Classifying 5-adic and 7-adic Galois Representations of Elliptic Curves

Abstract: We classify rational points on two curves: the modular curve $X_{E_3}(7)$, associated with $E_3:y^2=x^3-x^2-16x+29$, and the modular curve X_ns^{+}(25). Both classifications use quadratic Chabauty in the framework of Besser-Müller-Srinivasan's "p-adic adelic metrics and Quadratic Chabuty". These two results complete the classification 5-adic and 7-adic Galois representations attached to elliptic curves. We further discuss applying the same techniques for other curves of interest.

algebraic geometrynumber theory

Audience: researchers in the topic

FGC-HRI-IPM Number Theory Webinars

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