# p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin

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Let E be a CM elliptic curve over the rationals with conductor N and p a prime coprime to 6N. If the p^{infty}-Selmer group of E has Z_{p}-corank one, we show that the analytic rank of E is also one (joint with Chris Skinner and Ye Tian). We plan to discuss the setup and strategy in the ordinary case.