How to find two non-isomorphic elliptic curves with isomorphic products with another elliptic curve?

Question

The question is related to this MO question.

From the answer of the above question, we know T. Shioda in "Some remarks on Abelian varieties" found counter-examples of the "cancellation law" of abelian varieties. From the mathscinet review I found that in particular Shioda found elliptic curves $E$, $E^{\prime}$ and $E^{\prime\prime}$ such that $E\times E^{\prime\prime}$ is isomorphic to $E^{\prime}\times E^{\prime\prime}$ but $E$ is not isomorphic to $E^{\prime}$.

I don't have the access to the above paper. Is there anyone who has some ideas on how do construct this example?

Answer 1

Here is the paper you seek, by Tetsuji Shioda, on "Some remarks on Abelian varieties." Hope the counter-examples there help you.