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

Abstract

For the elliptic curve $E$ over $\mathbb{Q}(t)$ found by Kihara, with torsion group $\mathbb{Z}/4\mathbb{Z}$ 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 $E(\mathbb{Q}(t))$.