On elliptic curves over $\mathbb{Q}(T)$ and their ranks

Francesco Battistoni (Universite de Framche-Comte)

15-Jun-2021, 12:30-13:00 (3 years ago)

Abstract: We consider elliptic curves over $\mathbb{Q}(T)$ admitting Weierstrass model with coefficients being polynomials of small degree, so that they are rational elliptic surfaces. In joint work with Sandro Bettin and Christophe Delaunay, we apply Nagao's formula in order to detect the value of their ranks: this approach is orthogonal to other geometric investigations, and gives the values of the ranks by looking at purely algebraic properties like the factorization of some integer polynomials. We also prove that, whenever restricting to some specific families of curves, the generic curve in these families has rank $0$.

number theory

Audience: researchers in the discipline


POINT: New Developments in Number Theory

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Organizers: Jessica Fintzen*, Karol Koziol*, Joshua Males*, Aaron Pollack, Manami Roy*, Soumya Sankar*, Ananth Shankar*, Vaidehee Thatte*, Charlotte Ure*
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