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Let $p$ be a prime and $K$ a number field of degree $p$. We count the numberof elliptic curves, up to $\bar{K}$-isomorphism, having a prescribed property,where this property is either that the curve contains a fixed torsion group asa subgroup, or that it has an isogeny of prescribed degree.

On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree