Timeline for Where can I find a comprehensive list of equations for small genus modular curves?
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Jun 22, 2022 at 8:14 | history | edited | CommunityBot |
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Jun 22, 2022 at 8:13 | history | edited | CommunityBot |
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Feb 4, 2010 at 6:07 | comment | added | Pete L. Clark | @TL: good question! (Sounds familiar, in fact.) Off the top of my head, I would say that the key issue is which of these algorithms work over a field of positive characteristic, and for which characteristics? E.g. "my" algorithm (a.k.a.: the most immediately obvious algorithm) for $X_1(N)$ will work verbatim over a field of characteristic not dividing $N$, hence (I'm pretty sure) over $\mathbb{Z}[\frac{1}{N}]$. Doing things correctly at primes of bad reduction will be much harder in general, I fear, although in some very special cases (e.g. genus 0!) you can work these things out. | |
Feb 4, 2010 at 4:44 | comment | added | Tyler Lawson | Really nice answer. One question: Do any of the algorithmic methods you mention for computing defining equations work integrally, or only over Q? | |
Feb 4, 2010 at 4:10 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
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Feb 3, 2010 at 23:02 | vote | accept | David Zureick-Brown | ||
Feb 3, 2010 at 22:44 | history | answered | Pete L. Clark | CC BY-SA 2.5 |