Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $E$ be an elliptic curve with a $p$-torsion point. Denote this point by $P$. Why does is isogeny $\phi: E \rightarrow E/\langle P \rangle$ of degree $p$?

I do know that if $\phi$ is separable, then the degree is the order of the kernel which is $\#\langle P\rangle = p$. This gives the right answer but I'm not sure on how to show separability.

share|improve this question
1  
One way to show separability is by looking at the associated extension of function fields. What is the function field of $E/\langle P \rangle$ (considered as a subfield of $K(E)$ via $\phi$) and how is it constructed? –  Thom Tyrrell Dec 19 '12 at 20:36
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.