Jacobian fibrations on the singular K3 surface of discriminant 3

TL;DR

This paper provides explicit Weierstrass equations and Mordell-Weil group generators for Jacobian fibrations on a specific singular K3 surface with discriminant 3, advancing understanding of its geometric structure.

Contribution

It introduces explicit equations and generators for Jacobian fibrations on the singular K3 surface of discriminant 3, a novel detailed description in this context.

Findings

Explicit Weierstrass equations for the fibrations

Generators of the Mordell-Weil groups identified

Enhanced understanding of the K3 surface's structure

Abstract

In this paper we give the Weierstrass equations and the generators of Mordell-Weil groups for Jacobian fibrations on the singular K3 surface of discriminant 3.