At least rank 2 in elliptic curve y2=x3-2px

In form E_(-2p):y^2=x^3-2px we can obtain rank at least 2 when prime is p≡1(mod 8). In this case, generally the form is given as p=Hu^8+Iu^4 v^4+Kv^8. That is, the numbers of terms are 3. Our concern is whether it is possible that we attain more terms in primes. In this article, we will treat about this point.