# Computing Elliptic Curves of Conductor Divisible by a Large Prime Factor

A little while ago, I came across a paper (or slides from a talk or something) that seemed to suggest that the modular symbol method for computing elliptic curves over $\mathbf{Q}$ of prescribed conductor $N$ works better when $N$ lacks large prime factors.

I'm trying to find the reference again, but I'm having a really hard time. I have a feeling that it had some connection to John Cremona's program, but this could be wrong.

Could someone please point me in the direction of such a reference?

Did I imagine this paper/presentation? That is to say, is it even true that the modular symbol method is less efficient when $N$ has a large prime factor?

Thanks!

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I thought the other way around. The case of prime $N$ is best, see Mestre's method of graphs. And each prime divisor gives an Atkin-Lehner involution for more linear algebra, and more oldforms. But I do not know for sure. –  Junkie Oct 7 '11 at 3:34
Agreed. I'm pretty sure that the case of highly composite N is the worst case, based on what I've heard from John about how he does his computations. –  David Loeffler Oct 7 '11 at 11:55
Hmm. Perhaps what I (think I) read was specific to the situation where N has a few small prime factors raised to large powers and a few large prime factors. –  NPC Oct 7 '11 at 19:23