Timeline for Are there modular elliptic curves over a field extension of $\mathbb{Z}[i]$?
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| Apr 23, 2013 at 4:29 | comment | added | Felipe Voloch | @Pete: It's not obvious. See the appendix to Mazur's paper "Number Theory as gadfly". | |
| Apr 23, 2013 at 3:15 | comment | added | Pete L. Clark | Concerning the first sentence: is it completely obvious that one cannot have an elliptic curve $E$ with rational $j$-invariant which splits off as an isogeny factor of some $J_0(N)$ only over some larger number field? I remember this can't happen when $N$ is squarefree, because by a 1975 theorem of Ribet the geometric endomorphism ring of $J_0(N)$ is equal to its $\mathbb{Q}$-rational endomorphism ring. What about the general case? (I suspect I once knew the answer to this but have forgotten...) | |
| Apr 21, 2013 at 18:12 | history | answered | Felipe Voloch | CC BY-SA 3.0 |