The rank and generators of Kihara’s elliptic curve with torsion $\mathbf{Z}/4\mathbf{Z}$ over $\mathbf{Q}(t)$

Abstract

For the elliptic curve $E$ over $\\mathbf{Q}(t)$ found by Kihara, with torsion group $\\mathbf{Z}/4\\mathbf{Z}$ and rank $\\geq 5$, which is the current record for the rank of such curves, by using a suitable injective specialization, we determine exactly the rank and generators of $E(\\mathbf{Q}(t))$.