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Let $p>3$ be a prime, and let $m$ be an integer with $p\nmid m$. In thepaper, based on the work of Brillhart and Morton, by using the work of Ishiiand Deuring's theorem for elliptic curves with complex multiplication we solvesome conjectures of Zhi-Wei Sun concerning$\sum_{k=0}^{p-1}\binom{2k}k^2\binom{3k}km^{-k}\mod {p^2}$.

Congruences involving $\binom{2k}k^2\binom{3k}km^{-k}$