MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
3

1

Let $\mu$ be the roots of unity and $S$ be the image under the modular $j$-function of all imaginary quadratic $\tau$. Then what is $\mathbb{Q}(\mu)\cap\mathbb{Q}(S)$?

flag
This is a subcase of: mathoverflow.net/questions/15781/… – Dror Speiser Oct 3 2011 at 16:43
I think it isn't a subcase of that question, unless OP only wants elliptic curves with CM by the maximal order. Also, OP, do you want elliptic curves over Q, or over the algebraic closure of Q? – Hunter Brooks Oct 3 2011 at 16:50
I think it is a subcase, but I'm not certain: I think the answer is, kind of written in the other thread, that the $j$-invariant is in $\mathbb{Q}^\text{cyc}$ if and only if the class group of the order is an elementary abelian 2-group. And I think he means over the closure, which is the same as over $\mathbb{C}$. – Dror Speiser Oct 3 2011 at 16:59
I've edited the question to hopefully clear things up – Adam Harris Oct 3 2011 at 17:28
It's not clear to me why this is a subcase. Could anyone please expand a little? – Adam Harris Oct 4 2011 at 23:27
show 2 more comments

Your Answer

Get an OpenID
or

Browse other questions tagged or ask your own question.