Number Theory Seminar

Speaker: Jerson Caro (PUC Chile)

Title: Watkins’ conjecture for semi-stable elliptic curves

Abstract: In 2002 M. Watkins conjectured that for every elliptic curve defined over Q, its Mordell-Weil rank is at most the 2-adic valuation of its modular degree. In this talk, we will define these invariants related to this conjecture, and we will prove that every semi-stable elliptic curve E/Q, whose rational 2-torsion is isomorphic to Z/2Z, satisfies Watkins’ conjecture whenever every bad place has non-split multiplicative reduction or the number of places with non-split multiplicative reduction is odd. This is a joint work with Hector Pasten.