The Ars Technica article linked in the article is much better-written and more comprehensive. https://arstechnica.com/information-technology/2013/10/a-rel...
Fun fact: elliptic curves (specifically the Taniyama–Shimura conjecture about their relationship to modular forms) played a key role in Wiles' proof of Fermat's Last Theorem, one of the most famous problems in mathematics.