In 1976, Coates and Wiles showed that elliptic curves with complex multiplication
having an infinite number of solutions have 
-functions which are zero at the relevant fixed
point. This is a special case of the Swinnerton-Dyer
conjecture.
Coates-Wiles Theorem
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References
Cipra, B. "Fermat Prover Points to Next Challenges." Science 271, 1668-1669, 1996.Referenced on Wolfram|Alpha
Coates-Wiles TheoremCite this as:
Weisstein, Eric W. "Coates-Wiles Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Coates-WilesTheorem.html