01
The problem
For an elliptic curve over the rationals, the order of vanishing of its L-function at s = 1 should equal the rank of its group of rational points.
Date noteDeveloped in the early 1960s; 1965 is used as the canonical published date.
Open since1965approximate
Last checked2026.07.26Catalog verification
02
Reward offers
Offer 01$1,000,000Clay Mathematics Institute
InstitutionalClay does not accept direct submissions. A proposed solution must be published in a qualifying outlet, at least two years must pass, and the work must gain general acceptance in the mathematics community while resolving the complete official formulation.