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 $E/\mathbb{Q}$ be a semistable elliptic curve. Let $\ell$ be a prime of multiplicative reduction and consider $\# E_{\mathrm{ns}}(\mathbb{F}_{\ell})$. Given a prime $p \neq \ell$, are there any restrictions that I can put on $E$ which force $\# E_{\mathrm{ns}}(\mathbb{F}_{\ell})\not\equiv 0 \bmod{p}$?

share|improve this question

1 Answer 1

You can calculate the size of $E_\text{ns}(\mathbb{F}_\ell)$. See Chapter III, Exercise 3.5 of Silverman's "The Arithmetic of Elliptic Curves".

share|improve this answer

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.