|Xavier-François Roblot on Thu, 18 Dec 2008 11:11:13 +0100|
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|Functions elllderiv and ellanalyticrank|
Dear PARI-developers,I have committed to the SVN version of PARI/GP two new functions called elllderiv and ellanalyticrank. These functions have been implemented by Christophe Delaunay and myself after a script of Tom Womack and John Cremona and using results from Henri Cohen's book GTM 239. As you might have guessed by now the first function computes the derivatives at s=1 of the L-function of an elliptic curve, and the second one uses this computation to compute the analytic rank of an elliptic curve.
gp > e = ellinit("11a1"); gp > ellanalyticrank(e) %2 = [0, 0.2538418608559106843377589233] gp > e = ellinit("37a1"); gp > ellanalyticrank(e) %4 = [1, 0.3059997738340523018204836835] gp > e = ellinit("389a1"); gp > ellanalyticrank(e) %6 = [2, 1.518633000576853540460385214] gp > e = ellinit("5077a1"); gp > ellanalyticrank(e) %8 = [3, 10.39109940071580413875185035]Please try them out and let me know if you find any bugs and/or inefficiencies.
Have fun! -- Xavier-François Roblot Institut Camille Jordan Université Lyon 1 21 avenue Claude Bernard 69622 Villeurbanne cedex http://math.univ-lyon1.fr/~roblot