Manami Roy – Fordham University

Title: Local data of rational elliptic curves with non-trivial torsion.

Abstract: There are fourteen possible non-trivial torsion subgroups T of a rational elliptic curve E by Mazur’s Torsion Theorem. For each T, we consider a parameterized family E_T of elliptic curves with the property that they parameterize all rational elliptic curves which contain T in their torsion subgroup. Using these parameterized families, we explicitly classify the Nèron type, the conductor exponent, the local Tamagawa number at each prime p where E has additive reduction. As an application of these local data, we find all rational elliptic curves with a 2-torsion or a 3-torsion point that have global Tamagawa number 1. We can also find the automorphic representation explicitly associated with a rational elliptic curve using these local data. This is joint work with Alexander J. Barrios.