I'm looking for a detailed reference for modular curves over finite fields, such as $X(N)$, $X_1(N)$, and $X_0(N)$. There seems to be a lot of literature dealing with them over $\mathbb{C}$, but I'm specifically interested in them from the perspective of algebraic geometry. Also, do there exist tables of their point counts over $\mathbb{F}_q$ for some small (but hopefully at least up to $N=15$ or so) values of $N$, or algorithms (e.g. in Sage) for calculating such information? For genus 0 the Riemann hypothesis for curves over finite fields gives an exact formula, of course.

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    $\begingroup$ Do not crosspost: math.stackexchange.com/questions/1339197/…. $\endgroup$ – Dietrich Burde Jun 25 '15 at 19:03
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    $\begingroup$ Sorry about that! I wasn't aware of the policy. $\endgroup$ – mlbaker Jun 25 '15 at 19:20
  • $\begingroup$ Since it has been answered on Math.SE, maybe this question should be closed? $\endgroup$ – Kimball Jun 26 '15 at 5:15
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    $\begingroup$ I'm voting to close this question as off-topic because this was answered on math.stackexchange. $\endgroup$ – Daniel Loughran Jun 26 '15 at 7:37