Actually, one addition here: I said that there are lots of possible group laws on an elliptic curve, but IINM, the ones described here are the only ones that ar

Actually, one addition here: I said that there are lots of possible group laws on an elliptic curve, but IINM, the ones described here are the only ones that are algebraic (and as for what exactly that means, I'll definitely skip going into that because I would probably get it wrong :P ).