Nonexistence of elliptic curves having everywhere good reduction and cubic discriminant (Q5928556)

The author proves that if \(p\) is a prime number such that \(p\equiv 3(4)\) and \(p\not=3,11\), then there is no elliptic curve defined over \(K={\mathbb Q} (\sqrt{3p})\) with everywhere good reduction over \(K\) and whose discriminant is a cube in \(K\).