What’s an elliptic curve?

solutions to an equation of the
form

More or
less, the E :
y2 = x3 + a x + b

But over what field? What are x and y?

Over **C**, E is isomorphic to **C**/L,

where L is a lattice ½ **C** (A torus).

In fact, the set of solutions always has an *abelian group law**.*

Number Theory: study solutions over **F**p = **Z**/p**Z
**

or more generally over **F**q