MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $\mathbb{Q}(\mu)\cap\mathbb{Q}(S)$?

share|cite|improve this question
This is a subcase of:… – Dror Speiser Oct 3 '11 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 '11 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 '11 at 16:59
I've edited the question to hopefully clear things up – Adam Harris Oct 3 '11 at 17:28
It's not clear to me why this is a subcase. Could anyone please expand a little? – Adam Harris Oct 4 '11 at 23:27

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.