y²=x³ + 17 [here]

The Mordell Curve

My advice to any active researcher is to read two papers each week: one that is current and making an impact, and another from the past (and which pushes you to learn something new). And, so, stumbled upon this paper [1]:

In the elliptic cryptography field we use finite field and use a form of:

y² = x³ + a.x + b (mod p)

The Mordell curve does not constrain the computation into a finite field and has the form of:

y² = x³ + n

The Mordell Curve comes from Louis Mordell and who showed that there are only a finite number of integer solutions to this. The bit of the paper that stuck out for me is:

So where does the 16 come from? Well, if we plot the Mordell curve for y²=x³+17, we get this [here]:

y²=x³ + 17 [here]