Alexander J. Barrios

activity

20242026

collaborators

4 papers

math.NT2026

Isogeny graphs of elliptic curves in characteristic zero

Alexander J. Barrios, Enrique González-Jiménez, Ivan Novak

For an elliptic curve $E$ defined over a field $K$ of characteristic $0$ with $End_{K} E ≅ Z$ , we classify which isogeny graphs $G (E / K)$ can…

math.NT2025

On the Birch and Swinnerton-Dyer formula modulo squares for certain quadratic twists of elliptic curves

Alexander J. Barrios, Chung Pang Mok

Let $E / Q$ be an elliptic curve with conductor $N = N_{+} N_{-}$ , where $N_{+}$ and $N_{-}$ are coprime and $N_{-}$ is squarefree. Let $D$ be a positive fundamental discriminant satisfy…

math.NT2025

Local data of elliptic curves under quadratic twist

Alexander J. Barrios, Manami Roy, Nandita Sahajpal +3

Let $K$ be the field of fractions of a complete discrete valuation ring with a perfect residue field. In this article, we investigate how the Tamagawa number of $E / K$ changes under…

math.NT2024

Tamagawa Numbers of Elliptic Curves with an $ℓ$ -isogeny

Alexander Barrios, John Cullinan

Let $ℓ$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $Q$ . If $E$ has an $ℓ$ -torsion point, then there has been significant…

Isogeny graphs of elliptic curves in characteristic zero

On the Birch and Swinnerton-Dyer formula modulo squares for certain quadratic twists of elliptic curves

Local data of elliptic curves under quadratic twist

Tamagawa Numbers of Elliptic Curves with an ℓ-isogeny

Tamagawa Numbers of Elliptic Curves with an $ℓ$ -isogeny