Explicit upper bound for the rank of J₀(q)

1998/10/27 by Emmanuel Kowalski, Kowalski, Emmanuel, Philippe Michel +1
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #math.NT

paper · pdf · doi:10.48550/arxiv.math/9810209

arxiv created 1998/10/27 · arxiv updated 2009/12/01

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 X₀(q) for q prime large enough, namely rank J₀(q)< 6.5 dim J₀(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 J₀(q)''.

Related

• Upper bounds for the growth of Mordell-Weil ranks in pro-p towers of Jacobians
• Sur le rang de J₀(q)
• Bounds of the rank of the Mordell-Weil group of jacobians of hyperelliptic curves
• Parity of ranks of Jacobians of curves
• The Elkies Curve has Rank 28 Subject only to GRH