The article also explains why it is OK to say that elliptic curves come only in two types. Read the two paragraphs starting from "You may be wondering how it’s

The article also explains why it is OK to say that elliptic curves come only in two types. Read the two paragraphs starting from "You may be wondering how it’s possible...". It seems like the curves of rank 0 and 1 are infinite and curves of rank greater than 1 are also infinite. But infinities are strange. The infinity of curves with rank 0 and 1 is much much greater than those of rank > 1 so essentially the latter can be ignored. That's what I understood.