q}\) with rank \(r\) satisfies \((-1)^r= \omega(E)\), the sign of the functional equation of the Hasse-Weil \(L\)-function associated to \(E\)), how to construct infinitely many elliptic curves \(E(b): Y^2=X^3- (b^2+b)X\) with even rank \(\geq 2\). In general, deep theorems are applied to concrete problems, so it is a pleasure to see how they can work.