20
votes
3answers
2k views

Is there a nice proof of the fact that there are (p-1)/24 supersingular elliptic curves in characteristic p?

If $k$ is a characteristic $p$ field containing a subfield with $p^2$ elements (e.g., an algebraic closure of $\mathbb{F}_p$), then the number of isomorphism classes of supersingular elliptic curves ...
6
votes
2answers
2k views

What does “supersingular” mean?

Are supersingular primes and supersingular elliptic curves related? (this was essentially a subquestion in my earlier question, but still looks sufficiently different to me to deserve a separate ...
6
votes
1answer
425 views

Ways to characterize supersingular primes?

I've read the definition, and it basically says p is a supersingular prime iff the fundamental domain of a group generated by \Gamma(p) and a matrix ((0, 1), (-p, 0)) is rational. And there's a ...