# Elliptic curves with form$y^2$=$x^3$+$p^2$$x$

We Know that from a conjecture by Goldfeld says that half of all elliptic curves have rank zero. Are there any known infinite families of elliptic curves in form $y^2=x^3+p^2x$ where p is prime with rank 0 ?

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See also here. – Dietrich Burde Dec 30 '14 at 19:29