3 papers
math.NT2026
On the integral -adic Tate module of elliptic curves
Edwina Aylward
We show that the integral -adic Tate module of an elliptic curve over a complete discretely valued field of odd residue characteristic is determined by its -torsion represent…
math.NT2026
Reduction Types of Genus 2 Curves
Edwina Aylward, Lilybelle Cowland Kellock, Vladimir Dokchitser +1
Tate produced a table for elliptic curves over local fields that beautifully summarises their arithmetic invariants in terms of the Kodaira type. We present an analogous set of tab…
math.NT2025
Tamagawa numbers and positive rank of elliptic curves
Edwina Aylward
This paper addresses the prediction of positive rank for elliptic curves without the need to find a point of infinite order or compute L-functions. While the most common method rel…