Mestre's paper: http://www.aimath.org/~farmer/print/mestre_explicit.pdf Mathematica notebook that implements the explicit formula: http://www.aimath.org/~farmer/print/explicit_formula_demo1b.nb PDF of Mathematica notebook: http://www.aimath.org/~farmer/print/explicit_formula_demo1b.pdf Sage worksheet that implements the explicit formula [[attachment:explicit_formula_demo.sws]]. Much more user friendly and actually correct! Another sage file that has some explicit formula stuff, specific for elliptic curves [[attachment:explicit_formula.sage]]