The question is related to [this MO question](https://mathoverflow.net/questions/254240/do-we-have-cancellation-law-for-products-of-varieties). 


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?



How to find two non-isomorphic elliptic curves with isomorphic products with another elliptic curve?
Here is the paper you seek, by Tetsuji Shioda, on ["Some remarks on Abelian varieties."](http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6164/1/jfs240102.pdf) Hope the counter-examples there help you.


