Goldfeld's conjecture
Goldfeld's conjecture is a number theory conjecture that half of the quadratic twists of an elliptic curve have rank zero and half have rank one.
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Last mentioned Goldfeld's conjecture was proposed in 1979 by American mathematician Dorian Goldfeld. It predicts that among the quadratic twists of an elliptic curve over the rational numbers, the average rank is 1/2, with almost all twists split evenly between rank zero and rank one.
It is a central problem about how the ranks of elliptic curves are distributed and is studied together with the Birch and Swinnerton-Dyer conjecture.
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