Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves

Yuri Bilu (1) , Pierre Parent (1)

1 IMB - Institut de Mathématiques de Bordeaux

We bound the j -invariant of integral points on a modular curve in terms of the congruence group de?ning the curve. We apply this to prove that the modular curve Xsplit (p3 ) has no non-trivial rational point if p is a sufficiently large prime number. Assuming the GRH, one can replace p3 by p2 .

Domaines: Analyse classique [math.CA]

Yuri Bilu, Pierre Parent. Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves. 2008. ⟨hal-00294699⟩