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Sep 28, 2011 at 14:47 comment added Adam Harris Thanks Felipe - I should have given more information: I specifically am thinking of a situation where I have two non-CM, non-isogenous curves $E$ and $E'$ with $j$-invariants $j(\tau)$ and $j(\tau')$ which are transcendental over $\mathbb{Q}$ but $j(\tau')$ is algebraic over $\mathbb{Q}(j(\tau))$. Also $E$ is defined over $\mathbb{Q}(j(\tau))$ and $E'$ over $\mathbb{Q}(j(\tau'))$.
Sep 28, 2011 at 13:35 history answered Felipe Voloch CC BY-SA 3.0