$c_E$, the predicted constant in the frequency of rank two in the family of quadratic twists of $E$

For a fixed elliptic curve $E$ we conjecture that there are asymptotically

\begin{displaymath}c_E X^{3/4} (log X)^{-5/8}\end{displaymath}

prime discriminants $p\le X$ for which the twisted elliptic curve $E_p$ has rank 2. Can we conjecture a formula for $c_E$? There are examples for which $c_E=0$. Can we give a criterion for when that happens?



Back to the main index for Random Matrix Theory and central vanishing of L-functions.