Explicit upper bound for the rank of J_0(q)

Abstract

We provide, on the Birch and Swinnerton-Dyer conjecture, an explicit upper bound for the rank of the Mordell-Weil group of the Jacobian of the modular curve X_0(q) for q prime large enough, namely rank J_0(q)< 6.5 dim J_0(q). The file j0q-pari.dvi contains the .dvi version of the commented listing of the Pari/GP program used for the computations of the paper ``Explicit Upper Bound for the rank of J_0(q)&#39;&#39;.