Is there complex Gross - Zagier in this case? Their work also excludes this case. If there is, one can expect the p-adic height of that Heegner point to appear in p-adic version, as in the case of Perrin - Riou. There is a paper of Conrad on complex Gross - Zagier which includes this case. However, I do not know whether complex version follows from that paper. Probably some more work in needed.
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