Sachi Hashimoto

collaborators

4 papers

math.NT2026

Equationless quadratic Chabauty for non-split Cartan modular curves

Sachi Hashimoto, Guido Maria Lido, Davide Lombardo +2

The aim of this article is to describe an equationless method for determining the rational points on the non-split Cartan curve $X_{ns}^{+} (N)$ of prime level $N ⩾ 13$ .…

math.NT2026

Hyperelliptic Atkin-Lehner quotients of Shimura curves

Eran Assaf, Sachi Hashimoto

We work towards completely classifying all hyperelliptic Atkin-Lehner quotients of Shimura curves $X_{0} (D, N) / W$ with level $N$ coprime to $D$ and $W \leq W_{0} (D, N)$ , extending, on the…

math.NT2026

Rational points on modular curves: parameterization and geometric explanations

Maarten Derickx, Sachi Hashimoto, Filip Najman +1

We show that, conditional on Zywina's effective version of the Serre uniformity conjecture, there is a natural way to parameterize non-CM $Q$ -rational points on all modula…

math.NT2025

Local heights on hyperelliptic curves and quadratic Chabauty

L. Alexander Betts, Juanita Duque-Rosero, Sachi Hashimoto +1

Quadratic Chabauty is a $p$ -adic method for determining rational points on curves. Local heights are arithmetic invariants used in the quadratic Chabauty method. We present an algo…