Thank you both for your recommendations. Seeing that I'm new to SAGE and Python, could you explain what these different solutions actually do?
I've just been teaching myself out of Tate and Silverman's "Rational Points on Elliptic Curves" and I see that aplist has something to do with the fourier coefficients of the modular form associated with the elliptic curve. (Explanation of even this to a lowly undergrad such as myself is appreciated) I've further noticed that the produced output for Mr. Stein's is different from Mr. Cremona's solution. Furthermore Mr. Cremona's output closely matches what I got except it produces output for when p=11! The discriminant of this curve is -11 and thus the reduction should be bad there (thus I avoided it). I've also considered just using e.sea(p) since that supposedly gives me the number of points on the curve over F_p, but e.sea(3) throws me an error claiming that the curve is singular there and the value for e.sea(7) already doesn't match Mr. Cremona's and my output! Any suggestions? -Justin On Aug 10, 11:50 am, "William Stein" <[EMAIL PROTECTED]> wrote: > On 8/10/07, John Cremona <[EMAIL PROTECTED]> wrote: > > > > > Two comments, neither about memory management as such: > > > (1) Why do you need to store all the primes and curves? Why don't you > > loop through primes? > > > (2) EllipticCurve([0,-1,1,0,0]).aplist(10000) gives you almost what > > you want (just replace the i'th entry ap by 1+p-ap where p is the ith > > prime): > > > e=EllipticCurve([0,-1,1,0,0]); > > ap=e.aplist(10000); > > plist=prime_range(10000); > > [1+plist[i]-ap[i] for i in range(prime_pi(10000))] > > Moreover, even EllipticCurve([0,-1,1,0,0]).aplist(1000000) > will finish in a reasonable amount of time -- i.e., it's very very optimized > (thank you PARI). You can also do the following, which is basically > the same as above and even faster: > sage: e = EllipticCurve([0,1,-1,0,0]) > sage: v = [e.Np(p) for p in primes(10000)] > > William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
