Verification of Kolyvagin's Conjecture for Specific Elliptic Curves


by William Stein

Download it now as a PDF


We study Heegner points and Kolyvagin classes for elliptic curves over Q, with special focus on curves that have analytic rank at least 2. We reinterpret Kolyvagin's ``derived classes'' construction, in the context of divisors on modular curves directly in characteristic ell, and prove compatibility and multiplicity one results. We use these results to give the first complete algorithm for explicitly computing (certain) Kolyvagin classes, and thus verify a conjecture of Kolyvagin for some specific elliptic curves.