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