Field of definition of elliptic curves โ mathoverflow.net
Let $a,b$ be positive integers, $F=\mathbb{Q}(a^{1/3},b^{1/2})$. Let $E$ be the elliptic curve defined over $F$ by the cubic equation $$y^2=x^3+3a^{1/3}x+2b^{1/2}.$$
Then the $j$-invariant $j(E) = ...