  We give a proof of a soft version of the $p$-converse to a theorem of
Gross--Zagier and Kolyvagin for non-CM elliptic curves with good ordinary
reduction at $p >3$ under the irreducibility assumption on the residual
representation. In particular, no condition on the conductor is imposed.
Combining with the known results, we obtain that the Mordell-Weil rank is one
and the Tate-Shafarevich group is finite if and only if the analytic rank is
one for every elliptic curve over the rationals.
