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arXiv · 1410.6919

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

Andrej Dujella·Ivica Gusić·Petra Tadić
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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 $E(\mathbb{Q}(t))$.

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Andrej Dujella, Ivica Gusić, Petra Tadić. 2014-10-25. The rank and generators of Kihara's elliptic curve with torsion $\mathbb{Z}/4\mathbb{Z}$ over $\mathbb{Q}(t)$. https://doi.org/10.3792/pjaa.91.105

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